OT: Mathematics
san_jose_guy
money was invented for handing to women, but buying dances is a chump's game
Srinivasa Ramanujan
Srinivasa Ramanujan FRS was an Indian mathematician who lived during the British Rule in India. Though he had almost no formal training in pure mathematics, he made substantial contributions to mathematical analysis, number theory, infinite series, and continued fractions, including solutions to mathematical problems considered to be unsolvable.
1887 - 1920
https://en.wikipedia.org/wiki/Srinivasa_…
Ramanujan's first Indian biographers describe him as a rigorously orthodox Hindu. He credited his acumen to his family goddess, Mahalakshmi of Namakkal.
The Indian mathematician Srinivasan took notice of him and considered him a true mystic.
Ramanujan and his family were ardent devotees of the god Marasimha ( lion faced incarnation ), the sign of whose grace consisted in drops of blood seen during dreams. Ramanujan stated that after seeing such drops, scrolls containing the most coplicated mathematics used to unfold before him and that after waking, he could set down on paper only a fraction of what was shown to him.
He said once to his father, 'Sir, an equation has no meaning for me unless it expresses a thought of God'.
SJG
Claude Debussy - Clair de Lune, Arabesque no.1, Reverie & more piano music of Claude Debussy
https://www.youtube.com/watch?v=9uKVI6_F…
Wayward girl, no place to go. Some are just like this. The scene was actually posed. But it still caused controversy.
Degas L'Absinthe 1876
http://www.theartwolf.com/articles/impre…
https://en.wikipedia.org/wiki/L%27Absint…
Some Other Threads:
OT: Anglo-American Philosophy from Hobbes forward
https://www.tuscl.net/discussion.php5?id…
American's Will Not Be Free Until The Last Preacher Has Been Strangled To Death By The Entrails Of the Last Libertarian.
https://www.tuscl.net/discussion.php5?id…
OT: Bio-Magnetic Sensors
https://www.tuscl.net/discussion.php5?id…
R Programming Langauge
https://www.tuscl.net/discussion.php5?id…
Elliot Rodger, Isla Vista Shooter 2014
https://www.tuscl.net/discussion.php5?id…
OT: Assembler, C/C++, Embedded Systems, Machine Architectures, Development Systems, JTAG, Rust
https://www.tuscl.net/discussion.php5?id…
So What Do Women Like To Read?
https://www.tuscl.net/discussion.php5?id…
Vocels (Voluntary Celibates)
https://www.tuscl.net/discussion.php5?id…
OT: Power Semiconductors, recent books about
https://www.tuscl.net/discussion.php5?id…
Alternative Educations
https://www.tuscl.net/discussion.php5?id…
OT: Physics Texts
https://www.tuscl.net/discussion.php5?id…
Programable Hand Held Calculators
https://www.tuscl.net/discussion.php5?id…
SJG
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BTW yours and tx's posts are much more interesting. :D
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Lol! That's funnier than anything I've seen today but unfortunately it's probably accurate.
Anyway it's been brought up before, he does it here because it's the only place on the net that he can get away with it.
My threads and posts are about things which some people might reply to. You, not I, must think very low of TUSCL members.
SJG
I'm going to start expanding my reading to include mathematics books, starting with:
A First Course in Real Analysis (Undergraduate Texts in Mathematics)Mar 7, 1997
by Murray H. Protter and Charles B. Jr. Morrey
A First Course in Functional Analysis (Dover Books on Mathematics)
by Martin Davis
Notice this too:
Mathematical foundations of computational electromagnetism / Franck Assous, Patrick Ciarlet, Simon Labrunie (2018)
A First Course in Numerical Analysis: Second Edition (Dover Books on Mathematics) Second Edition
by Anthony Ralston (Author), Philip Rabinowitz (Author)
Complex Analysis: A First Course with ApplicationsOct 4, 2013
by Dennis G. Zill and Patrick D. Shanahan
Here, this is the book I was trying to find:
""This rigorous textbook is intended for a year-long analysis or advanced calculus course for advanced undergraduate or beginning graduate students. Starting with detailed, slow-paced proofs that allow students to acquire facility in reading and writing proofs, it clearly and concisely explains the basics of differentiation and integration of functions of one and several variables, and covers the theorems of Green, Gauss, and Stokes. Minimal prerequisites are assumed, and relevant linear algebra topics are reviewed right before they are needed, making the material accessible to students from diverse backgrounds. Abstract topics are preceded by concrete examples to facilitate understanding, for example, before introducing differential forms, the text examines low-dimensional examples. The meaning and importance of results are thoroughly discussed, and numerous exercises of varying difficulty give students ample opportunity to test and improve their knowledge of this difficult yet vital subject." -- Provided by publisher"
A first course in analysis / John B. Conway (2018)
https://www.amazon.com/Course-Analysis-C…
SJG
So considering:
A first course in analysis / John B. Conway (2018)
https://www.amazon.com/Course-Analysis-C…
Lets compare it to the established standard: Walter Rudin, what I find for the table of contents is:
Table Of Contents:
Chapter 1: The Real and Complex Number Systems
Introduction
Ordered Sets
Fields
The Real Field
The Extended Real Number System
The Complex Field
Euclidean Spaces
Appendix
Exercises
Chapter 2: Basic Topology
Finite, Countable, and Uncountable Sets
Metric Spaces
Compact Sets
Perfect Sets
Connected Sets
Exercises
Chapter 3: Numerical Sequences and Series
Convergent Sequences
Subsequences
Cauchy Sequences
Upper and Lower Limits
Some Special Sequences
Series
Series of Nonnegative Terms
The Number e
The Root and Ratio Tests
Power Series
Summation by Parts
Absolute Convergence
Addition and Multiplication of Series
Rearrangements
Exercises
Chapter 4: Continuity
Limits of Functions
Continuous Functions
Continuity and Compactness
Continuity and Connectedness
Discontinuities
Monotonic Functions
Infinite Limits and Limits at Infinity
Exercises
Chapter 5: Differentiation
The Derivative of a Real Function
Mean Value Theorems
The Continuity of Derivatives
L'Hospital's Rule
Derivatives of Higher-Order
Taylor's Theorem
Differentiation of Vector-valued Functions
Exercises
Chapter 6: The Riemann-Stieltjes Integral
Definition and Existence of the Integral
Properties of the Integral
Integration and Differentiation
Integration of Vector-valued Functions
Rectifiable Curves
Exercises
Chapter 7: Sequences and Series of Functions
Discussion of Main Problem
Uniform Convergence
Uniform Convergence and Continuity
Uniform Convergence and Integration
Uniform Convergence and Differentiation
Equicontinuous Families of Functions
The Stone-Weierstrass Theorem
Exercises
Chapter 8: Some Special Functions
Power Series
The Exponential and Logarithmic Functions
The Trigonometric Functions
The Algebraic Completeness of the Complex Field
Fourier Series
The Gamma Function
Exercises
Chapter 9: Functions of Several Variables
Linear Transformations
Differentiation
The Contraction Principle
The Inverse Function Theorem
The Implicit Function Theorem
The Rank Theorem
Determinants
Derivatives of Higher Order
Differentiation of Integrals
Exercises
Chapter 10: Integration of Differential Forms
Integration
Primitive Mappings
Partitions of Unity
Change of Variables
Differential Forms
Simplexes and Chains
Stokes' Theorem
Closed Forms and Exact Forms
Vector Analysis
Exercises
Chapter 11: The Lebesgue Theory
Set Functions
Construction of the Lebesgue Measure
Measure Spaces
Measurable Functions
Simple Functions
Integration
Comparison with the Riemann Integral
Integration of Complex Functions
Functions of Class L²
I have read some of the above book years ago. But I will start with:
A first course in analysis / John B. Conway (2018)
Black Magick Volume 1: Awakening I
https://www.amazon.com/Black-Magick-Awak…
Black Magick Volume 2: Awakening II
https://www.amazon.com/gp/product/153430…
The Necromancer (The Secrets of the Immortal Nicholas Flamel Book 4)
https://www.amazon.com/Necromancer-Secre…
https://www.amazon.com/Secrets-Immortal-…
https://www.amazon.com/s/ref=nb_sb_noss_…
https://en.wikipedia.org/wiki/List_of_AM…
AMD site
https://www.amd.com/en
HP EliteDesk 705 Workstation Edition
AMD Ryzen™ PRO processors¹
AMD Ryzen, clock rates up to 3.7 Ghz! Prices up to $1k!
https://en.wikipedia.org/wiki/List_of_AM…
extended precision, 80 bits, like on Intel 8087, this is what I am looking for.
https://en.wikipedia.org/wiki/Extended_p…
Some C/C++ implementations (e.g., GNU Compiler Collection (GCC), Clang, Intel C++) implement long double using 80-bit floating point numbers on x86 systems. However, this is implementation-defined behavior and is not required, but allowed by the standard, as specified for IEEE 754 hardware in the C99 standard "Annex F IEC 60559 floating-point arithmetic". GCC also provides __float80 and __float128 types.[29]
D programming language implements real using largest floating point size implemented in hardware, 80 bits for x86 CPUs or double precision, whichever is larger.
Object Pascal (Delphi) has in addition to SINGLE and DOUBLE, an EXTENDED type.
The Racket run-time system provides the 80-bit extflonum datatype on x86 systems.
The Swift standard library provides the Float80 datatype.
Okay, so GNU C/C++ does it for x86. But anything besides Intel?
SJG
https://www.vinc17.net/research/extended…
IEEE-754 standard, includes 'extended precision'
https://en.wikipedia.org/wiki/IEEE_754
lots of online paper links.
Beagle Board Black, $69
https://www.element14.com/community/docs…
NEON floating-point accelerator
https://developer.arm.com/technologies/n…
BeagleBoard Green, $45
https://beagleboard.org/green/
http://wiki.seeedstudio.com/BeagleBone_G…
datasheet PDF, 253 pages
https://github.com/SeeedDocument/Bazaar_…
What Every Computer Scientist Should Know About Floating-Point Arithmetic
https://docs.oracle.com/cd/E19957-01/806…
Floating Point Units
https://en.wikipedia.org/wiki/Floating-p…
https://en.wikipedia.org/wiki/Floating-p…
Simply FPU, 2003
http://www.website.masmforum.com/tutoria…
https://superuser.com/questions/790227/h…
Does anyone do 80 bits besides Intel?
SJG
https://devtalk.nvidia.com/default/topic…
Systems for multiprocessors and array processors
https://en.wikipedia.org/wiki/Multiproce…
Intel Xeon processors dominated the multiprocessor market for business PCs and were the only major x86 option until the release of AMD's Opteron. ( do these do 80 bit floating point? )
Array Processing
https://en.wikipedia.org/wiki/Array_proc…
^^^^ more about signal processing than simulation
for plotting, though in Fortran
PLplot 'plplot.sf.net'
GNU, gcc, gfortran, gnuplot, of Free Software Foundation
Michael Metcalf, author very involved with Fortran.
SQLite, written in C. For Fortran there is fsqlite, developed by Markus.
SQLite developed by D. Richard Hipp, March 2012, 'www.sqlite.org'
PLplot, collection of libraries for plotting technical and scientific data
Tcl/Tk
Tklib, library of Tk extensions, 'tcllib.sf.net'
^^^^ works with GUI.
Gabriele Jost, Chapman, Ruud van der Pas, Using OpenMP: Portable Shared Memory Parallel Programming 2008.
Lusk, Gropp, Skjellum. Using MPI: portable parallel programming with message passing, 1999.
OpenMP and MPI are the two ways of doing parallel processing in Fortran.
Unit Testing, Junit is for java
For Fortran we have Funit, pfunit, FRUIT, and Ftnunit. All for Fortran or Fortran and Ruby.
Les Hatton, 'Safer C, Developing software for High-Integrity and Safety-critical systems' 1994
also:
Code complete : [a practical handbook of software construction] / Steve McConnell
Redmond, Wash. : Microsoft Press, [2004]
XML Files, a very practical kind of compromise idea in my opinion.
used extensively in docbook.
Making TEX work / Norman Walsh (1994)
DocBook 5: The Definitive Guide: The Official Documentation for DocBook, by Walsh Norman
Beyond Objectivism and Relativism: Science, Hermeneutics, and Praxis First Edition Edition
by Richard J. Bernstein 1983, very good book
Circuit Design Using Personal Computers, by Thomas Cuthbert, 1983
^^^ has at least one other book too.
So what I was looking for: OpenMP and MPI are the two ways of doing parallel processing, in Fortran, but probably works in C too.
SJG
Some previous threads:
OT: Computer Programming
https://www.tuscl.net/discussion.php5?id…
Web Programming, HTML, CSS, and more
https://www.tuscl.net/discussion.php5?id…
OT: Programmable Logic Devices
https://www.tuscl.net/discussion.php5?id…
Looks really good:
C++ without fear : a beginner's guide that makes you feel smart / Brian Overland. (2016)
Finite Elements For Electrical Engineers, Peter P. Silvester and Ronald L. Ferrari.
1996 third edition, but originally 1983.
Says to use Fortran, Pascal, or C.
But the examples in the book, dated 1995, are in Fortran.
TJ Street
https://farm6.staticflickr.com/5488/9620…
Says OpenMP works with C and Fortran, and on Windows, Linux, and MacOS.
https://en.wikipedia.org/wiki/OpenMP
"OpenMP is managed by the nonprofit technology consortium OpenMP Architecture Review Board (or OpenMP ARB), jointly defined by a group of major computer hardware and software vendors, including AMD, IBM, Intel, Cray, HP, Fujitsu, Nvidia, NEC, Red Hat, Texas Instruments, Oracle Corporation, and more.["
MPI=Message Passing Interface, its for parallel computing and it works with C and Fortran, and some other stuff too like Java, Python, R, and MatLab.
https://en.wikipedia.org/wiki/Message_Pa…
Says it is a defacto standard.
Example C program:
https://en.wikipedia.org/wiki/Message_Pa…
So obviously I need more than the Wikipedia. I need books, and then online info and downloads.
Using advanced MPI : modern features of the Message-Passing-Interface / William Gropp, Torsten Hoefler, Rajeev Thakur, and Ewing Lusk (2014 caution)
An introduction to parallel programming / Peter S. Pacheco. (2011)
Parallel programming in C with MPI and openMP / Michael J. Quinn. (2004)
Today I think it has been established that Fortran is still part of the present, not just retro. But are the reasons only legacy? Do not know.
I've talked about building an organization. As should be obvious by now, one of its primary functions will be as Think Tank. Can't know everything alone.
SJG
SJG Portal
https://sites.google.com/site/sjgportal/
Trump, separating children and parents:
https://www.democracynow.org/2018/10/15/…
Vatican Canonizes Salvadoran Archbishop Óscar Romero, Who Was Killed by a U.S.-Backed Death Squad
www.democracynow.org/2018/10/15/vatican_…
They tried to film this in El Salvador, but they quickly got ejected. So it was filmed in Mexico.
Romero (1989) Trailer - John Duigan, Raul Julia
www.youtube.com/watch?v=8G27jc6l_Zk
www.youtube.com/watch?v=OGffLSS3dkY
www.imdb.com/title/tt0098219/mediaviewer…
Pope Francis Canonizes, Oscar Romero ( and this has been long awaited )
www.youtube.com/watch?v=QOOivnHwHOc
and more
https://www.democracynow.org/2018/10/15/…
Missouri Woman Fired For Blocking Black Man From Entering Apartment Complex
www.yahoo.com/news/missouri-woman-fired-…
The Jeff Healey Band - While My Guitar Gently Weeps (live), anyone know who the black girl is?
https://www.youtube.com/watch?v=NCaL_v2E…
Robin Trower - Full Concert - Rockpalast Crossroads, Bonn - 2005
https://www.youtube.com/watch?v=ZmoMb0gN…
TJ Street
https://farm6.staticflickr.com/5488/9620…
https://en.wikipedia.org/wiki/Claude_Sha…
The logician and the engineer : how George Boole and Claude Shannon created the information age / Paul J. Nahin. (2013)
The mathematical theory of communication / Claude E. Shannon and Warren Weaver ; foreword by Richard E. Blahut and Bruce Hajek (1998)
Shannon-Hartley Theorem
https://en.wikipedia.org/wiki/Shannon%E2…
SJG
Deconstructing Gurdjieff : biography of a spiritual magician / Tobias Churton. (2017 Inner Traditions)
Bruce Chilton
https://www.youtube.com/watch?v=sN3brxti…
TJ Steet
https://farm6.staticflickr.com/5488/9620…
https://farm8.staticflickr.com/7290/9620…
https://c2.staticflickr.com/6/5497/96200…
https://c2.staticflickr.com/8/7361/96322…
https://c1.staticflickr.com/6/5539/96203…
https://c2.staticflickr.com/6/5449/96322…
https://c2.staticflickr.com/6/5520/96203…
http://i1.ytimg.com/vi/nkeeS3HHJrU/hqdef…
Jeff Healey, While My Guitar Gently Weeps
https://www.youtube.com/watch?v=NCaL_v2E…
Dragnet 106 "The Bank Examiner Swindle" Original Air Date February 23, 1967
https://www.youtube.com/watch?v=yj4kM5LQ…
Joe Bonamassa - "Midnight Blues" - Beacon Theatre - Live From New York
https://www.youtube.com/watch?v=8z74lr3t…
Here's Why the Ferrari Portofino Is Worth $250,000
https://www.youtube.com/watch?v=qjsc8it2…
Here's Why the Ferrari F40 Is Worth $1.3 Million
https://www.youtube.com/watch?v=7mZdkfEe…
The Lamborghini Diablo Was the Craziest Car of the 1990s ( Diablo was a really wild car. Much better designed than Contach )
https://www.youtube.com/watch?v=t0zOKlVE…
Joe Bonamassa - "Sloe Gin" - Muddy Wolf at Red Rocks
https://www.youtube.com/watch?v=pvvgZMGp…
https://en.wikipedia.org/wiki/Bifurcatio…
https://www.amazon.com/Complexity-Guided…
SJG
Simplexity : why simple things become complex (and how complex things can be made simple) / Jeffrey Kluger (2008)
https://www.amazon.com/Simplexity-Simple…
SJG
TJ Street
https://farm6.staticflickr.com/5488/9620…
https://c1.staticflickr.com/8/7290/96201…
http://www.adelitasbartijuanamexico.com/…
http://farm4.static.flickr.com/3680/9633…
https://www.amazon.com/Calculus-Chaos-In…
and:
https://www.amazon.com/Fractals-Chaos-Po…
SJG
Baker Gurvitz Army
https://www.youtube.com/watch?v=VkJC6XQ5…
https://www.wickedtemptations.com/standa…
https://www.wickedtemptations.com/standa…
https://www.wickedtemptations.com/standa…
TJ Street
https://farm6.staticflickr.com/5488/9620…
https://c1.staticflickr.com/8/7290/96201…
https://www.tuscl.net/discussion.php5?id…
http://farm4.static.flickr.com/3680/9633…
So the main registers are all now 32 bit mode.
Okay, but there are some 64 bit registers, and maybe a 128 bit register? You used different op codes to access those. So compatibility is maintained.
And then for floating point, you have 80 bit registers. These are in a stack of 8, and it is POSTFIX, just like on an HP Calculator.
And Hyde confirms that this is in most all Intel processors.
So I am not sure if this is the most current info, 2010, but still good info. 80bit floating point is really good, and big improvement over the 64 bits for the ARM processors.
SJG
JS69 Front Room Makeout Session
https://www.tuscl.net/discussion.php5?id…
https://www.wickedtemptations.com/standa…
https://www.wickedtemptations.com/standa…
https://www.wickedtemptations.com/standa…
https://www.wickedtemptations.com/standa…
https://www.lingeriediva.com/collections…
Joe Bonamassa - "Midnight Blues" - Beacon Theatre - Live From New York
https://www.youtube.com/watch?v=8z74lr3t…
Beth Hart and Joe Bonamassa- I'd Rather Go Blind
https://www.youtube.com/watch?v=AnXgZZkP…
Joe Bonamassa - "Sloe Gin" - Muddy Wolf at Red Rocks
https://www.youtube.com/watch?v=pvvgZMGp…
TJ Street
https://farm6.staticflickr.com/5488/9620…
https://c1.staticflickr.com/8/7290/96201…
http://www.adelitasbartijuanamexico.com/…
http://farm4.static.flickr.com/3680/9633…
God in the 21st Century: Bishop John Shelby Spong
https://www.youtube.com/watch?v=PwNmj5h1…
Bishop John Shelby Spong(9am) - "From a Tribal God to a Universal Presence: The Story Of The Bible"
https://www.youtube.com/watch?v=87rokCqk…
https://www.gnu.org/software/libc/manual…
Hyperbolics
https://www.gnu.org/software/libc/manual…
GNU C Library
https://www.gnu.org/software/libc/manual…
Adding New Functions
https://www.gnu.org/software/libc/manual…
GNU .org
https://www.gnu.org/
GNU Packages, 402 of them
https://directory.fsf.org/wiki/GNU
16062 approved packages
https://directory.fsf.org/wiki/All
Mathematics Category
https://directory.fsf.org/wiki/Category/…
Calc is an arbitrary precision arithmetic system that uses a C-like language. It's useful as a calculator, an algorithm prototype, and as a mathematical research tool. More importantly, calc provides a machine-independent means of computation.
https://directory.fsf.org/wiki/Calc
http://www.isthe.com/chongo/tech/comp/ca…
calc: C-style arbitrary precision system ( arbitrary precision is no small task )
https://sourceforge.net/projects/calc/fi…
calc 2.12.6.8
https://sourceforge.net/projects/calc/fi…
seems to genuinely be written in C, but I am still not seeing real source code.
Gnuplot, well known, 5 meg download
https://sourceforge.net/projects/gnuplot…
GZ file means winzip
SJG
JS69's Front Room Makeout Session, but because he is so cranky he describes it in negative terms and blames it on the girl.
https://www.tuscl.net/discussion.php5?id…
TJ Street
https://mail.google.com/mail/#drafts/FMf…
https://c1.staticflickr.com/8/7290/96201…
http://www.adelitasbartijuanamexico.com/…
http://farm4.static.flickr.com/3680/9633…
https://www.gnu.org/software/libc/manual…
Top
https://www.gnu.org/software/libc/manual…
https://www.gnu.org/software/libc/manual…
Now I understand, this is just the standard library you use with the C compiler.
GNU.org
https://www.gnu.org/
Short Descriptions of All GNU Packages
https://www.gnu.org/manual/blurbs.html
Archimedes, Semiconductor Device Simulation
https://www.gnu.org/software/archimedes/
AUCTEX, can write TEX files in GNU Emacs text editor
https://www.gnu.org/software/auctex/
Automake, part of GNU build
https://www.gnu.org/software/automake/
libavl, binary and balanced tree routines
http://adtinfo.org/
Bash, the GNU command shell, compatible with Borne Shell, but also with features of Korn Shell and C Shell
https://www.gnu.org/software/bash/
bc, arbitrary precision numerics processing language
https://www.gnu.org/software/bc/
GNU MathProg modeling ?
74 page pdf
http://gusek.sourceforge.net/gmpl.pdf
SJG
https://jbonamassa.com/
Joe Bonamassa - "Sloe Gin" - Muddy Wolf at Red Rocks
https://www.youtube.com/watch?v=pvvgZMGp…
And now his own forum, harmonic notes:
https://forum.jbonamassa.com/viewtopic.p…
Midnight Blues
https://www.youtube.com/watch?v=8z74lr3t…
Guitar Harmonics
https://en.wikipedia.org/wiki/String_har…
Beth and Joe - Black Coffee ( a Steve Marriott song, quite a vocal legend to try and imitate )
https://www.youtube.com/watch?v=NooMzmbE…
Beth and Joe - I'd Rather Go Blind ( Live Amsterdam )
https://www.youtube.com/watch?v=UEHwO_UE…
Robin Trower, live ( more harmonic notes )
https://www.youtube.com/watch?v=ZmoMb0gN…
Real and complex analysis
Table Of Contents:
Preface
Prologue: The Exponential Function
Chapter 1: Abstract Integration
Set-theoretic notations and terminology
The concept of measurability
Simple functions
Elementary properties of measures
Arithmetic in [0, infinity]
Integration of positive functions
Integration of complex functions
The role played by sets of measure zero
Exercises
Chapter 2: Positive Borel Measures
Vector spaces
Topological preliminaries
The Riesz representation theorem
Regularity properties of Borel measures
Lebesgue measure
Continuity properties of measurable functions
Exercises
Chapter 3: L^p-Spaces
Convex functions and inequalities
The L^p-spaces
Approximation by continuous functions
Exercises
Chapter 4: Elementary Hilbert Space Theory
Inner products and linear functionals
Orthonormal sets
Trigonometric series
Exercises
Chapter 5: Examples of Banach Space Techniques
Banach spaces
Consequences of Baire's theorem
Fourier series of continuous functions
Fourier coefficients of L¹-functions
The Hahn-Banach theorem
An abstract approach to the Poisson integral
Exercises
Chapter 6: Complex Measures
Total variation
Absolute continuity
Consequences of the Radon-Nikodym theorem
Bounded linear functionals on L^p
The Riesz representation theorem
Exercises
Chapter 7: Differentiation
Derivatives of measures
The fundamental theorem of Calculus
Differentiable transformations
Exercises
Chapter 8: Integration on Product Spaces
Measurability on cartesian products
Product measures
The Fubini theorem
Completion of product measures
Convolutions
Distribution functions
Exercises
Chapter 9: Fourier Transforms
Formal properties
The inversion theorem
The Plancherel theorem
The Banach algebra L¹
Exercises
Chapter 10: Elementary Properties of Holomorphic Functions
Complex differentiation
Integration over paths
The local Cauchy theorem
The power series representation
The open mapping theorem
The global Cauchy theorem
The calculus of residues
Exercises
Chapter 11: Harmonic Functions
The Cauchy-Riemann equations
The Poisson integral
The mean value property
Boundary behavior of Poisson integrals
Representation theorems
Exercises
Chapter 12: The Maximum Modulus Principle
Introduction
The Schwarz lemma
The Phragmen-Lindelöf method
An interpolation theorem
A converse of the maximum modulus theorem
Exercises
Chapter 13: Approximation by Rational Functions
Preparation
Runge's theorem
The Mittag-Leffler theorem
Simply connected regions
Exercises
Chapter 14: Conformal Mapping
Preservation of angles
Linear fractional transformations
Normal families
The Riemann mapping theorem
The class µ
Continuity at the boundary
Conformal mapping of an annulus
Exercises
Chapter 15: Zeros of Holomorphic Functions
Infinite Products
The Weierstrass factorization theorem
An interpolation problem
Jensen's formula
Blaschke products
The Müntz-Szas theorem
Exercises
Chapter 16: Analytic Continuation
Regular points and singular points
Continuation along curves
The monodromy theorem
Construction of a modular function
The Picard theorem
Exercises
Chapter 17: H^p-Spaces
Subharmonic functions
The spaces H^p and N
The theorem of F. and M. Riesz
Factorization theorems
The shift operator
Conjugate functions
Exercises
Chapter 18: Elementary Theory of Banach Algebras
Introduction
The invertible elements
Ideals and homomorphisms
Applications
Exercises
Chapter 19: Holomorphic Fourier Transforms
Introduction
Two theorems of Paley and Wiener
Quasi-analytic classes
The Denjoy-Carleman theorem
Exercises
Chapter 20: Uniform Approximation by Polynomials
Introduction
Some lemmas
Mergelyan's theorem
Exercises
Appendix: Hausdorff's Maximality Theorem
Notes and Comments
Bibliography
List of Special Symbols
^^^^^^ I love this stuff!
looking for a particular book, but I do find:
Fundamentals of complex analysis for mathematics, science, and engineering / E. B. Saff, A. D. Snider. (1976)
SJG
Lady Zep
https://www.youtube.com/watch?v=IO4Idvfd…
Led Zeppelin Heartbreaker / Living Loving Maid (She's Just a Woman)
https://www.youtube.com/watch?v=nwmCOSYU…
Principles of Mathematical Analysis, his first, but then a second edition
Fourier analysis on groups 1962, seems to be his second book
Real and Complex Analysis his 3rd book
But we can just go by this:
https://en.wikipedia.org/wiki/Walter_Rud…
I want to read and understand most all of his stuff
SJG
SJG
Story of O Dress
http://fap.to/images/full/51/169/1691900…
http://fap.to/images/full/41/127/1276134…
So I want to record some of his references:
Dana Z. Anderson, ed. Neural Information Processing Systems, 1988
Ross W. Ashby, Variety, Constraint, and the Law of Requisite Variety, in An Introduction to Cybernetics, 1956
Richard Dawkins, The Blind Watchmaker, 1987
Gerald M. Edelman, Neural Darwinism: The THeory of Neuronal Group Selection, Basic Books, 1987
Gerald M. Edelman, The Remembered Present: A Biological Theory of Consciousness, Basic Books, 1990
Matthew L. Ginsberg, ed., Readings in Nonmonotonic Reasoning, 1987
Christopher G. Langton, ed., Artificial Life, 1989
Carver Mead, Analog VLSI and Neural Systems 1989
Dynamic Patterns in Complex Systems 1988
seems to be Dynamic patterns : the self-organization of brain and behavior / J.A. Scott Kelso. (1995)
Thompson and Stewart, Nonlinear Dynamics and Chaos, 1986
Weber, Depew, Smith, eds., Entropy, Information, and Evolution, 1988
L. A. Zadeh,
and a chapter author with Autodesk, brilliant man:
Carl Tollander
Brenda Laurel
https://en.wikipedia.org/wiki/Brenda_Lau…
SJG
Waring of Rising Nationalism
https://www.independent.co.uk/news/world…
https://www.abc.net.au/news/2018-11-11/w…
https://www.realclearpolitics.com/2018/0…!
Adam Hochschild
https://www.democracynow.org/2018/11/12/…
Tomb of the Unknown Soldier, underneath the Arch of Triumph, should be visible from this East side angled view
https://www.google.com/maps/place/Arc+de…
http://www.paris-pictures.com/tomb-of-un…
https://en.wikipedia.org/wiki/Arc_de_Tri…
https://architecturebehindmovies.files.w…
Theatre Chochotte - Paris
http://a403.idata.over-blog.com/3/52/36/…
Hookers in Paris
http://smallworldtravels.com/hookers-in-…
Baker Gurwitz
https://www.youtube.com/watch?v=cte9Bk_f…
Eric Clapton May 26, 2018 Complete show
https://www.youtube.com/watch?v=mYmlwrCp…
So he talks about non-Euclidean Geometry. As I know, this is geometry without the seventh postulate, that parallel lines never cross.
He says the two people who pursued this, in the 19th Century, are:
Nikolai Lobachevsky
https://en.wikipedia.org/wiki/Nikolai_Lo…
https://en.wikipedia.org/wiki/Hyperbolic…
János Bolyai
https://en.wikipedia.org/wiki/János_Boly…
https://en.wikipedia.org/wiki/Non-Euclid…
Introduction to non-Euclidean geometry / Harold E. Wolfe (2012, Dover Publications (always good) )
SJG
Chicago: Police Shoot and Kill a Black On-Duty Security Guard
"
In the Chicago suburb of Midlothian, a black security officer was shot and killed by a white police officer Sunday as he was restraining a shooting suspect while on duty at a bar. Twenty-six-year-old Jemel Roberson reportedly grabbed and held a bar patron to the ground after the patron opened fire early Sunday morning. When police officers arrived on the scene, witnesses say Roberson was immediately shot, despite people at the bar screaming that he was a security guard. At the time, Roberson was armed and held a valid gun owner’s license. One patron who witnessed the killing said the cops “saw a black man with a gun, and basically killed him.” An autopsy Monday concluded that Roberson’s death was a homicide.
"
https://www.democracynow.org/2018/11/14/…
https://en.wikipedia.org/wiki/G._Spencer…
https://web.archive.org/web/200706292156…
But also, using the name James Keys, he wrote, "Only Two Can Play This Game", its about relations between men and women.
But a Dirk Baeker wrote: A Calculus for Autopoiesis, trying to use the Laws of Form mathematics for the ideas of Maturana and Varela. No one else has done this.
https://www.researchgate.net/publication…
We also have this book Living Systems
https://www.amazon.com/Living-Systems-In…
I know though from having examined the book, that Maturana and Varela wrote their own book using the math of Spencer-Brown, the special symbols.
SJG
Rosicrucian Order AMORC San Jose
http://pansophers.com/wp-content/uploads…
https://www.amorc.org/img/gallery/rosicr…
http://salemos.tripod.com/sitebuildercon…
https://sites.google.com/a/amorc.rosicru…
https://www.terragalleria.com/images/us-…
https://www.rosicrucian.org/images/diges…
https://678d7c627720ddde2df2-c5b158543cb…
AMORC Paris
https://upload.wikimedia.org/wikipedia/c…
https://www.blog-rose-croix.fr/wp-conten…
https://www.fm-mag.fr/sites/default/file…
AMORC, location unknown
http://www.esoblogs.net/wp-content/uploa…
AMORC, NY illustration from long ago?
https://amorc.org.uk/sites/default/files…
AMORC, probably Brazil
https://www.amorc.org.br/wp-content/uplo…
http://www.magiadourada.com.br/rctemple.…
?????
https://c8.alamy.com/comp/B3WD3H/middle-…
Free Masons
https://i.pinimg.com/236x/87/51/c9/8751c…
BOTA, illustration, based in Los Angeles
http://files.abovetopsecret.com/files/im…
AMORC, Atlantis
https://www.rosicrucian.org/images/diges…
AMORC, unknown
https://i.pinimg.com/236x/a4/a8/bc/a4a8b…
Brian Eno - Ambient 1: Music for Airports [Full Album]
https://www.youtube.com/watch?v=vNwYtlly…
Maturana and Varela provided some of the first conceptual works which really challenged me!
SJG
https://en.wikipedia.org/wiki/Bernhard_R…
Riemann, topology, and physics / Michael Monastyrsky ; with a foreword by Freeman J. Dyson. (1999)
SJG
Saturday I reported on a man who had vanished from a 49er's stadium game the previous Monday. Saturday they found a body in the water near the old unused Alviso Marina and some old concrete boat ramps. The stuff is unused because silt comes in from the bay and fills it up.
I have years ago explored all around there. It is interesting, but even in the day time potentially dangerous. I once got stuck hip deep in mud and a shoe came off. Getting my foot back into the shoe I was able to recover it. But I was taking more risks in doing so.
This man was in the military, maybe Special Forces. So likely he handles himself quite well in the outdoors, even at night.
Not sure if any conclusions have been reached, but to me it sounds more and more like a suicide. Left his cell phone, battery run down to zero, in his car at the stadium. Also left his girl friend and her two kids there. But talking on the phone and using video up until the point he vanished.
https://590kqnt.iheart.com/featured/morn…
http://www.khq.com/story/39481212/santa-…
Here SJPD say that the body was found floating face down about 1 mile out from the Marina and the Ramps.
https://www.yahoo.com/gma/body-discovery…
https://heavy.com/news/2018/11/ian-power…
I believe that police probably have more tidbits of information which they are not going to disclose until they are ready to close the case.
In a homicide it is usually those closest to the deceased who did it, and they are exposed by the contradictions in their stories. To me, this is sounding more and more like a suicide.
Here it sound like he was found at the boat launch, though those concrete ramps are unusable do to silt.
https://thespun.com/news/body-found-amid…
https://www.oxygen.com/crime-time/body-f…
Still waiting to hear that they have confirmed the identity, and then of course for any conclusions.
http://www.ksro.com/2018/11/19/body-disc…
Jeff Healey Band, full concert
https://www.youtube.com/watch?v=s_ufNFTA…
Theatre Chochotte, Paris
http://bird-production.com/photographers…
http://a403.idata.over-blog.com/3/52/36/…
Here, outside view, use zoom outs and changing back to maps to see exactly where this is:
https://www.google.com/maps/uv?hl=en&pb=…
Inside scene
https://www.google.com/maps/uv?hl=en&pb=…
34 Rue Saint-André des Arts, 75006 Paris, France
Here:
https://www.google.com/maps/@48.8533376,…
Very close to the Seine
and to the Luxembourg Gardens park.
http://cdn.kabook.fr/bk21125/pic_85465_1…
https://i.pinimg.com/736x/78/d0/3d/78d03…
http://info.xineurope.com/uploadfile/201…
Here, their own page:
https://www.theatre-chochotte.com/englis…
https://www.theatre-chochotte.com/englis…
https://www.theatre-chochotte.com/englis…
https://www.theatre-chochotte.com/englis…
Emmanuel Marcon
‘Patriotism is the exact opposite of nationalism. Nationalism is a betrayal of patriotism’
https://www.independent.co.uk/news/world…
The US and Russian leaders listened in silence as Mr Macron took a swipe at the rising tide of populism in the US and Europe, warning: “The old demons are rising again, ready to complete their task of chaos and of death.”
“In saying, ‘Our interests first, whatever happens to the others’, you erase the most precious thing a nation can have, that which makes it live, that which causes it to be great and that which is most important: its moral values.”
https://www.abc.net.au/news/2018-11-11/w…
https://www.abc.net.au/news/2018-11-12/e…
https://www.nytimes.com/2018/04/18/opini…
EXPLORING PARIS: The Red Light Sex Shop Area (Pigalle)
https://www.youtube.com/watch?v=2D_Zx8aY…
http://www.khq.com/story/39502486/body-d…
SJG
a much loved book from way back
Div, grad, curl, and all that : an informal text on vector calculus / H.M. Schey. (2005)
SJG
https://www.amazon.com/patrick-modiano-B…
An Introduction to Heidegger: Being and Time
https://www.youtube.com/watch?v=eDAyhsZ-…
Bill Moyers, Forrest Church Interview
https://www.youtube.com/watch?v=yJbFGevv…
Stravinsky: The Firebird / Gergiev · Vienna Philarmonic · Salzburg Festival 2000
https://www.youtube.com/watch?v=RZkIAVGl…
So you folks like these no proscenium concert halls?
Disney Music Center
https://meyersound.com/wp-content/upload…
San Jose Center for the Performing Arts, not designed that way.
https://c2.staticflickr.com/4/3127/27685…
TJ Street
https://farm8.static.flickr.com/7318/961…
https://farm8.staticflickr.com/7290/9620…
https://c2.staticflickr.com/6/5449/96322…
https://c1.staticflickr.com/3/2849/96290…
real old one, 1963
https://www.amazon.com/Introduction-Elec…
https://www.amazon.com/dp/1118571363?aax…
Roger F. Harrington, reprinted by Dover
https://www.amazon.com/Time-Harmonic-Ele…
and
https://www.amazon.com/Introduction-Elec…
Electromagnetic Fields and Waves - Lorrain and Corson
and is this really the whole book made into a PDF?
https://www.zuj.edu.jo/download/electrom…
Electromagnetic fields and waves : including electric circuits / Paul Lorrain, Dale R. Corson, François Lorrain 1988
But the one I have found to be the most demanding, and a new one at that, gets into relativity and tensor analysis:
Introduction to electrodynamics / David J. Griffiths (Reed College, Oregon) (2017)
SJG
The Jeff Healey Band - Live In Belgium (Full Concert 1993)
https://www.youtube.com/watch?v=s_ufNFTA…
TJ Street
https://farm8.static.flickr.com/7318/961…
https://farm8.staticflickr.com/7290/9620…
https://c2.staticflickr.com/6/5449/96322…
https://c1.staticflickr.com/3/2849/96290…
https://en.wikipedia.org/wiki/Cantor_set
Old calculus book talk about this. I is necessary for getting people to understand real numbers. Today people just take it all for granted, already adapted to computerization of math.
This is why we still need access to old books, as well as new.
Modern calculus and analytic geometry / Richard A. Silverman (2002, but originally published 1969, republished by Dover )
http://store.doverpublications.com/?mscl…
https://doverpublications.ecomm-search.c…
Richard A. Silverman is good.
And so is Dover Publications.
https://www.amazon.com/Richard-A.-Silver…
SJG
Why I Left an Evangelical Cult | Dawn Smith | TEDxNatick
https://www.youtube.com/watch?v=-U4Cq-dg…
The Broken Scales Of Wendy Carlos
https://www.youtube.com/watch?v=RuT6Y53L…
Wendy Carlos Alpha Scale
https://www.youtube.com/watch?v=vLT6E4zS…
Music Revolutionaries - Robert Moog & Wendy Carlos
https://www.youtube.com/watch?v=AtPJtSBB…
Equal Temperament vs Just Intonation
https://www.youtube.com/watch?v=Yqa2Hbb_…
Why Not Admit There is a Problem With Math and Music? Dan Formosa at TEDxDrexelU
https://www.youtube.com/watch?v=gHSv94aT…
Serious Earthquakes In Alaska
https://www.yahoo.com/gma/large-earthqua…
If we have justice, then no one will ever be without what they need.
If we do not have justice, then money will never be a reliable substitute.
Medicare For All
https://www.democracynow.org/2018/11/30/…
Bernie Sanders, Economic Justice
https://www.democracynow.org/2018/11/30/…
Let it be:
Modern calculus and analytic geometry / Richard A. Silverman.
And he has lots of books:
http://csul.iii.com/search~S0?/aSilverma…
As my organization develops I will want to be buying books, instead of borrowing, as sharing books in our libraries will be yet another of the things which helps bind the group together. We will make our own catalog software, and we will be able to make comments on the books and compile lists of recommendations. So if I am going to take the time to read it, even if it only turns out to be so so, still better to have bought it.
SJG
Highest gender wage gap in the Bay Area:
https://www.mercurynews.com/2018/12/03/w…
TJ Street
https://farm8.static.flickr.com/7318/961…
https://farm8.staticflickr.com/7290/9620…
https://c2.staticflickr.com/6/5449/96322…
https://c1.staticflickr.com/3/2849/96290…
The Cube oF Space and the 22 Paths Of initiation
https://www.youtube.com/watch?v=7cXWcnHb…
⚡️ Arcanum 1⚡️ The Magician ⚡️ Tarot & Alchemy And Kabbalah
https://www.youtube.com/watch?v=05HTe25N…
https://doverpublications.ecomm-search.c…
The Dover Physics books don't have the same timelessness to them. But this 1967, still relevant, at least as a background:
http://store.doverpublications.com/04866…
Also very good and related:
Out of the crystal maze : chapters from the history of solid state physics / edited by Lillian Hoddeson ... [and others] (1992)
https://www.amazon.com/Out-Crystal-Maze-…
https://en.wikipedia.org/wiki/Euclid%27s…
SJG
Considered the most successful math text book ever. Second only to the Bible in number of editions printed.
"
Proclus (412–485 AD), a Greek mathematician who lived around seven centuries after Euclid, wrote in his commentary on the Elements: "Euclid, who put together the Elements, collecting many of Eudoxus' theorems, perfecting many of Theaetetus', and also bringing to irrefragable demonstration the things which were only somewhat loosely proved by his predecessors".
"
Is this the same Proclus who influenced Pseudo Dionysus?
Proclus Lycaeus (/ˈprɒkləs laɪˈsiːəs/; 8 February 412 – 17 April 485 AD), called the Successor (Greek Πρόκλος ὁ Διάδοχος, Próklos ho Diádokhos), was a Greek Neoplatonist philosopher, one of the last major classical philosophers (see Damascius). He set forth one of the most elaborate and fully developed systems of Neoplatonism. He stands near the end of the classical development of philosophy, and was very influential on Western medieval philosophy (Greek and Latin).
https://en.wikipedia.org/wiki/Proclus
Yes, indeed, he is the influence behind Pseudo- Dionysus, and others of the Renaissance.
"
Proclus can be considered as the spokesman of mature Neoplatonism. His works had a great influence on the history of western philosophy. The extent of this influence, however, is obscured by the channels through which it was exercised. An important source of Procline ideas was through the Pseudo-Dionysius.[5] This late-5th- or early-6th-century Christian Greek author wrote under the pseudonym Dionysius the Areopagite, the figure converted by St. Paul in Athens. Because of this fiction, his writings were taken to have almost apostolic authority. He is an original Christian writer, and in his works can be found a great number of Proclus's metaphysical principles.
"
Proclus Lycaeus
Proclus Lycaeus
http://www.goddess-athena.org/Encycloped…
https://web.archive.org/web/201307020257…
The anatomy of Neoplatonism / A.C. Lloyd. (1990)
Plotinus : ǂb The Enneads
The enneads / Plotinus ; edited by Lloyd P. Gerson, University of Toronto ; translated by George Boys-Stones, Durham University, John M. Dillon, Trinity College, Dublin, Lloyd P. Gerson, University of Toronto, R.A.H. King, University of Berne, Switzerland, Andrew Smith, University College, Dublin, James Wilberding, Ruhr-Universitat Bochum.
(2018) over 900 pages.
All from one : a guide to Proclus / edited by Pieter d'Hoine and Marije Martijn ( 400 plus pages, 2017 )
SJG
TJ Street
https://farm8.staticflickr.com/7290/9620…
san_jose_guy - commonly referred to as SJG this forum member is usually mocked or ignored, his comments should NOT be taken in any way as legitimate
http://moreisdifferent.com/2015/07/16/wh…
So I guess they are saying that it has legacy code and that it is just easier to use for people who do not have a major commitment to professional grade programming and complex applications.
So this settles it for me, no reason to worry why R has some parts written in fortran. As far as using fortran legacy code, no problem. As far as writting parts of some stuff in fortran, probably only if it connects somehow to some of the other code.
As far as performance, for math it is the same as C. Intel, Microsoft, and Cray offer both C/C++ and Fortran.
This settles the matter for me.
SJG
Egg Cream - Lou Reed
https://www.youtube.com/watch?v=d5KUHWKH…
The Velvet Underground -- Oh! Sweet Nuthin'
https://www.youtube.com/watch?v=rwo0gpa6…
X - The Have Nots
https://www.youtube.com/watch?v=F6e1zPok…
https://www.youtube.com/watch?v=_AOH_thC…
X Some Other Time
https://www.youtube.com/watch?v=3jUvluq4…
https://www.youtube.com/watch?v=LlnTjVDQ…
X - Los Angeles
https://www.youtube.com/watch?v=fUiZHt6s…
Daily Digit: Believe it or not, Chicago is not the murder capital of the U.S.
https://news.yahoo.com/daily-digit-belie…
"But when adjusting for its large population, Chicago has fewer deaths per capita than many other cities. St. Louis has had the nation’s highest murder rate for the past four years, followed by Baltimore, Detroit, New Orleans and Baton Rouge."
Farm, Psychedelic Blues-Rock 1971
https://www.youtube.com/watch?v=plfEvepn…
Steppenwolf - The Pusher
https://www.youtube.com/watch?v=3XqyGoE2…
Magic Carpet Ride
https://www.youtube.com/watch?v=GLuUGblO…
Fairies Wear Boots - Black Sabbath
https://www.youtube.com/watch?v=ab-ZNU76…
Paranoid - Full Album
https://www.youtube.com/watch?v=fWvKvOVi…
TJ Street
https://farm8.static.flickr.com/7318/961…
https://farm8.staticflickr.com/7290/9620…
https://c2.staticflickr.com/6/5449/96322…
Naked Woman On The Altar - Church of Satan
https://www.youtube.com/watch?v=e2JIyncS…
https://www.youtube.com/watch?v=T1zsIk6W…
https://www.churchofsatan.com/
https://aleisternacht.files.wordpress.co…
What these guys do is interesting, but what my organization will do will be vastly superior!
https://bookstore.ams.org/bourbaki/
https://www.britannica.com/topic/Nicolas…
The Bourbaki writings commenced in 1939 with the first volume of their Éléments de mathématique (“Elements of Mathematics”). The still-incomplete series of more than 30 monographs soon became a standard reference on the fundamental aspects of modern mathematics. The various historical notes included at the ends of chapters were published as a collection in 1960 in Eléments d’histoire des mathématiques (“History of the Elements of Mathematics”).
https://en.wikipedia.org/wiki/Nicolas_Bo…
First learned of these guys from Deleuze and Guattari's "A Thousand Plateaus".
Seen one of their books on sale, back when we used to have some awesome bricks and mortar bookstores, "Tech Guru".
SJG
SJG
Though I first encountered this in college, I have always had reservations about preparing for any kind of a career which would make me bound to academia.
Need other kinds of venues, and this is indeed what I am working on intensely now.
SJG
Rarely are people called upon to show moral the kind of moral courage needed by those who served in French Resistance
Nancy Wake: Gestapo's Most Wanted
https://www.youtube.com/watch?v=qNXKovYM…
https://www.amazon.com/gp/product/073227…
Gary Clark Jr. - Bright Lights and notice Doyle Bramhall II, playing left handed and with a left hander's body, but with it strung for a right hander. Look close and you can see this, and if you listen to him play and watch close you can hear it. He learned always using borrowed guitars from right handers
https://www.youtube.com/watch?v=x_ZeDn-h…
SJG
The Jeff Healey Band - Live In Belgium (Full Concert 1993)
https://www.youtube.com/watch?v=s_ufNFTA…
disappointed in yo ass SJG.
The Princeton companion to mathematics / editor, Timothy Gowers ; associate editors, June Barrow-Green, Imre Leader. (2008, over 1000 pages)
A panorama of pure mathematics, as seen by N. Bourbaki / Jean Dieudonné ; translated by I.G. Macdonald. (1982)
SJG
The Theosophical Society in America: An Illustrated History
https://www.youtube.com/watch?v=bueOQUDN…
A pre-Socratic Greek philosopher who lived circa 582-507 B.C. Although the neo-Platonists Proclus (circa 232-304) and Porphyry (410?-484) both wrote biographies of him, little is known historically about his life. He was born on the Greek island of Samos, but migrated to Italy (called Magna Graecia in his day) and founded a school at Krotona, which taught an esoteric doctrine to a group of disciples who revered Pythagoras as a demigod. He and his ideas appear frequently in Theosophical literature, such as The Secret Doctrine and Isis Unveiled by Helena P. Blavatsky, The Masters and the Path by Charles W. Leadbeater, and The Lives of Alcyone by Leadbeater and Annie Besant. In the last two books, Pythagoras is identified as a previous incarnation of Mahātma Koot Hoomi, one of Blavatsky’s teachers.
"
https://www.theosophyforward.com/article…
So the Krotona name is from a school which Pythagoras founded in Italy
SJG
Official Parking Lot Bouncer
As Most Diverse Congress in History Takes Office, Dems Push to End Shutdown Without Funding for Wall
https://www.democracynow.org/2019/1/4/mo…
'Leaked' Video Of Alexandria Ocasio-Cortez Proves She... Has Friends, Can Dance
https://www.yahoo.com/huffpost/apos-leak…
https://www.youtube.com/watch?v=1noBAbLa…
https://www.youtube.com/watch?v=ZBeuzWWK…
Edwin Starr
https://www.youtube.com/watch?v=ztZI2aLQ…
https://www.youtube.com/watch?v=01-2pNCZ…
War - The World Is a Ghetto 1972 Full Album
https://www.youtube.com/watch?v=VmheOZtL…
How To Tell If Someone Is Truly Smart Or Just Average
https://getpocket.com/explore/item/how-t…
TJ Street
https://farm8.static.flickr.com/7318/961…
https://c2.staticflickr.com/6/5488/96200…
https://farm8.staticflickr.com/7290/9620…
https://c2.staticflickr.com/6/5449/96322…
Warren Haynes with Joe Bonamassa -- Guitar Center's King of the Blues 2011
https://www.youtube.com/watch?v=KX14smq2…
Beth & Joe - I'd Rather Go Blind - Live in Amsterdam
https://www.youtube.com/watch?v=UEHwO_UE…
Beth & Joe - I Love You More Than You'll Ever Know - Live in Amsterdam
https://www.youtube.com/watch?v=bOQ07fVV…
Amazing Performance by Gary Clark Jr. - When My Train Pulls In
https://www.youtube.com/watch?v=gYXMDCNj…
http://www.theosophydownunder.org/librar…
https://theosophy.wiki/en/Neoplatonism
https://www.universaltheosophy.com/bios/…
From MPH's Secret Teaching of All Ages
http://66.media.tumblr.com/e31dea6a630a3…
Max Heindel writting about Blavatsky's Secret Doctrine, introduced by Manly P. Hall
https://www.amazon.com/H-P-Blavatsky-Sec…
SJG
SJG's New Headquarters, coming soon to a strip club parking lot near you.
12' x 20', and with over 9' of center stand up height.
https://www.cabelas.com/product/Cabelas-…
TJ Street
https://farm8.static.flickr.com/7318/961…
https://c2.staticflickr.com/6/5488/96200…
https://farm8.staticflickr.com/7290/9620…
https://c2.staticflickr.com/6/5449/96322…
Nirvana-Come as you are lyrics
https://www.youtube.com/watch?v=YqN0ZOEO…
Casino Royale 1967 Sound Track Album
https://www.youtube.com/watch?v=EhmZULZX…
Mobile Kitchens, by Carlin, Fresno CA
https://kitchenstogo.com/products/mobile…
just saw one built in a huge 24,000 GVWR Walk-In Van, still okay for Class C License, huge diesel auxiliary power unit.
Mister Bond - A Jazzy Cocktail Of Ice Cold Themes
https://www.youtube.com/watch?v=XVQ8lpPu…
Sexiest Ladies of Jazz - The Trilogy! - Full Album - New 2017
https://www.youtube.com/watch?v=CsJs_hEC…
Soundgarden Half, playlist
https://www.youtube.com/watch?v=EHh-2T84…
Mitch Horowitz: H. P. Blavatsky, Manly P. Hall, and the Secret Teachings of all Ages ( really good )
https://www.youtube.com/watch?v=SIqlw020…
https://mobile-cuisine.com/off-the-wire/…
https://mobile-cuisine.com/running-a-foo…
Running a Food Truck for dummies
https://www.amazon.com/Running-Food-Truc…
SJG
New Field Headquarters, In The Parking Lot
https://www.cabelas.com/product/Cabelas-…
Donald Trump
https://pixel.nymag.com/imgs/fashion/dai…
jeff healey live at nottoden 2006
https://www.youtube.com/watch?v=U5Qb-6Qk…
AC/DC - Girls Got Rhythm ( and with the original lead singer, which I have always found to be one of the group's best features. Clever song, and in my opinion underplayed.
https://www.youtube.com/watch?v=GStgyL2V…
Female Tribute Band
https://www.youtube.com/watch?v=nQWmpNPZ…
Amy Winehouse/Paul Weller - I heard it through the grapevine.Hootynanny 2006.
https://www.youtube.com/watch?v=C1799Yps…
Amy Winehouse I love you more than you'll ever know LIVE
https://www.youtube.com/watch?v=362JArvh…
Gary Clark Jr. - Bright Lights
https://www.youtube.com/watch?v=x_ZeDn-h…
https://www.amazon.com/Pythagoras-Life-T…
Pythagoras, his life and teachings : being a photographic facsimile of the ninth section of the 1687 edition of the History of philosophy / by Thomas Stanley ; foreword by Manly P. Hall ; introductory essay by Henry L. Drake.
And published by PRS ( Philosophical Research, Hall's org 1970)
Some is right here:
https://www.amazon.com/Pythagoras-Life-T…
SJG
Steve Blank, Lean Startup Model
https://en.wikipedia.org/wiki/Steve_Blan…
https://steveblank.com/
Baker Gurvitz Army - Love Is / Memory Lane / Drum Solo / People - Live 1975 (Remastered) HD
https://www.youtube.com/watch?v=y8dX1iPe…
Deep Purple - Lazy
https://www.youtube.com/watch?v=9EvYI5OT…
THE MOODY BLUES - RIDE MY SEE-SAW
https://www.youtube.com/watch?v=nfy8NJtg…
THE GUESS WHO - NO TIME
https://www.youtube.com/watch?v=meIuAUnZ…
But there can also be bad. If a young man wants to study and learn, that can make him into a target for scorn and contempt, and even for exploitation. And sorry to say, its just the way our society is set up, I see this targeting as coming from women.
The organization I am building will remedy all of this.
SJG
Steve Blank
https://en.wikipedia.org/wiki/Steve_Blan…
https://steveblank.com/
https://www.amazon.com/Personal-Storage-…
What is this for and how does this work?
https://www.zyxel.com/us/en/homepage.sht…
https://en.wikipedia.org/wiki/Zyxel
https://www.newegg.com/Product/Product.a…
https://en.wikipedia.org/wiki/RAID
SJG
Ep. 008 - Legends of the Craft: Freemasonry and the Tower of Babel
https://www.youtube.com/watch?v=nBzWx2Bb…
Now this is Le Droit Humaine, Phoenix, and after the Universal Co-Masons separated
https://www.youtube.com/watch?v=sCA1s6i7…
See, the guy has got two books white with a red band, and two more white with a blue band. Well those are Blavatsky's Isis Unveiled and The Secret Doctrine.
Darren Lorente-Bull - Le Droit Humain Freemasonry
https://www.youtube.com/watch?v=jX1pyWYn…
Ep 25 The History Behind Le Droit Humain
https://www.youtube.com/watch?v=HWQ54Tnf…
Ro Khanna: Regime Change Is Not the Answer
https://www.youtube.com/watch?v=E3IbZlC8…
The Ancient War Between Gnostics and Neoplatonists
https://www.youtube.com/watch?v=E3IbZlC8…
Apocalypse of the Alien God: Platonism and the Exile of Sethian Gnosticism
https://www.amazon.com/gp/product/081224…
Apocalypse of the alien god : Platonism and the exile of Sethian gnosticism / Dylan M. Burns (2014)
jeff healey live at nottoden 2006
https://www.youtube.com/watch?v=U5Qb-6Qk…
https://www.zyxel.com/products_services/…
355 pages
ftp://ftp2.zyxel.com/NAS326/user_guide/N…
SJG
Saw this woman's picture somewhere and it reminded me:
https://www.youtube.com/watch?v=TFZPBSh0…
https://www.e-chords.com/chords/shocking…
But while most all the videos for this song are clearly lip sync, and they even require people playing instruments not shown on stage, I have finally found this:
https://www.youtube.com/watch?v=qWb8_DH8…
I'm not against acoustic guitar, its just that I like electric guitar music so much. And electric guitar can do things which acoustic guitar cannot. Needs to feel like you are there with them, not like it is just a contrived television show. Letting this finally be the psychedelia it was intended to be.
Richard Smoley: Magic and the Occult
https://www.youtube.com/watch?v=Bh8ahm7B…
Ecstasy of St. Teresa
https://s3.amazonaws.com/test.classconne…
Ferdinand de Saussure
https://en.wikipedia.org/wiki/Ferdinand_…
Heart - All I Wanna Do Is Make Love To You
https://www.youtube.com/watch?v=lBfP63T0…
https://tabs.ultimate-guitar.com/tab/hea…
Richard Feynman. Why. ( magnets )
https://www.youtube.com/watch?v=36GT2zI8…
Mike Oldfield - Tubular Bells III CONCIERTO
https://www.youtube.com/watch?v=gZq5huke…
Conscious Love: Insights from Mystical Christianity, by Richard Smoley
https://www.amazon.com/gp/product/078798…
Personal Cloud, kind of like an external hard drive. And they explain how to do backups.
SJG
https://en.wikipedia.org/wiki/Foxconn
http://www.foxconn.com/
Nano PC, video
https://www.youtube.com/watch?v=CDCXrB9o…
Foxconn Nano PC AT-7330 Intel Core i3 (i3-3227U) 1.9Ghz 4GB DDR3 250GB HDD ( sale price, refurbished, $142, 250 GB hard disk )
https://www.pcliquidations.com/p71967-fo…
SJG
TJ Street
https://c2.staticflickr.com/4/3752/96322…
Jefferson Airplane 5-7-1970 Fillmore East Complete Show
https://www.youtube.com/watch?v=xrVqhs4I…
Richard Smoley - The Kabbalah: Key to Hidden Knowledge
https://www.youtube.com/watch?v=g-R4sOrW…
https://en.wikipedia.org/wiki/Bubble_mem…
Says that Bubble disappeared entirely by the late 1980's, and mostlly due to Semi-Conductor Flash.
But what about the write cycle limits?
SJG
Jimi Hendrix Live Full Concert 1969 Amazing Clear Footage
https://www.youtube.com/watch?v=PbwUH_eJ…
TJ Street
https://farm8.static.flickr.com/7318/961…
https://farm8.staticflickr.com/7290/9620…
http://www.adelitasbartijuanamexico.com/…
https://farm8.static.flickr.com/7403/961…
https://www.flickr.com/photos/navymailma…
https://c2.staticflickr.com/4/3752/96322…
https://c2.staticflickr.com/6/5449/96322…
HP EliteOne 800 G1 All-in-One PC Product Specifications
https://support.hp.com/us-en/document/c0…
Typical hard drive is 500GB, solid state drives start at 120GB
https://support.hp.com/us-en/document/c0…
HP EliteOne 800 G1 Hard Disk Drive / Solid State Drive Replacement, 5 inch DVD removable media storage also
https://www.ifixit.com/Guide/HP+EliteOne…
Windows 7: Hard Drive - Turn Off Hard Disk After Idle or Never
https://www.sevenforums.com/tutorials/14…
SJG
Baby's Lookin' Hot
https://www.youtube.com/watch?v=s_ufNFTA…
Robin Trower - Full Concert - Rockpalast Crossroads, Bonn - 2005 ( I listen to this, and sorry to say, I can't understand how anyone could ever settle for acoustic guitar music. And then of course, I think solid body is the best of the best )
https://www.youtube.com/watch?v=ZmoMb0gN…
https://www.sweetwater.com/insync/what-a…
"Increased durability due to no moving parts to wear out or fail"
SJG
El Chapo's Trial
https://nypost.com/2018/11/07/juror-sobs…
https://www.pcmag.com/article2/0,2817,24…
SJG
Sexy Girls World Map ( consider Ecuador and Argentina )
https://static.boredpanda.com/blog/wp-co…
Argentina
https://www.argentinaxp.com/wp-content/u…
Year of the Pig
http://media.gettyimages.com/vectors/hap…
TJ Street
https://c2.staticflickr.com/4/3752/96322…
http://www.metroactive.com/features/colu…
Intel NUC (Next Unit of Computing) Core i5 Barebone PC BOXNUC7I5BNH
https://www.frys.com/product/9211999
w/ manufacturer's specs
Barebones PC's
https://www.newegg.com/Barebone-PCs/SubC…
SJG
Mexico City, has so many people and cars on the streets, that if one is interested in hookers, likely best to find a bar, or you would really have to know that area.
http://doxyspotting.com/?p=70423
http://doxyspotting.com/yellow-dress/
http://doxyspotting.com/?p=129645
http://doxyspotting.com/?p=97293
http://doxyspotting.com/?p=70423
http://doxyspotting.com/?p=88173
http://doxyspotting.com/?p=112750
Richard Smoley, Inner Christianity
https://www.youtube.com/watch?v=52xShzP5…
Business Law Today, 10th and 11th Edition, Roger LeRoy Miller
https://www.textbooks.com/Fundamentals-o…
New, Used, purchase as ebook (pdf) and in libraries
Esoteric Christianity -- Don Baker -- Theosophical Society in Seattle
https://www.youtube.com/watch?v=TdN4uI70…
https://www.thermaltake.com/cooler.aspx
Cannot tell where this is, might be China or Turkey
SJG
The End of Work and the Case for Universal Basic Income
Andy Stern, former President of the Service Employees International Union (SEIU), author of Raising the Floor: How a Universal Basic Income Can Renew Our Economy and Rebuild the American Dream, and Senior Fellow at Columbia University's Center for Business, Law, and Public Policy
https://www.youtube.com/watch?v=aKzNBXFn…
How Ayn Rand Became a Hero to Right Wing Nerds -- Thom Hartmann
https://www.youtube.com/watch?v=ZY1ik8bu…
Thom Hartmann: Atlas Shrugged - bizarre philosophy at work -- Thom Hartmann
https://www.youtube.com/watch?v=hHnnnmuY…
Alec Baldwin: Trump's 'SNL' Attack May Be 'A Threat To My Safety'
https://www.yahoo.com/huffpost/alec-bald…
Kim Kardashian
https://www.yahoo.com/entertainment/kim-…
Thierry Mugler
https://en.wikipedia.org/wiki/Thierry_Mu…
https://www.muglerusa.com/
http://www.livingly.com/The+Most+Beautif…
Intimidation, Pressure and Humiliation: Inside Trump’s Two-Year War on the Investigations Encircling Him -- New York Times
https://www.nytimes.com/2019/02/19/us/po…
Venus, Shocking Blue, actually live, with only what you see on stage, and not hamming for the camera, quite good, a coffee house grade performance
https://www.youtube.com/watch?v=qWb8_DH8…
Alvin Lee – The Bluest Blues
https://www.youtube.com/watch?v=rB6OlJqV…
JEFF BECK -Brush With the Blues
https://www.youtube.com/watch?v=TlqyLqDt…
Joe Bonamassa - I'll Play The Blues For You
https://www.youtube.com/watch?v=6-Jzcu5S…
http://www.metroactive.com/features/colu…
SJG
A most impressive article:
https://www.nytimes.com/2019/02/19/us/po…
Ending the Punishment of Poverty: Supreme Court Rules Against High Fines & Civil Asset Forfeiture
https://www.democracynow.org/2019/2/21/e…
Frances Fox Piven, Professor of Political Science and Sociology at the Graduate Center, CUNY
https://www.youtube.com/watch?v=oQBgRPtL…
https://www.amazon.com/gp/product/B00IHG…
NOLO, Bourbon Street
http://doxyspotting.com/?p=131772
AZTECA
https://www.youtube.com/watch?v=yS9WVbQT…
Peter Green - In The Skies ( Full Album ) 1979
https://www.youtube.com/watch?v=U_Llz6n8…
I love the smell of napalm in the morning
https://www.youtube.com/watch?v=ALi78xSa…
https://us.msi.com/Motherboard/MPG-Z390-…
SJG
Oakland CA
http://doxyspotting.com/?p=118715
In Poland, this is what their Lot Lizards look like
http://doxyspotting.com/lot-lizards-pola…
Italy, Lot Lizards
http://doxyspotting.com/lot-lizards/
http://www.shuttle.eu/fileadmin/resource…
Has heat pipe and 2x 60mm fans
External DC Supply, 19v or 12v, keeps heat down. 19v would be better at that.
SJG
Kenneth Grant & Typhonian References
https://www.youtube.com/watch?v=ex33k5hv…
Bernie Sanders Kicks Off 2020 Run in Brooklyn, New York
Sen. Rand Paul Likely to Oppose Nat’l Emergency in Decisive Vote
https://www.democracynow.org/2019/3/4/he…
7 March 1922 – 12 January 2004
https://en.wikipedia.org/wiki/Olga_Ladyz…
Nonlinear equations and spectral theory / M.S. Birman, N.N. Uraltseva, editors (2007)
https://www.amazon.com/Linear-Quasilinea…
SJG
Nation Exclusive: ICE Has Kept Tabs on ‘Anti-Trump’ Protesters in New York City
https://www.thenation.com/article/ice-im…
SONNY ROLLINS-LIVE IN DENMARK´68
https://www.youtube.com/watch?v=dKxd7LoK…
Willpower always was a stupid idea
https://getpocket.com/explore/item/again…
Nighthawk AC3200 Tri-Band WiFi Router
https://www.netgear.com/home/products/ne…
802.11ac Tri-Band Gigabit
"
There's never been WiFi like it. The Nighthawk X6 AC3200 Router with breakthrough Tri-Band WiFi technology was built to connect to each and every device in your home—automatically and simultaneously. Laptops, tablets, phones, TVs, game consoles, music streamers, cameras – if it’s WiFi enabled, it’s X6 accelerated. A powerful combination of features —wireless speed of up to 3.2Gbps, 3 WiFi bands, Smart Connect intelligence, and Dynamic QoS— guarantees every device is assigned the fastest WiFi connection possible and optimized for maximum speed. Using Amazon Alexa™, control your home network with voice commands. NEW: Circle with Disney - Smart Parental Controls.
"
"
Tri-Band WiFi with Smart Connect changes the game for today’s home WiFi networks. With one 2.4GHz band and two 5GHz WiFi bands to work with, the X6 has the capacity, flexibility, and intelligence to assign each device to the WiFi band where it can connect at its maximum possible speed. The result is that faster devices can connect and perform unhindered by slower or older devices—meaning ALL devices load, stream, and game at their maximum speed.
"
https://www.netgear.com/home/products/ne…
SJG
http://www.mexicolindobar.com/
Led Zeppelin - Achilles Last Stand (Live Knebworth 1979)
https://www.youtube.com/watch?v=YWOuzYvk…
https://www.newegg.com/Product/Product.a…
Can be 240GB, 3.4 GHZ
Can this be run entirely via Ethernet? Can it boot without the keyboard?
Can you slow the CPU down and then shut the fan down?
Can you run it off of DC, what voltage range?
SJG
TJ Street
https://farm6.staticflickr.com/5488/9620…
https://c1.staticflickr.com/8/7290/96201…
http://www.adelitasbartijuanamexico.com/…
Pleaser 9" and 10"
https://www.pleaserusa.com/regular.asp?d…
Sister is frightened of her own people
https://www.youtube.com/watch?v=4OkrYf4q…
https://www.gigabyte.com/
as I suspected, Taipei City, Taiwan
https://en.wikipedia.org/wiki/Gigabyte_T…
lots of products, like
https://www.gigabyte.com/Mini-PcBarebone…
https://www.gigabyte.com/Mini-PcBarebone…
Still many questions
SJG
https://www.crunchbase.com/organization/…
????
http://www.archonix.com/
https://www.achronix.com/company/
SJG
https://www.achronix.com/company/
https://www.achronix.com/product/speedco…
Sounds interesting, but it is fabless
SJG
Christianity and Unknowing, Richard Rohr
https://www.youtube.com/watch?v=MnTC4NNI…
Pablo Sender - The Secret Doctrine: Part 1 - How to Study The Secret Doctrine
https://www.youtube.com/watch?v=_O2hdnG6…
Social Entrepreneurship
https://en.wikipedia.org/wiki/Social_ent…
Robert A. Caro on the means and ends of power
https://www.nytimes.com/interactive/2019…
The Irrationality of Alcoholics Anonymous
https://getpocket.com/explore/item/the-i…
Origins of the Perennial Philosophy School of Thought
https://www.youtube.com/watch?v=P_CNg4dp…
Ananda Coomaraswamy
https://en.wikipedia.org/wiki/Ananda_Coo…
Pretend You Have A Cold, Pelosi to Biden
http://www.msn.com/en-us/news/politics/p…
https://www.achronix.com/product/speedco…
They want you to embed their FPGA into your chip. This would seem to mean that you have to use the same FAB they use, likely in Asia, and so that they are really just a promoter for that fab?
SJG
Joe Golem: Occult Detective Volume 2--The Outer Dark
https://www.amazon.com/Joe-Golem-Occult-…
Brian Eno ( quite good )
https://www.youtube.com/watch?v=ggLTPyRX…
Is it possible to have computers generate such music on their own, and even in real time?
Pablo Sender - The Secret Doctrine: Part 1 - How to Study The Secret Doctrine
https://www.youtube.com/watch?v=_O2hdnG6…
SJG
Irish Republican Army
https://www.youtube.com/watch?v=knltGsRc…
https://www.amazon.com/Provisional-Irish…
The Provisional Irish Republican Army and the morality of terrorism / Timothy Shanahan. (2009)
SJG
SJG
Police live 2018
https://www.youtube.com/watch?v=VXZTcL8k…
4 cylinder 2.3L, direct injection 270hp
Payload can be as high as 1860 lbs
7,500 max tow weight
https://www.ford.com/trucks/ranger/model…
SJG
LG Group (Corporation)
https://en.wikipedia.org/wiki/LG_Corpora…
http://www.lgcorp.com/
SJG
Michelle Alexander on The New Jim Crow, at Union Theological Seminary ( she wrote a very important book )
https://www.youtube.com/watch?v=T79I1PLT…
Paul Tillich Symposium: John Caputo Lecture
https://www.youtube.com/watch?v=Cog1v44W…
http://www.sanjoseinside.com/2019/05/17/…
SJG
Alain Badiou / edited by A.J. Bartlett and Justin Clemens (2010)
SJG
https://tuscl.net/discussion.php?id=7078…
Here, back in our old archives I find some treatment of this:
https://tuscl.net/discussion.php?id=3731…
http://www.cnsi.ucsb.edu/research/areas/…
https://en.wikipedia.org/wiki/Fraunhofer…
https://www.kjmagnetics.com/neomaginfo.a…
https://www.amazon.com/Rare-Earth-Perman…
https://www.amazon.com/gp/product/019505…
https://en.wikipedia.org/wiki/Message_Pa…
https://en.wikipedia.org/wiki/Well_car
https://en.wikipedia.org/wiki/Double-sta…
https://cms.mpi.univie.ac.at/vasp/vasp/v…
https://en.wikipedia.org/wiki/Fortran#Fo…
https://www.amazon.com/Molecular-Modelli…
https://en.wikipedia.org/wiki/Jaguar_C-X…
But as the old thread was 2015, I find now that a lot of the links have gone bad.
SJG
Why Are Americans Not Protected Against COVID-19? (w/ Dr. Leana Wen)
https://www.youtube.com/watch?v=rmxOi-1k…
TJ Street
https://tuscl.net/photos/5d699507cd73c
https://tuscl.net/photo.php?id=1061
https://tuscl.net/photo.php?id=3513
https://tuscl.net/photo.php?id=3560
https://tuscl.net/photo.php?id=2305
https://tuscl.net/photos/5cbf9f521a3ae
Graham Bond ✪ Holy Magick [full album]
https://www.youtube.com/watch?v=G0Exbl-S…
Grahame Bond - Love Is the Law [full album / bonus tracks]
https://www.youtube.com/watch?v=wyg8x36f…
M Davis Bitches Brew 1970 Full Album
https://www.youtube.com/watch?v=50fB5L1v…
Thelonious Monk - Live Zurich 1964
https://www.youtube.com/watch?v=iD_4EftN…
Neil Young - Imagine
https://www.youtube.com/watch?v=R15uLXHq…
Pearl Jam with Neil Young - Rockin in the free world Toronto 2011
https://www.youtube.com/watch?v=hvtdbfI1…
At least now I am harvesting what is still good from it.
SJG
Neodymium Magnet Information
https://www.kjmagnetics.com/neomaginfo.a…
Rare-Earth Iron Permanent Magnets (Monographs on the Physics and Chemistry of Materials) 1st Edition
J. M. D. Coey, also has written other books
Out of the Crystal Maze: Chapters from The History of Solid State Physics (outstanding book, text, not formulae and diagrams)
Molecular Modelling for Beginners, Second Edition (2008)
Alan Hinchliffe (written lots of other related books)
https://www.amazon.com/Molecular-Modelli…
And then the most interesting link:
Manual for VASP, a simulation software for multiple electron molecules, and including the electron to electron interactions.
https://cms.mpi.univie.ac.at/vasp/vasp/v…
How here I have what may actually be the most relevant part of that manual, the bibliography.
https://cms.mpi.univie.ac.at/vasp/vasp/B…
And then here is the VASP Wiki, most informative.
https://www.vasp.at/wiki/index.php/The_V…
Now, this thread has dealt with a range of topics. But this old material that I have harvested from the 2015 thread deals with how to simulate multiple electron molecules. There is no real way just to hand calculate or closed from solve for such things.
If one wants to broaden their area of knowledge, finding the key books and key authors is a first step, as well as identifying any particular softwares used. And U Vienna has long been a leader in Mathematical Physics.
If we don't keep on learning new and challenging things, then we turn into Archie Bunker.
The basic focus of these materials is the development of solids with desirable properties in the areas of semiconductor electronics, optics, and magnetics. The latter is in some ways the most challenging because it pretty much comes down to electron angular momentum, and this can even get into relativistic effects.
Much of the interest in this now is simply because of the development of Array Processing Super Computers, and these can be quite cheap. It is possible not to have on your desk top, or in your server rack, a tremendous amount of floating point computing power. It's just a matter of learning how to set it up and how to use it.
The interest in high strength magnets is motivated by man things, I list here only some:
1. High efficiency motors for electric vehicles
2. Coatings and heads for high density magnetic storage devices
3. Bio-Medical measurement devices
4. Small scale electricity generation, usually DC or out of sync with grid
Interest in semi-conductor electronics and optonics is real simple, advances in computing and communications technologies depends more and more on a merger of electronic and optical technologies, and on pursuing some extic material types, looking at band gap size, direct or indirect, carrier mobilities and velocities, and then all the chemical properties which make these things usable.
The world is getting more and more complex and what people are expected to know to be considered competent continues to expand.
Now some people here might only be interested in talking about Right Wing News and Politics, Financial Speculation, and various kinds of Reactionary and Misogynist views.
But to say that this is all the members of this forum and the patrons of strip clubs could be interested in, is to sell us all way too short.
Returning to this, not Quantum Entanglement, but a very good book about the Industrial Applications of Quantum Mechanics:
https://www.amazon.com/gp/product/013747…
SJG
And the reason that some of the old 2015 links expired was just that the managers of those sites made changes. They put some new stuff up, and they took some old stuff down.
SJG
Carly Simon, You're So Vain
https://www.youtube.com/watch?v=mQZmCJUS…
https://tuscl.net/discussion.php?id=3731…
SJG
https://www.colorado.edu/search?cse=mult…
And from UC Santa Barbara, spintronics:
As an alternative to electronic charge, the storage and transport of electronic spin in semiconductor devices - "spintronics", may revolutionize the electronic device industry, with spin based transistors , opto-electronic devices, and memory.
http://www.cnsi.ucsb.edu/research/areas/…
Here we seem to have a tutorial:
https://courses.lumenlearning.com/boundl…
Here again is the VASP manual
https://www.vasp.at/
^^^^^ a whole bunch of presentation slides about this matter, lots of lectures.
https://www.vasp.at/vasp-workshop/comput…
full manual pdf
https://cms.mpi.univie.ac.at/vasp/vasp.p…
And it looks like with VASP they give you a C++ program to compile and run. That helps you direct the big compilation.
But the actual VASP program is written in FORTRAN!
I say this in light of the fact that on that 2015 thread I did not know if anyone still did anything in FORTRAN. And Dougster was completely incredulous.
So since I learned about the newer versions of FORTRAN, and VASP uses FORTRAN 90.
When I had started looking into these matters a while back the best I could find was that people felt it was probably a wash as to whether FORTRAN or C++ compilers would generate the fastest executing code.
So if you really want to make it the fastest, you just have to do it yourself in assembler. Don't use the inline assembler provision in Microsoft C++. because there you are making assumptions about how the compilers is using the CPU registers. You might be wrong, and to beat the compiler you probably do have to find some uncommon way.
So instead just get from the compiler the assembly files it can generate. The pick ones to re-write, or functions to bring back inline with what calls them. Just elimination some function call protocols will probably help.
You will have to really study the CPU and its instruction set. Some are very symmetrical, and others are not. And this is floating point, but in the interger indexing portions of the code you might find ways to speed it up.
And then as much of this now is being done on multi-processor systems, that adds a whole 'nother magnitude of complexity.
SJG
Best of the 60's
https://www.youtube.com/watch?v=1981EXif…
Not impressed? Well Intel and Microsoft are doing exactly the same thing.
Pascal is dead, but Ada has taken its place. Though I am not seeing evidence of this kind of wide spread use of Ada, or any acceptance of its basic claim that it makes safer programs. Books make the pitch, but the message seems to be no longer accepted.
Going further and further into Object Oriented Programming, you can make your own variable types and the "methods" for accessing them, and so you can also put in what you want of Pascal/Ada style run time bounds checking.
SJG
https://www.natureindex.com/institution-…
US Naval Research Laboratory
https://www.nrl.navy.mil/mstd/6393
^^^^^ all of this stuff is being driven by the availability of Array Processor Super Computers, and by the need for better magnetic, optical, and semi-conductor materials.
SJG
September 18, 2015
https://tuscl.net/discussion.php?id=3731…
So here, use this link to find it, and then move pages forward or back to find more from that era.
https://tuscl.net/discussions.php?member…
And yes indeed, this is the next thread like that:
https://tuscl.net/discussion.php?id=3731…
and look what we find:
https://www.materialsdesign.com/
http://doxyspotting.com/?p=108868
https://ambri.com/
And here is one about magnets that I really wanted to find:
mint.ua.edu/wp-content/uploads/2012/12/M…
32 page pdf
There is a trove of information in these old threads!
SJG
Black Sabbath, War Pigs, Paris 1970
https://www.youtube.com/watch?v=K3b6SGoN…
https://www.youtube.com/watch?v=uWAhd4Kk…
Let me try and assimilate what I can.
Materials Design ( now in San Diego, where as the people who handled the licensing for VASP were in Taos NM.)
https://www.materialsdesign.com/
Does look like VASP is used with this new MediA
https://www.materialsdesign.com/medea-so…
Molecular quantum mechanics / Peter Atkins and Ronald Friedman (2011, and Atkins always writes good books )
Structure elucidation in organic chemistry : the search for the right tools / edited by Maria-Magdalena Cid and Jorge Bravo (2015)
SJG
OT: Computer Programming (open)
https://tuscl.net/discussion.php?id=6939…
crosby stills nash young almost cut my hair CSNY 1974
https://www.youtube.com/watch?v=AVsbqVJL…
https://www.materialsdesign.com/medea-so…
https://info.materialsdesign.com/Datashe…
MedeA is used throughout many industries from academic research to industrial materials design and optimization, where atomistic modeling has become an integral part of the Computational Materials Engineering value-creation chain.
Yeah, this is an industry now, and the software will be used as a busy box. Seen this in other fields.
SJG
https://www.materialsdesign.com/medea-so…
Yeah, this is tremendous incursion and deskilling of work environments. No longer research area, not an industry.
Needs to be a counter, open-source, open-data, response.
SJG
Trying to learn more about the above, which I do not like.
But here:
https://en.wikipedia.org/wiki/Austin_Mod…
and then:
https://en.wikipedia.org/wiki/Semi-empir…
and then:
https://en.wikipedia.org/wiki/Semi-empir…
and finally:
https://en.wikipedia.org/wiki/List_of_qu…
^^^^^ and notice, a whole tone of stuff written in FORTRAN
Would I start something totally new in FORTRAN? I think not, I think I would go for C++. But I would be willing to listen if there were arguments for FORTRAN.
SJG
TJ Street
https://tuscl.net/photo.php?id=3560
Wes Montgomery - Round Midnight
https://www.youtube.com/watch?v=MOm17yw_…
Berkeley
https://www2.eecs.berkeley.edu/Research/…
https://www.nersc.gov/
https://www.nersc.gov/systems/
https://www.nersc.gov/systems/computatio…
So they seem to use Cray XC40.
I believe that these are modules which you can connect together.
https://en.wikipedia.org/wiki/Cray_XC40
https://www.cray.com/products/computing/…
https://www.cray.com/products/computing/…
https://www.cray.com/resources/the-cray-…
https://www.cray.com/resources/the-cray-…
^^^^^ Not really getting the kinds of info I want.
https://www.intel.com/content/www/us/en/…
What is this board:
https://harddiskdirect.com/d56657-001-in…
SJG
https://www.design-reuse.com/sip/floatin…
Multicore Architectures, 2007
https://www.cs.cmu.edu/~fp/courses/15213…
Open Source Floating Point
https://stackoverflow.com/questions/4740…
Intel Floating Point Exception Handers, for IA-64
https://www.intel.com/content/www/us/en/…
main intel processor manual
https://www.intel.com/content/www/us/en/…
This stuff looks military, way over priced.
https://tridentinfosol.com/digitalsignal…
BUt then
https://tridentinfosol.com/engineeringso…
just selling MATLAB / Simulink
https://tridentinfosol.com/numericalcomp…
FPGA Floating Point Accererator, 2011
http://tesla.rcub.bg.ac.rs/~zeljkoj/rado…
Accelerator Board(2011)
https://www.techopedia.com/definition/56…
^^^^^^^^^^^ Mostly talking about grahics acceleration, not floating point numerical analysis.
Well here, a CRC Book about R
https://www.amazon.com/Computational-Num…
Accelerator Board, 2014
https://www.researchgate.net/publication…
SIAM Journal on Numerical Analysis
https://www.siam.org/publications/journa…
^^^^ $114 per year, print and online, but 80% discount on you first four selected journals.
SJG
https://en.wikipedia.org/wiki/Attractor
https://en.wikipedia.org/wiki/Attractor#…
THis kind of thing has stimulated much interest. In my opinion this is because of computers, as you need computers to explore stuff like this, to make the phase diagrams.
But the strangeness of it is all is not related to quantum mechanics, and it is not cause by the round off error and finite bit precision of computers.
More it is just some highly non-linear equations and the fact that in real life you never fully know the starting conditions. Some natural phenomenon do run entirely on extreme non-linearity. This is the sort of things which technology and engineering have historically avoided.
SJG
Eric Clapton Layla 2008
https://www.youtube.com/watch?v=rbceFpLY…
crosby stills nash young almost cut my hair CSNY 1974
https://www.youtube.com/watch?v=AVsbqVJL…
TJ Street
https://tuscl.net/photo.php?id=1132
https://tuscl.net/photo.php?id=2305
Pleaser 10"
https://pleasershoes.com/collections/ple…
https://pleasershoes.com/products/beyond…
https://www.ansys.com/products/electroni…
https://en.wikipedia.org/wiki/Ansys
Canonsburg, Pennsylvania, U.S., 18 miles South West of Pittsburg
https://www.antennasimulator.com/Resourc…
___________________________________________
AN-SOF
https://www.ema-eda.com/products/cadence…
https://www.antennasimulator.com/Resourc…
https://www.pressreader.com/uk/radio-use…
https://www.antennasimulator.com/
https://antennasimulator.com/downloadpro…
264 Pages, Golden Engineering
not sure if this is the same company
http://www.goldenengineering.com/
https://en.calameo.com/books/0016326447e…
EMA Design
https://www.ema-eda.com/products/cadence…
established in 1989 by Manny Marcano, EMA Design Automation is a leader in product development solutions ranging from electrical CAD tools, data management and PLM systems, services, training, and technical support.
not on this list:
https://en.wikipedia.org/wiki/List_of_ED…
https://en.wikipedia.org/wiki/SmartSpice
SJG
Anyway, name is altered a bit. Maybe someone decided to restart it.
https://www.windriver.com/?utm_source=go…
https://www.windriver.com/studio/tour
Yes, always been impressed with these people.
SJG
Wynton Marsalis & The Young Stars of Jazz - "Take The 'A' Train"
https://www.youtube.com/watch?v=cFs7cyPm…
Acquired by Intel 2009, acquired by TPG 2018
https://en.wikipedia.org/wiki/Wind_River…
TPG, now based in San Francisco
https://en.wikipedia.org/wiki/TPG_Capita…
https://www.tpg.com/
SJG
Processes of Inference, Learning, and Discovery
John H. Holland etal, 1986
MIT Press
https://www.amazon.com/Induction-Process…
SJG
Other John H. Holland material I have read, and much of it is challenging
2014
https://www.amazon.com/Signals-Boundarie…
Not read this:
https://www.amazon.com/Complexity-Very-S…
SJG
Evanescence - Bring Me To Life (Live at Las Vegas)
https://www.youtube.com/watch?v=5E-N8RSW…
Complexity : a very short introduction / John H. Holland (2014)
SJG
BBW full backdoor
https://curvynbeautiful.com/collections/…
https://curvynbeautiful.com/collections/…
https://en.wikipedia.org/wiki/Stuart_Kau…
long wanted to read this guy
video
https://www.closertotruth.com/interviews…
https://www.sciencedirect.com/science/ar…
The origins of order : self-organization and selection in evolution / Stuart A. Kauffman. (1993), 700 pages. First of many books.
Complexity : a very short introduction / John H. Holland (2014, location warning)
SJG
full backdoor
https://ohlalacheri.com/plus-size-amber-…
open cage bra
https://www.etsy.com/listing/1066131123/…
Nonlinear Dynamics, Chaos and Fractals
Steeb, W.-H,
+
Fractal Horizons
the Future Use of Fractals
Clifford A. Pickover
+
SJG
IBIZA SUMMER MIX 2021 ↠ Ibiza, Maldives, Thailand, Bali, Paradise
https://www.youtube.com/watch?v=6OS54BXp…
Lacey, understands highest of heels
https://tuscl.net/photo.php?id=4626
https://www.spicylingerie.com/bc-vip1002…
https://www.spicylingerie.com/ey-w6712x.…
https://www.spicylingerie.com/bc-vip1003…
https://pleasershoes.com/products/beyond…
https://pleasershoes.com/collections/ple…
https://www.pleasershoes.com/products/lo…
https://www.pleasershoes.com/products/ad…
https://www.pleasershoes.com/products/de…
https://www.etsy.com/uk/listing/85431392…
Roissy
https://tuscl.net/photo.php?id=8901
https://tuscl.net/photo.php?id=8902
OMS Martinism
https://www.youtube.com/watch?v=j46T-7ha…
Operations Research
Frederick S Hillier and Gerald J. Lieberman
For example
https://www.amazon.com/Introduction-Oper…
over 1000 pages!
Introduction to operations research / Frederick S. Hillier, Gerald J. Lieberman
I will get this and read it and I largely agree with you. Thanks
SJG
high heels bondage
https://tuscl.net/photo.php?id=8935
https://en.wikipedia.org/wiki/Operations…
TensorFlow for dummies / Matthew Scarpino. (2018)
I best find a smaller book than that 1000+ page one.
SJG
Operations research : a practical introduction / Michael W. Carter, Camille C. Price. (CRC Press 2001) 394 pages
++
SJG
backdoor harness
https://supernaturallingerie.com/product…
"Lingerie For The Modern, Magical Woman"
SJG
A Practical Introduction
Michael W. Carter and Camille C. Price
CRC Press (2000)
INFORMS
Institute for Operations Research and the Management Sciences
https://www.informs.org/
Alan Turing, unsolvable or undecidable problems
P, computational time required proportional to a polynomial
NP, proportional to exponential
NP-complete
NP-hard
2^n is worse than polynomial, and n! is even worse, n^n is the very worst!
IMSL C Numerical Libraries
https://www.imsl.com/products/imsl-c-lib…
AMPL, a modeling language for mathematical programming, developed by AT&T Bell Labs
AMPL book
https://ampl.com/resources/the-ampl-book…
RASON
https://www.solver.com/rason?utm_source=…
SIMPLEX METHOD, slack variables and surplus variables
LAMPS Linear and Mathematica Programming System
SAS
https://www.sas.com/en_us/curiosity.html…
PROJECT MANAGEMENT: Critical Path Method (CPM). Program Evaluation and Review Technique (PERT)
Lagrangian Relaxation
Multi-Variable Seach: Gradient Method, Newton's Method, Hessian Matrix
Markov Processes, stochastic process
Queuing Models, A. K. Erlang
GASP, General Activity Simulation Program
SIMSCRIPT, from Rand Corporation
GPSS, General Purpose Simulation System
SLAM
MODSIM
Decision Analysis: Maximin, Laplace Principle, Hurwicz Principle
Heuristic Techniques: Simulated Annealing, Parallel Annealing, Genetic Algorithms, Neural Networks
SJG
20 pages
http://stats-www.open.ac.uk/TechnicalRep…
https://www.real-statistics.com/multivar…
https://stats.stackexchange.com/question…
https://en.wikipedia.org/wiki/Principal_…
A user's guide to principal components / J. Edward Jackson. (1991)
Induction
Processes of Inference, Learning, and Discovery
John H. Holland etal (1986)
SJG
collar
https://tuscl.net/photo.php?id=9342
The earlier recommended book, and most of the others I found, were 1000 pages.
Now, Principal Component Analysis. R-language has an excellent expansion module to do this. I would like to write my own for C++ and Ruby. Something I did years ago could have been improved with this.
A user's guide to principal components / J. Edward Jackson. (1991, 569 pages)
*
Wiley series in probability and mathematical statistics., 75 readily available listings
Numerical methods for stochastic processes / Nicolas Bouleau and Dominique Lepingle (1994)
*-
Markov decision processes : discrete stochastic dynamic programming / Martin L. Puterman. (1994)
*
Probability, random variables, and random signal principles / Peyton Z. Peebles, Jr. (1987 2ne edition)
Communication systems : an introduction to signals and noise in electrical communication / A. Bruce Carlson (1986 3rd ed)
- problem
Communication systems : an introduction to signals and noise in electrical communication / A. Bruce Carlson. (1985 2nd ed)
*
Linear systems in communication and control / [by] Dean K. Frederick and A. Bruce Carlson. (1971)
*
Circuits : engineering concepts and analysis of linear electric circuits / A. Bruce Carlson. (2000)
*
McGraw-Hill series in electrical engineering.
Voice and speech processing / Thomas W. Parsons (1986)
*
Signals and systems in electrical engineering [by] William A. Lynch [and] John G. Truxal (1962)
*
and then all the newer books following
like
Signals and systems / Simon Haykin, Barry Van Veen. (1998)
*
and also book about MATLAB
Signals and systems : principles and applications / Shaila Dinkar Apte (2016, newest on paper)
*
SJG
I like what this Asian girls is wearing. This bondage harness design is becoming more and more common. Credit to LDK82
https://www.redgifs.com/watch/darlingins…
Title Complexity : a very short introduction / John H. Holland
* -
SJG
https://tuscl.net/photo.php?id=425
*
Introduction to Dynamical Systems
Brin, Michael
Introduction to dynamical systems / Michael Brin, Garrett Stuck (2002)
*
SJG
Consider this:
Practical data science with R / Nina Zumel and John Mount ; foreword by Jeremy Howard and Rachel Thomas.
-!
Well, lots and lots of books, but which gives what I want is hard to say. But I need to become well versed. So it is worth the time.
An Introduction to Statistical Learning
With Applications in R
+
Advanced R Statistical Programming and Data Models
Analysis, Machine Learning, and Visualization
Wiley, Matt,
+
R for Dummies
De Vries, Andrie,
+
R for Data Analysis
in Easy Steps
McGrath, Mike,
+
SJG
Dio - Heaven And Hell Live In London 2005
https://www.youtube.com/watch?v=_G6NtIVZ…
Nonlinear control and filtering for stochastic networked systems / Lifeng Ma, Zidong Wang, Yuming Bo (2019)
Multi-agent systems : platoon control and non-fragile quantized consensus / Xiang-Gui Guo, Jian-Liang Wang, Fang Liao and Rodney Swee Huat Teo (2020 CRC Press)
Apache commons FFT
https://commons.apache.org/proper/common…
math3
https://commons.apache.org/proper/common…
java docs
https://commons.apache.org/proper/common…
Commons Math: The Apache Commons Mathematics Library
https://commons.apache.org/proper/common…
Apache Commons
https://commons.apache.org/
so much to try and assimilate
SJG
I think this is AMORC France, its Martinist Order. Antoine Faivre is a highly regarded academic esotericist. This is in French.
https://www.youtube.com/watch?v=as8PwDa_…
Martinism 4/5 OMS
https://www.youtube.com/watch?v=ZaZ1Uqvd…
(4 February 1921 – 6 September 2017)
https://en.wikipedia.org/wiki/Lotfi_A._Z…
SJG
Mark C. Chu-Carroll
https://www.amazon.com/Good-Math-Computa…
+
SJG
Bill Evans '64 - '75
https://www.youtube.com/watch?v=uco5FNbj…
Advanced R (Chapman & Hall/CRC The R Series) 1st Edition
by Hadley Wickham
https://www.amazon.com/Advanced-Chapman-…
R for data science : import, tidy, transform, visualize, and model data / Hadley Wickham and Garrett Grolemund.
Imprint Sebastopol, CA : O'Reilly Media, 2016.
+
and
R Packages
+
SJG
*
^^^ widely referenced
also this new book:
Linear algebra and its applications / David C. Lay, University of Maryland, College Park, with Steven R. Lay, Lee University and Judi J. McDonald, Washington State (2016)
*
Linear algebra and its applications / Gilbert Strang. (1976, keeping the page count down)
SJG
Grace Potter and Joe Satriani cover Cortez the Killer
https://www.youtube.com/watch?v=paeNnR33…
https://tuscl.net/photo.php?id=8726
Personally I am fan of compiled langauges, like especially C++.
About the only time I see that one wants to use an interpretive langauge would be:
1. JavaScript for the users browser
2. For when you want the user to be able to change some of the code
3. For when some of the code is generated at run time
Otherwise you want to stick compiled langauges.
Now, the key feature about R, Python, and Ruby is that you can by using Dynamic Linking add your own C++ code to the interpreter, you can expand the language yourself without having to fork the interpreter code.
Of the three I am more pleased with the newest, Ruby. But I have responsibilities which require me to be abreast of all of them.
Welcome to TUSCL!
SJG
Chaka Khan - Melody Still Lingers On (Live, 1981)
https://www.youtube.com/watch?v=XyzrlndL…
I feel that much of the literature about Functional Programming is very disingenuous.
SJG
*-
Linear algebra and its applications / Gilbert Strang (1976 first edition) widely referenced. I lots of later editions, but they are bigger and bigger. I got this early version because it is shorter. Looks good, a subject I have always been attracted to and have substantial experience with. I will have to follow up with other books though.
SJG
Silverman, Richard A.
many books, some by this Dover reprints company. Such books are usually good.
Essential calculus with applications / Richard A. Silverman
Silverman, Richard A
Dover 1989
Calculus and analytic geometry
Stein, Sherman K. (1992)
Here at UC Berkeley people can major in mathematics
https://math.berkeley.edu/programs/under…
It is in the College of Letters and Science
https://math.berkeley.edu/programs/under…
The Department of Mathematics offers an undergraduate major in Mathematics leading to the Bachelor of Arts (BA) degree. The program provides an excellent preparation for advanced degrees in math, physical sciences, economics, and industrial engineering as well as graduate study in business, education, law, and medicine. The program also prepares students for post-baccalaureate positions in business, technology, industry, teaching, government, and finance.
SJG
I hope to write a lot about this, but for now I want to start recording the references. These references are of great interest to me. I like the old text books. And the math books are always good, no matter how old.
ABSTRACT LINEAR ALGEBRA
F. R. Gantmacher, "Theory of Matrices" Chelsea, New York, 1959
The theory of matrices / by F.R. Gantmacher ; [translation by K.A. Hirsch] ( 2 volumes)
P. R. Halmos, "Finite-Dimensional Vector Spaces" Van Norstrand_Reinhold, Princeton, 1958
Finite-dimensional vector spaces, Paul Richard Halmos
*
K. Hoffman and R. Kunze, "Linear Algebra" 1971
Linear algebra, by Kenneth Hoffman and Ray Kunze.
T. Muir, "Determinants" Dover, 1960, 4 volumes, originally 1923
https://www.amazon.com/Treatise-Theory-D…
The theory of determinants in the historical order of development / by Sir Thomas Muir (yes, 4 volumes, from 1923)
SJG
by Gershenfeld, Neil A (1999)
https://www.amazon.com/Nature-Mathematic…
The nature of mathematical modeling / Neil Gershenfeld
*-
Ordinary Differential Equations (Dover 1985)
An Elementary Textbook for Students of Mathematics, Engineering, and the Sciences
Tenenbaum, Morris
Dynamical systems : differential equations, maps, and chaotic behaviour / D.K. Arrowsmith and C.M. Place (1992)
*
Elementary differential equations with boundary value problems / Robert H. Martin Jr. (1984)
+
Ordinary differential equations / Robert H. Martin, Jr. (1983)
+
Gilbert Strang, Linear Algebra, additional references
APPLIED LINEAR ALGEBRA
A. Ben-Israel and T.N.E. Greville, "Generalized Inverses: Theory and Applications, Wiley (1974)
Generalized inverses: theory and applications / [by] Adi Ben-Israel [and] Thomas N. E. Greville (1974)
*
SJG
Nina Hartley
http://www.nina.com/ninahartley.php
Our Big-Block crate engines have evolved to become more innovative, more powerful, and bigger than they’ve ever been. The new Chevrolet Performance ZZ632/1000 DELUXE Big-Block Crate Engine is no exception. It's our most powerful crate engine ever, with the modern convenience of EFI technology, providing more than 1,000 horsepower on 93-octane pump gas. (8 quart oil pan)
https://www.chevrolet.com/performance-pa…
APPLIED LINEAR ALGEBRA
R. Bellman, "Introduction to Matrix Analysis" McGraw-Hill (1974)
many many books about matrix math and control theory and even adaptive controls
Introduction to matrix analysis / Richard Ernest Bellman. (1960)
*
and then of course Luenberger, D. G.
A number of books.
Introduction to dynamic systems : theory, models, and applications / David G. Luenberger (1979)
*
SJG
I will be reading this soon:
https://www.amazon.com/Pandemia-Coronavi…
Karlheinz Stockhausen: Telemusik (1966)
https://www.amazon.com/Pandemia-Coronavi…
more references:
APPLIED LINEAR ALGEBRA
B. Noble, "Applied Linear Algebra" 1969
NUMERICAL LINEAR ALGEBRA
G. Forsythe and C. Moler, "Computer Solution of Linear Algebraic Systems" 1967
C. L. Lawson and R. J. Hanson, "Solving Least Squares Problems" 1974
G. W. Stewart, "Introduction to Matrix Computations", 1973
R. S. Varga, "Matrix Iterative Analysis", 1962
J. M. Wilkinson, "Rounding Errors in Algebraic Processes", 1963
J. M. Wilkinson, "The Algebraic Eigenvalue Problem", 1965
J. M. Wikinson and C. Reinsch, eds, "Handbook for Automatic Computation II, Linear Algebra", Springer, 1971
D. M. Young, "Iterative Solution of Large Linear Systems", 1971
Gilbert Strang
Linear Algebra and Its Applications
1976, 1st edition
Strang was at MIT
Before forget, let me say that Strang does talk some about Regression Analysis, Factor Analysis, and Principle Component Analysis
So he starts out explaining that primarily linear algebra is about simultaneous equations and Gaussian elimination. The second idea will be determinants and Cramer's rule.
He will show Gaussian Elimination and talk about zero pivots and when you have a singular matrix. It will get into LU factorization, which results from Gaussian Elimination. And then you use back substitution.
Tends to be n^2 operations for Gaussian Elimination.
So he talks about Matrix Multiplication.
So you will be doing Gaussian Elimination, and you will be logging the results in an Elementary Matrix, E.
So you will premultiply Ax with E, on both sides, and matrix multiplication is associative.
So you get this upper triangular matrix, and these various E matrices which log what was done to get it, cause you will want to back substitute for your solution.
Usually you will want to do row substitution in order to get bigger pivots, to avoid zero, but also to minimize round off errors. I think it is actually biggest ABS pivot.
And so a P matrix to log this is introduced, Permutation Matrix. You also premultiply both sides by this.
So you are finding the inverse of the original A matrix. ( the other way of doing this, Determinant and Adujunct Matrices, is extremely slow )
So you use the Gauss-Jordan method:
https://en.wikipedia.org/wiki/Gaussian_e…
And then he talks about Band Matrices, which are matrices where the only non-zero elements are close to the diagonal. I guess this is a particular form of the Sparse Matrix
Good links on this:
Sparse Matrix
https://en.wikipedia.org/wiki/Sparse_mat…
Band Matrix
https://en.wikipedia.org/wiki/Band_matri…
He looks at a differential equation with a two point boundary condition. A geometrical spacer, h, is introduced. This makes the problem discrete, and how small h is determines the number of equations and the number of unknowns, and of course this results in a band matrix.
So he goes into a more formal theory of simultaneous linear equations, and gets into Vector Spaces and Subspaces, and he goes into graphic representations.
And so we are talking about the row space of A, the nullspace of A, the column space of A, and the left nullspace of A.
Talks about Orthogonality of Vectors and Subspaces.
Fundamental Theorem of Linear Algebra, Part 1 and Part 2.
So, talks about Orthogonal Projections and Least Squares, and starts off talking about Inner Products and Transposes, and the Schwarz Inequality
Projections onto Subspaces and Least Squares
Least Squares solution satisfies "normal equations".
Projection Matrices, P
Least Squares Fitting of Data
Orthogonal Bases, Orthogonal Martices, And Gram-Schmidt Orthogonalization
Hilbert Space
Fourier Series
Legendre Polynomials
Pseudoinverse and the Singular Value Decomposition
Weighted Least Squares
now there is a big change in the book as he shifts to the discussion of Determinants
pg 146:
"The determinant provides and explicit "formula," a concise and definite expression in closed form, for quantities such as A^-1"
gives test for invertibility
gives volume of parallelepiped
Jacobian Determinant
https://en.wikipedia.org/wiki/Jacobian_m…
finding determinants needs n! computations!!!
Cramer's Rule
Expansion in cofactors, and finding inverse from adjugate matrix
Then book makes big shift to Eigenvalues and Eigenvectors
SJG
A Brief History of Quantum Mechanics - with Sean Carroll
https://www.youtube.com/watch?v=5hVmeOCJ…
Karlheinz Stockhausen: Telemusik (1966)
https://www.youtube.com/watch?v=vdIe2Cro…
So starting with Ax = b
But now we will be looking for values that make A singular (Det = 0)
We will be subtracting an identity matrix multiplied by Lambda from it. (We need to tell founder that we need comprehensive mathematical notation)
So we will want to find values of Lambda such that Det(A - Lambda * I) =0
This is not that easy to program because you need to be doing Lambda symbolically so that you will get a characteristic polynomial and then can find the roots, real or complex.
These are the eigenvalues, and this is being looked at in the context of simultaneous differential equations.
Often homogenous, so you can add the solutions from the different eigenvalues together.
Sometimes you also want difference equations.
So he talks about Fibonacci Sequences, and about Stability.
Routh–Hurwitz stability criterion
https://en.wikipedia.org/wiki/Routh%E2%8…
Lyapunov stability
https://en.wikipedia.org/wiki/Lyapunov_s…
Markov Processes
and I know that the Eliahu Ibrahim Jury test works best for z-transform digital stuff
https://en.wikipedia.org/wiki/Eliahu_I._…
so to program this type of stuff is quite involved, especially when matrix elements can be polynomial in a complex variable, and even rational polynomial functions, so you need long polynomial division and partial fraction expansion, and the when the rational polynomial coefficients are algebraic combinations of system parameters which you want to be able to alter. Good time to supplement your project with an interpretive language like R, Python, or Ruby on the top, for the user.
Hermeitian Matrices
pg 215, Regression Analysis, Factor Analysis, and Principal Component Analysis
Jordan Form
Positive Definite Matrices, Minima, Maxima, and Saddle Points
Iterative Methods for Ax=b
Linear Programming and Game Theory, Simplex Method, Linear Inequalities.
This has been a complex book, covers lots of stuff. But people who really understand this subject matter will be able to read books like this just like they were the morning newspaper because they already understand the subject matter and they already know all the standard examples.
And when it comes to math I have always found that if you have programmed it, then you do know it well, because you have had to account for all the exceptional cases and have had to come up with a comprehensive test suite.
In the organization I am working to build, people will be supported in building a broad base of understanding which goes this deep. The bulk of the population has turned into Homer Simpsons, and this need not be so.
SJG
Mr. Rob Arthur on keyboards
https://www.youtube.com/watch?v=K5PgG4ak…
Nord
https://www.nordkeyboards.com/
This is an old 1960 edition of a text which was still being updated more than 25 years later.
https://www.amazon.com/Feedback-Synthesi…
I love the old books because in reading them and comparing them to the new books you can understand how the thinking has developed. You can put ideas into context, and you can understand better the new ideas too. This old book probably tells you how you can purchase a Spirule.
https://www.nzeldes.com/HOC/Spirule.htm
For root locus diagrams.
Here is a very new book:
Control Systems Engineering 8th Edition
by Norman S. Nise, 2020
https://www.nzeldes.com/HOC/Spirule.htm (2015)
SJG
Ansys
https://www.ansys.com/products/electroni…
https://en.wikipedia.org/wiki/Ansys
Ansys is an American company based in Canonsburg, Pennsylvania. It develops and markets CAE/multiphysics engineering simulation software for product design, testing and operation and offers its products and services to customers worldwide.
Ansys was founded in 1970 by John Swanson, who sold his interest in the company to venture capitalists in 1993. Ansys went public on NASDAQ in 1996. In the 2000s, the company acquired numerous other engineering design companies, obtaining additional technology for fluid dynamics, electronics design, and physics analysis. Ansys became a component of the NASDAQ-100 index on December 23, 2019.
https://en.wikipedia.org/wiki/John_A._Sw…
John A. Swanson is an American engineer, entrepreneur, and philanthropist. Swanson is the founder of ANSYS, Inc., a John Fritz Medal winner, and a member of the National Academy of Engineering. He is internationally regarded as an authority and pioneer in the application of finite-element methods to engineering.
https://en.wikipedia.org/wiki/Finite_ele…
D-Space ( I think Germany )
https://www.dspace.com/en/inc/home/produ…
now open source!
https://en.wikipedia.org/wiki/DSpace
Lyrasis is a non-profit which owns it.
https://en.wikipedia.org/wiki/Lyrasis
https://www.lyrasis.org/Pages/Main.aspx
LYRASIS
1438 West Peachtree Street, NW
Suite 150
Atlanta, GA 30309
and then GNU Octave:
https://www.gnu.org/software/octave/inde…
https://wiki.octave.org/Using_Octave
and Octave Forge
https://octave.sourceforge.io/
books of interest:
Autodesk Inventor: Finite-Element-Methode (FEM). with Thomas Gruber (2020)
Interval Finite Element Method with MATLAB [electronic resource] / Nayak, Sukanta (2018)
Introduction to Finite Element Analysis and Design, 2nd Edition [electronic resource] / Kim, Nam (2018)
SOLIDWORKS: Simulation for Finite Element Analysis. with Tony Abbey (2017)
Magnetic Materials and 3D Finite Element Modeling [electronic resource] / Bastos, João (2017 CRC Press)
Finite elements for electrical engineers / Peter P. Silvester, Ronald L. Ferrari (1996)
Finite elements for electrical engineers / Peter P. Silvester, Ronald L. Ferrari.
*-
Practical Transformer Handbook [electronic resource] / Gottlieb, Irving (1998)
The electrical engineering handbook / editor-in-chief, Richard C. Dorf (1997 CRC Press, 2700 pages!!)
*********************************
Feedback control system analysis and synthesis [by] John J. D'Azzo [and] Constantine H. Houpis (1960)
This is going to be a pleasure to go thru, like eating cheese cake.
SJG
Psychedelic Jazz Rock Fusion - Gambardella from Barcelona, Spain @ White Noise Sessions 30-10-2017
https://www.youtube.com/watch?v=oJmQihbW…
*
2700 pages!
SJG
The reason I wanted such an old book is real simple. I wanted to see what it talks about and what it fails to talk about. I wanted to see what they feel they must explain, and what they feel they can just assume people understand.
This is one of the classic texts and I am familiar with later editions. They are interesting, but there is also a lot of stuff they do not cover.
Today, if you want to do anything with this, you want to develop computer software. You want programs to do the computations. But you also want embedded software to go into your system. And then you want test bench software to chronicle how your stuff works, and to the the necessary model parameters.
And you want newer much more sophisticated theory, going further than what this book covers.
And then I also want the old references in this book, especially the math books. So let me start with these references.
References:
Trinks, W. "Governors and the Governing of Prime Movers" 1919
Governors and the governing of prime movers / by W. Trinks, 140 illustrations.
+
Bode, H. W. "Network Analysis and Feedback Amplifier Design", 1945
Network analysis and feedback amplifier design, by Hendrik W. Bode (1945)
+
Blackburn, J. F. "Components Handbook" McGraw-Hill, 1948
Components handbook / ed by John F. Blackburn [under the supervision of the Office of Scientific Research and Development, National Defence Research Committee. (1949)
Blackburn, John Francis
+
Wylie, C. R. Jr. "Advanced Engineering Mathematics", McGraw-Hill, 1951
Wylie, Clarence Raymond, 1911- Advanced engineering mathematics (1951) first edition, 640 pages. Later editions of this too, but they have more pages.
+
Corcoran, G. F., and R. M. Kerchner, "Alternating-current Circuits", 3rd edition, John Wiley and Sons, 1951
Alternating-current circuits, by Russell M. Kerchner ... and George F. Corcoran ... (1943, and then also later editions)
Gardner, M. F. and J. L. Barnes "Transients in Linear Systems" John Wiley and Sons, 1942
Transients in linear systems studied by the Laplace transformation [by] Murray F. Gardner ... and John L. Barnes (1942)
*
Trimmer, J. D. "Response of Physical Systems" John Wiley and Sones, 1950
Trimmer, J. D., Response of physical systems., New York, Wiley [1950]
*
"Flow Meters, Their Theory and Application" American Society of Mechanical Engineers, 1937
0
but there is also this: Notes on small flow meters for air : especially orifice meters / by Edgar Buckingham, Physicist, Bureau of Standards. 1921
0
SJG
Burns, R. A., and R. M. Saunders "Analysis of Feedback Control Systems" McGraw-Hill, 1955
Analysis of feedback control systems; servomechanisms and automatic regulators [by] Robert A. Bruns [and] Robert M. Saunders (1955)
Doherty, R. E., and E. G. Keller "Mathematics of Modern Engineering", Wiley, 1936
Mathematics of modern engineering ... by Robert E. Doherty ... and Ernest G. Keller (1936, 2 volumes)
Weber, E. "Linear Transient Analysis" Wiley, 1954
0
Electrical Engineering Staff, Massachusetts Institute of Technology, "Electric Circuits" MIT Press, 1940
0
Truxal, J. G. "Automatic Feedback Control Systems Synthesis", McGraw-Hill, 1955
Automatic feedback control system synthesis
*
Gardner, M. F. and J. L. Barnes "Transients in Linear Systems", Wiley, 1942
Transients in linear systems studied by the Laplace transformation [by] Murray F. Gardner ... and John L. Barnes (1942)
*
Churchill, R. V. "Operational Mathematics" McGraw-Hill 1958
Operational mathematics / [by] Ruel V. Churchill (1971 3rd edition, earlier 1958 edition also available)
*
Thomson, W. T. "Laplace Transformation" Prentice-Hall, 1950
Thomson, William Tyrrell. Laplace transformation : theory and engineering applications. (1950)
*
Guillemin, E. A. "The Mathematics of Circuit Analysis", Wiley, 1949
The mathematics of circuit analysis : extensions to the mathematical training of electrical engineers / Ernst A. Guillemin. (1950)
*
Brown, G. S., and D. P. Campbell, "Principles of Servomechanisms", Wiley, 1948
Principles of servomechanisms; dynamics and synthesis of closed-loop control systems [by] Gordon S. Brown [and] Donald P. Campbell (1948)
0
SJG
James, H. M, N. B. Nichols, and R. S. Phillips, "Theory of Servomechanisms", McGraw-Hill, 1947
Theory of servomechanisms; ed. by Hubert M. James, Nathaniel B. Nichols [and] Ralph S. Phillips [under the supervision of the] Office of Scientific Research and Development, National Defense Research Committee (1947)
Chestnut, H. and R. W. Mayer "Servomechanisms and Regulating System Design", 1959
Servomechanisms and regulating system design / [by] Harold Chestnut and Robert W. Mayer. 1951 - 55
*
SJG
Smith, Otto Joseph Mitchell, 1917-
*
Feedback control systems.
Imprint New York : McGraw-Hill, 1958.
*
Savant, C. J. Jr. "Basic Feedback Control System Design 1958
Savant, C. J
Title Basic feedback control system design
Imprint New York : McGraw-Hill, 1958
New York : McGraw-Hill, 1958
*
Evans, W. R., "Control-system Dynamics", McGraw-Hill, 1954
Evans, Walter R
Title Control-system dynamics
Imprint New York : McGraw-Hill, 1954
*
SJG
Fundamental theory of servomechanisms, by LeRoy A. MacColl. (1968 Dover ed, originally 1945)
*
Nixon, F. E. "Principles of Automatic Controls" Prentice-Hall 1953
Nixon, Floyd E. Principles of automatic controls, New York : Prentice-Hall, 1953
*
SJG
Art Blakey and the Jazz Messengers - Caravan ( Full Album )
https://www.youtube.com/watch?v=DGJRJTOE…
Stewart, John Lawrence
TitleCircuit theory and design (1956)
*
SJG
Circuit design using personal computers / Thomas R. Cuthbert, Jr.
*
First of his two books. Title sounds stupid, but book is very good.
SJG
*
A number of refs of this sort, from about the same time interval.
Not many other book references. I skipped over journal article refs because they are harder to get.
Now I want to say something overall about what the book is saying:
In 1960, I think this book was legit. But many were using the book largely unchanged, in school, 25 years later.
Talks about Electric Circuits, Mechanical Translation, Mechanical Rotation, Thermal Systems, Hydraulics, and as always the Servo.
Talks about differential equations and the standard types of inputs and responses sought.
Laplace transform, and Heavyside's Partial Fraction Expansion.
Block diagrams,
Root Locus and Spirules.
How to get roots of polynomials
Frequency Response and all the sorts of plots.
Nyquist Stability and Routh-Hurwitz test, and the Nichols Chart
Cascade and Feedback Comp. But not the Feedforward or the type of capacitor comp used today in OP-AMP circuits.
Optimum Response ? Talking about steady state error, and solution time, but no rigorous approach to this,
Non-linearities, this along with dead spots and backlash is what makes this all fall apart.
Analog Computers, and using things like anti-parallel tube diodes, no doubt with separate filament windings, to simulate dead spots.
Does not yet talk about the Air Force Fortran program TOTAL.
Does not even tough upon modern or stochastic controls, or Fuzzy or Neural Controls or anything like that.
SJG
Linear Control System Analysis and Design: Fifth Edition, Revised and Expanded (Automation and Control Engineering) 5th Edition
by Constantine H. Houpis (Author), Stuart N. Sheldon (Author), John J. D'Azzo (Author)
THis is from CRC Press:
Linear control system analysis and design with MATLAB / Constantine H. Houpis, Stuart N. Sheldon
Boca Raton, FL : CRC Press, c2014
0
This was 1988
Linear control system analysis and design : conventional and modern / John J. D'Azzo, Constantine H. Houpis.
New York : McGraw-Hill, [1988]
*
Need to see how the ideas have developed over time.
SJG
Then there are always high order poles in the response of systems, and if you use enough loop gain, these come back onto the other side of the j-omega axis and cause instability.
What you can do depends on what computer tools you have before you. You need much more than a programmable scientific calculator. You need what today would be Matlab, Octave, or D-Space, or even more. These guys were slow to move to these. And you need stuff to be open source as Octave and D-space are.
You also though need a more sophisticated theory. You need modern controls, you need adaptive controls, and you need to do like with Matlab and D-space and let the computer control your prototype so you can verify you system model.
And you will usually now want embedded software to go directly into your system.
D'Azzo and Houpis don't get much into Network Theory. You need to be able to solve simultaneous equations and unknows. You need matrices of polynomials. And since you are going to use detreminants and cramers rule, these get turned into rational polynomial functions.
And then Root Locus is a way of finding roots as you vary a parameter, but you need more powerful tools than that.
You need all the ways of visualizing the dynamics, but then you still need more powerful math to get the results you want.
SJG
Clearly they are motivated by the technology of heavy aircraft. Like how to design the powered controls for a B-29, or the servo gun turrets. And they do give translational and rotational mechanical examples. But they don't give aeronautical examples. They don't specifically give mechanical examples where external forces are pressing upon them.
There is in aerospace engineering a standardized way of setting up problems. It is done though in the time domain and with first order differential equations. You have one for each of the 3 translational axes, and then one more for each of the 3 rotational axes. And then since Newton's laws depend on the second derivative, you need another 6. So you get a 12th order matrix.
Maybe the authors feel that that would be beyond the scope of their book or their audience. But I think they should at least mention it and endorse a text.
Then, by even 1960 NASA had committed to Modern Stochastic Controls. Certainly in the later editions they should have spend the necessary time to develop this.
And then even in a phase locked loop today, you have the rudiments of such controls.
I think the D'Azzo and Houpis text in handicapped because its students, while knowing the basic theory, lack access to sufficient computer tools to really do much with the concepts they are being presented with. And then with Modern Controls the lack would be even more dramatic. So I think much more is needed.
I look for the newest version which I can find, probably posthumus, and it is 2014. I notice that it is being presented as being based entirely around MatLab. That would be good, but Matlab is very expensive. Need something which is open source, like Octave or D-Space.
I also think there needs to be more treatment of things like amplifier circuits and of their basic issues, like stability and compensation, and slew rate.
I offer here a trade show demo I saw, or D-Space. Now this was 25 years ago at a trade show. D-Space was not yet open source, and it came from Germany.
They had a simulation of an automobile, an AUDI, and with that VW VR6 engine. They were simulating the throttle valve, the ignition and fuel injection timing, and the load on the crankshaft. Now to make this work you would have to simulate cylinder by cylinder and have a good modelling of the intake and exhaust manifolds too. It was working.
In my view this kind of a simulation would be of most value when you had the features of today's advanced engines, and had variable valve timing. And say you wanted to see the trade offs with different fuel injection approached, like sequential manifold injection versus high pressure direct injection, and how this delimited your range of valve timing options, and then what more range you might get with fly by wire throttle.
This could be very useful. And then imagine if you had this quality of simulation running on board the vehicle and driving the control functions. To be knowledgeable and competent today one would have to be completely fluent in these approaches. And this is not for the Pentagon or NASA, this would be for consumer passenger cars, of the type the US should have been building, instead of leaving it to Germany, Sweden, Japan, and Korea, and China.
SJG
Jennifer Fischer
https://jenniferfisherjewelry.com/collec…
Peter Frampton - Do You Feel Like We Do (Live in Detroit)
https://www.youtube.com/watch?v=yVCWaWFm…
Thank You Mr. Churchill / Peter Frampton
https://www.youtube.com/watch?v=ZUNMmX5w…
Control System Design: An Introduction to State-Space Methods (Dover Books on Electrical Engineering) Illustrated Edition
by Bernard Friedland
https://www.amazon.com/Control-System-De…
This does get into Kalman Filtering which is what NASA used during the Apollo Era. But it does not get into H-Infinity, which as I know is still the cutting edge of adaptive controls. And of course all of this equally well applies to signal processing, as it does to mechanical, aeronautical, chemical, and thermal systems.
availability is still a bit weak for this author.
Advanced control system design / Bernard Friedland (1996, and not what I'd sited above, more rudamentary)
*
Modern control systems / Richard C. Dorf, University of California, Davis, Robert H. Bishop, The University of South Florida. (2017)
0
Modern control systems / Richard C. Dorf, Robert H. Bishop. (2008, 1018 pages!)
*
This Richard C. Dorf has got tons of books spanning decades!
SJG
Jazz Messengers
https://www.youtube.com/watch?v=_3vpiTgG…
Jennifer Fischer
https://jenniferfisherjewelry.com/collec…
D'Azzo and Houpis say nothing about this.
And do you want to do it analog or digital, and conventional controls or modern. It seems kind of emblematic of the Apollo program and its 300 foot high launches.
But I think it also applies to phase locked loops and lots more.
SJG
Oliver Heaviside: The Life, Work, and Times of an Electrical Genius of the Victorian Age
by Paul J. Nahin | Nov 13, 2002
The Forgotten Genius of Oliver Heaviside: A Maverick of Electrical Science
The Forgotten Genius of Oliver Heaviside: A Maverick of Electrical Science
by Basil Mahon
Electromagnetic Theory
by Oliver Heaviside and James Zimmerhoff | Sep 3, 2017
Heaviside's operational calculus as applied to engineering and physics / by Ernst Julius Berg (1929)
*
Heaviside operational calculus : an elementary foundation / [by] Douglas H. Moore. (1971)
*
Oliver Heaviside, sage in solitude : the life, work, and times of an electrical genius of the Victorian age / Paul J. Nahin. (IEEE Press 1988)
*
The forgotten genius of Oliver Heaviside : a maverick of electrical science / by Basil Mahon.
Oliver Heaviside (2017)
*
SJG
This guy was way out there:
https://en.wikipedia.org/wiki/Gabriel_Kr…
Lots of good stuff he did. I know of two books.
He wanted to use Tensor Analysis for AC circuits.
Usually Tensor Analysis is only used for General Relativity. And that is used by AstroPhysicists. I does not have industrial applications. People analyze AC circuits, but without Tensor Analysis. I need to learn more to be able to fully appraise Kron's work.
D'Azzo and Houpis, Principles of Electrical Engineering, 1968. Of interest because it will ground all their Air Force related talk about feedback control systems. Need to understand how things were being discussed, if you expect to be able to appraise how they are being discussed today.
SJG
Weather Report - Live at Montreux (1976) [Remastered]
https://www.youtube.com/watch?v=LfvfXA2S…
Andrei Vladimirescu
University of California, Berkeley
The SPICE Book 1st Edition
by Andrei Vladimirescu (Author)
The Spice book / Andrei Vladimirescu. (1994)
*
SJG
So are you ready for the mathematical modeling of a triode vacuum tube? How about a pentode, which is quite different.
Langmiur-Child model of triode vacuum tube
https://en.wikipedia.org/wiki/Space_char…
Lots of plate characteristics. And for the 6L6 beam power pentode they run all the way from -35 volts on the grid, to +15. Positive grid voltage, to me, seems strange.
Amplidyne
https://en.wikipedia.org/wiki/Amplidyne
Lots of good stuff in the book. The Nichols Plot
https://en.wikipedia.org/wiki/Nichols_pl…
on Mathematica
https://reference.wolfram.com/language/r…
Good book to have on your shelf, because they lay out the equations and set up the examples so well. But to use any of this stuff you really need to be writing computer programs to do it.
Some References:
Houpis, C. H. and Jerzy Lubelfeld, Outline of Pulse Circuits (1966)
Millman, Jacob and Herbert Taub, Pulse, Digital, and Switching Waveforms (1965)
Gray, A. and G. A. Wallace, Principles and Practice of Electrical Engineering 8th ed, 1962
Sad News - Professor Emeritus Augustine Gray
https://chancellor.ucsb.edu/memos/2019-1…
No readily available books by Gray
Langmiur-Child model of triode vacuum tube
https://en.wikipedia.org/wiki/Space_char…
Network Analysis / [by] M. E. Van Valkenburg. (1974, written lots of books and they are good!)
Active filters: lumped, distributed, integrated, digital, and parametric. Lawrence P. Huelsman, editor. With contributions by William J. Kerwin [and others] (1970, also lots of real good books)
Ernest Alexanderson
https://webarchive.nla.gov.au/awa/200402…
SJG
Why 'Sports Illustrated Swimsuit' will only work with brands that 'prove they are creating change for women'
https://www.yahoo.com/lifestyle/sports-i…
Weather Report - Live at Montreux (1976) [Remastered]
https://www.youtube.com/watch?v=LfvfXA2S…
LTspice® is a high performance SPICE simulation software, schematic capture and waveform viewer with enhancements and models for easing the simulation of analog circuits. Included in the download of LTspice are macromodels for a majority of Analog Devices switching regulators, amplifiers, as well as a library of devices for general circuit simulation.
https://www.analog.com/en/design-center/…
andrei vladimirescu, SPICE the thrid decade,
Valid Logic Systems, San Jose, 1990
https://web.engr.oregonstate.edu/~karti/…
Mentor, Valid, and Cadence
https://ieeexplore.ieee.org/author/37283…
SJG
The Gnostic Origins of Christianity, featuring Tim Freke and Peter Gandy
https://www.youtube.com/watch?v=94tvaGrB…
https://ieeexplore.ieee.org/author/37283…
^^^^ recent papers
SJG
Linear control system analysis and design : conventional and modern / John J. D'Azzo, Constantine H. Houpis (1988)
SJG
Steely Dan
https://www.youtube.com/watch?v=ZBtHA6PO…
So this is newer than the last edition I had ever seen. But it is similar. A very big book.
It has all the old stuff going back to 1960.
But it also has stuff about Time Domain Modern Controls. I would still say that this is only scratching the surface. No adaptive controls, and no H-Infinity controls or anything like that, and certainly no fuzzy or neural network controls. THough I suspect that some don't see that as stuff to be taken seriously. I would like to read the differing views though.
Last chapter is on z-transform, as opposed to Laplace transform, for digital. But I would still say that this is just scratching the surface.
And of course I will be wanting to record lots of references.
SJG
Mile Davis
https://www.youtube.com/watch?v=-8TdZFVj…
This 3rd edition has most of the material which was in the earlier two, but with the new material added, it exceeds 900 pages.
Now they do have a much newer book, but I suspect that that was not written by the original authors. The newest one is written around the Matrix Math program, MATLAB.
I will get through used book channels a copy to keep of this 3rd edition.
So I look mostly at the new material, so I am at about the midway point in the book.
They introduce the idea of Control-Ratio Modelling, which is mostly about designing your stead state error coefficients. And then to get zero error you need to be integrating one more time for each level of error reduciton. ( step, ramp, parabola).
They site the Guillemin-Truxal method.
Truxal, J. G. Automatic Feedback Control System Synthesis, McGraw Hill 1955.
And of course this is still frequency domain, s-plane.
And they are concerned about steady state errors relative to disturbances, as well as the reference input.
So in the next chapter they introduce State-Variable Feedback, Closed Loop Pole-Zero Assignment.
And this is time domain, using matrix notation.
There will be the A, B, C, and D martices used throughout, and talk about states being observable, and being controllable.
And this is still totally deterministic.
Showing phase diagrams and discussing them.
And again, error coefficients, and relative to the reference input and to disturbance inputs.
And zero error requires an extra level of integration.
Now as this gets to plant poles and zeros, of course it is again frequency domain.
some references:
Schultz, D. G. and J. L. Melsa: State Functions and Linear Control Systems, McGraw Hill, 1967
Anderson, B. D. O. and J. B. Moore: Linear Optimal Control, 1971
Friedland, B. Control System Design, 1986 (he is at Technion in Israel)
Chen, C. T. Introduction to Linear System Theory, 1970
Barnett, S. Polynomial and Linear Control Systems, 1983 **
Volowich, W. A. Linear Multivariable Systems, 1974
Owens, D. H. Feedback and Multivariable Systems, 1978
SJG
Mile Davis Big Fun
https://www.youtube.com/watch?v=-UT3qeqz…
Also I know that when you want to get zero steady state error and start adding open loop integrations, 1/s terms, then you are raising the order of your system. It is from this that when it is close loop, that instabilities can come from. The poles move off of the origin, and there usually are higher frequency left side poles which come into play.
And then often your integrations are not perfect integrations, they are low freq pole zero pairs, lag compensations.
So this is complicated, not often working as it does on paper.
You need simulation tools too, not just theoretical design tools.
Modern Controls evolved out of Classical Controls, and it happened in stages. This is one of the first, but it is far from the final word on the matter.
SJG
Introduction to Algorithms
3rd ed.
Thomas Cormen is Professor of Computer Science at Dartmouth College. Charles Leiserson is Professor of Computer Science and Engineering at MIT. Ronald L. Rivest is Andrew and Erna Viterbi Professor of Electrical Engineering and Computer Science at MIT. Clifford Stein is Professor of Industrial Engineering and Operations Research at Columbia University.
https://www.amazon.com/Introduction-Algo…
https://www.amazon.com/Introduction-Algo…
1250 pages
So the high point of classical (frequency domain) controls was this control ratios or error coefficients approach. So I am going to read the seminal text, though I really do already understand it.
Truxal, J. G. Automatic Feedback Control System Synthesis, McGraw Hill 1955.
Truxal, John G, Automatic feedback control system synthesis, (1955), almost 700 pages, and Truxal has other books and others that he has written forwards to.
Now Modern Controls (time domain) developed gradually, and the first move to that is this was this closed-loop pole-zero assignment, state-variable feedback.
But as you shall see, you often don't have direct access to state variables, so you have to use an observer, and that merges with you compensator. And then as this is formulated, Poles and Zeros, it is still bound to frequency domain, S-plane, Laplace Transform.
SJG
70s Electric Miles Davis Mix (Jazz, Jazz Funk, Jazz Rock, Fusion..)
https://www.youtube.com/watch?v=EBTQzsxf…
Miles Davis The Dark Side Of Bitches Brew (unpublished tracks)
https://www.youtube.com/watch?v=EBTQzsxf…
Linear Control Systems Analysis and Design
Conventional and Modern
Third Edition
John D'Azzo and Constantine Houpis
1988
Development of Digital Aircraft Controls
SAS - Stability Augmentation System
CAS - Command Augmentation System
FBW - Fly By Wire
DFCS - Digital Flight Control System
Laplace Transform and 1932 Nyquist paper on steady-state frequency-response techniques for feedback amplifier design.
Work by Black, H. S. 1934
Bode, H. W. 1945
Hall, A. C. 1946
Harris, H. 1946
Nyquist, H. 1932
Talks about writing system equations, usually LTI, Linear Time Invariant
Talks about Lagrange's Equation
Talks about every kind of system, even electromagnetic with capacitive coupling. Talks about hydraulic actuators.
Talks about thermal, modeled as a circuit, capacitor being charged by a voltage source through a resistor. Then they add a second resistor and capacitor to show heat transfer to something more remote. You could add another resistor, a bleeder, to account for heat losses beyond this.
DeRusso, P. M. et al "State Variables for Engineers", Wiley 1965
State variables for engineers [by] Paul M. DeRusso, Rob J. Roy [and] Charles M. Close (1965)
Blackburn J. F. ed "Components Handbook" McGraw-Hill 1948 ( a book of this type this old would be trip to look at )
Wylie, C. R. jr "Advanced Engineering Mathematics" 4th ed, McGraw-Hill 1975
Wylie, Clarence Raymond, 1911- Advanced engineering mathematics, first edition 1951, only 640 pages
Kinariwala, B. et al "Linear Circuits and Computation" 1973
Gantmacher, F. R. "Applications of the Theory of Matrices" 1959
Gantmakher, F. R. (Feliks Ruvimovich) Applications of the theory of matrices / Translated and rev. by J. L. Brenner, with the assistance of D. W. Bushaw and S. Evanusa New York : Interscience Publishers, 1959
Kalman, R. E. "Mathematical Description of Lineal Dynamical Systems" paper , 1963
^^^ a NASA big wig and a leader in the movement to Stochastic Controls, and for filtering and even for phased locked loops
Kalman, R. E. (Rudolf Emil), 1930-
Topics in mathematical system theory [by] R. E. Kalman, P. L. Falb [and] M. A. Arbib
New York : McGraw-Hill, [1969]
https://en.wikipedia.org/wiki/Rudolf_E._…
The Kalman Filter
http://www.cs.unc.edu/~welch/kalman/
SJG
A Kalman filter primer / R.L. Eubank. (2006)
Introduction to random signals and applied Kalman filtering : with MATLAB exercises and solutions / Robert Grover Brown, Patrick Y.C. Hwang. (1997)
An introduction to Kalman filtering with applications / Kenneth S. Miller and Donald M. Leskiw (1987)
Mathematics of Kalman-Bucy filtering / P.A. Ruymgaart, T.T. Soong (1985)
Kalman filtering : theory and application / edited by Harold W. Sorenson. (1985)
Introduction to random signal analysis and Kalman filtering / Robert Grover Brown. (1983) oldest ref I found
SJG
Gardner, M. F. and J. L. Barnes: "Transients in Linear Systems" 1942
Takahashi, Y. et al "Control and Dynamic Systems 1970
D'Azzo and Houpis give their final chapter to Digital or Discrete Time control systems. But they also reference a book I am familiar with and know to be quite good. Actually several books:
Houis and G. B. Lamont: "Digital Control Systems, Theory, Hardware, Software, McGraw-Hill 1985
Frankin, G. F. and J. D. Powell: "Digital Control of Dynamic Systems", 1980 *known to be really good!
Kuo, B. C.: "Discrete-Data Control Systems", 1970 (very old ref for this)
Cadzow, J. A. and H. R. Martens, "Discrete-Time and Computer Control Systems, 1970 (very old ref for this)
Ward, J. R. and R. D. Strum: "State Variable Analysis", 1970
Churchill, R. V.: "Operational Mathematics, 3rd ed, 1972
Thomson, W. T.: "Laplace Transformation", 2nd ed, 1966
Aseltine, J. A.: "Transform Method in Linear System Analysis", 1958
Etkin, B.: "Dynamics of Atmospheric Flight", 1972
Those signal flow graphs and the Mason Gain Rule!
Kuo, B. C.: "Linear Networks and Systems", 1967
James, H. M., N. B. Nichols, and R. S. Phillips: Theory of Servomechanisms 1947 (Nichols Charts)
Gibson, J. E.: "Nonlinear Automatic Control" 1963
Thaler, G. J. and M. P. Pastel: "Analysis and Design of Nonlinear Feedback Control Systems", 1960
Kuo, F. F.: "Network Analysis and Synthesis" 2nd ed, 1966
Mitra, S. K. "Analysis and Synthesis of Linear Active Networks", Wiley 1969
Blakelock, J. H.: "Automatic Control of Aircraft and Missiles", Wiley 1965
Thompson, P. M. "User's Guide to Program CC, Version 3", Systems Technology Inc, Hawthorne, CA, March 1985
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Anderson, B. D. O. and J. B. Moore: "Linear Optimal Control" 1971
Kailath, T. "Linear Systems" 1980
Friedland, B. "Control System Design" 1986
Chen, C. T. "Introduction to Linear System Theory" 1970
SJG
*** Barnett, S.: "Polynomial and Linear Control Systems", Marcel Dekker, New York, 1983
Wolowitch, W. A.: "Linear Multivariable Systems" Springer-Verlag, 1974
Owens, D. H.: "Feedback and Multivariable Systems" 1978
Cruz, J. B. jr: "Feedback Systems" 1972
Now talking about Liapunov's Second Method. This is where this subject matter gets the closest to "Dynamic System's Theory" or "Chao Theory" and it is fully workable for nonlinearity.
Andrownow, A. A., etal: "Theory of Oscillations", 1966
Thaler, G. J. and M. P. Pastel: "Analysis and Design of Nonlinear Feedback Control Systems", 1962
Sylvester's Criterion for matrix stuff
Minorsky, N.: "Theory of Nonlinear SYstems" 1969
Csaki, F.: "Modern Control Theories", Budapest, 1972
Gibson, J. E.: "Nonlinear Automatic Control", 1963
Parzen, E.: "Modern Probability and Its Applications" 1960
And I also add:
Probability, Random Variables, and Random Signal Principles 4th Edition
by Peyton Peebles (Author)
Now talking about Optimal Control
Oldenbourg, R. C., and H. Sartorius: "The Dynamics of Automatic Controls, 1948 Society of Mechanical Engineers
Butterworth, S. "On the theory of filter amplifiers" 1930
Kirk, D. E.: "Optimal Control Theory" 1970
Athans, M. and P. L. Falb: "Optimal Control" 1966
Chang, S. S. L.: "Synthesis of Optimal Control Systems" 1961
*** Van Valkenburg, M. E. "Introduction to Modern Network Synthesis" 1960
Bryson, A. E. and Y. C. Ho: "Applied Optimal Control" 1975
Now: Optimal Design By Use Of Quadratic Performance Index
SJG
OMS 4of5
https://www.youtube.com/watch?v=ZaZ1Uqvd…
Porter, B. and T. R. Crossley: "Modal Control Theory and Applications", 1972
Sage, A. P. and C. C. White, III: "Optimum Systems Control" 2d ed, 1977
Now: Structural Propterties of Linear Multivariable Control Systems
Kwakernaak, H. and R. Sivan: "Linear Optimal Control Systems" 1972
Reid, J. G.: "Linear Systems Fundamentals: Continuous and Discrete, Classic and Modern" 1983
Rosenbrock, H. H.: "State Space and Multivariable THeory" 1970
And now, "Design of Tracking Systems Using Output Feedback"
A lot of the refs now are papers, which are harder to get, so I am not recording them here.
And now, "Quantitative Feedback Theory (QFT) Technique"
Horowitz, I. M. ( main name in the refs for this )
Okay, and now it gets to the chapter on Digital Control, and I have already recorded the refs for this.
SJG
OMS 2 of 5
https://www.youtube.com/watch?v=j46T-7ha…
So I see some here worth trying on though. x is the variable in question. In the book they put a (dot) over the x to indicate derivative. I will do this with the (apostrophe), as x'
So when you get to the time domain treatment, it is written in matrix form with A, B, C, and D being the matrices. u(t) is the input, y(t) the output, and x(t) are the state variables. And these are column matrices.
x'(t) = Ax(t) + Bu(t)
y(t) = Cx(t) + Du(t)
Now this is a very standard treatment. And it gets to controllability and observability.
It all comes down to the central matix, A.
So the Homogeneous Solution is known as the State Transition Matrix
x' = Ax
So you can look at a scalar case and have an exponential solution.
You might write the exponential out as a power series.
Remember, A is a square matrix
so the 'state transition matrix' or 'fundamental matrix' they indicate with the letter Phi, and this is known as STM (state transition matrix)
Phi(t) = e^[A(t)], where Phi and A are n x n matrices.
Now if we again look at x'= Ax
Then we can consider a case where x and x' are going the same direction, differing only by a scalar proportionality factor Lambda.
So x' = Lambda x
SJG
[Lambda I - A]x = 0 where Lambda is an n x n identity matrix.
And so for this to have a nontrival solution, x is not zero, then [Lambda I - A] must not be full rank, so its determinant must equal zero.
SJG
But as there is this identity matrix multiplied by an unknown variable Lambda in there, you will get an nth order polynomial in Lambda.
This is known as the "characteristic equation".
Q(Lambda) === Det[Lambda I - A] = 0
Q(Lambda) is a polynomial in Lambda
Q(Lambda) = 0
The roots may be distinct, repeated, or complex conjugates.
The entire set of roots with a complex conjugate in there is "self-conjugate".
And Q(Lambda) can be written in factored form.
The roots of the characteristic equation Q are the eigenvalues of A. The product of these eigenvales is equal to the determinant of A, and the sum of the eigenvalues is equal to the sum of the elements on the main diagonal (the trace) of A.
And to do anything with this stuff you have to have a specifically made computer program. Otherwise it just goes no where. In Aerospace Engineering the standard thing is a 12 x 12 matrix. You could never do that having to punch numbers into a scientific calculator.
SJG
OMS 2 of 5
https://www.youtube.com/watch?v=j46T-7ha…
https://en.wikipedia.org/wiki/Cayley%E2%…
"every square matrix over a commutative ring (such as the real or complex numbers or the integers) satisfies its own characteristic equation."
And they also apply the Laplace Transform in this.
SJG
https://en.wikipedia.org/wiki/Quaternion
SJG
another ref:
Wiberg, D. M. "State Space and Linear Systems" Schaum's Outline Series, McGraw-Hill, 1971
SJG
OMS Martinism 2 of 5
https://www.youtube.com/watch?v=j46T-7ha…
TJ Street
https://farm6.staticflickr.com/5488/9620…
But this use of matrices for differential equations is beyond my present understanding. I read the words, but I cannot a test to what they are saying. Such is Modern Controls. I have so much more to say.
SJG
Jefferson Starship - Miracles
https://www.youtube.com/watch?v=iH_55j-O…
So A is the systems matrix, and the homogeneous state equation, input u(t) = 0, is:
x' = Ax
So you can have exponential scalar solutions, and you can write this out as a power series with factorials in the denominators.
And you can with the matrix equation write e^At = exp[At] = a power series in with the term (At) in the numerators that are raised to integer powers.
So this is called the State Transition Matrix, STM, and it is often denoted by Phi(t).
The STM is the solution to the homogeneous state equation.
Now this gets us into the characteristic equation for the matrix A. It comes from the case for a solution where x and x' are going the same direction, but are just of a different magnitude, by a scalar proportionality factor, Lambda.
And so I is an n by n identity matrix. The characteristic equation comes from finding the determinant of [Lambda I - A].
And so there are n + 1 terms in it, and there will be n roots. These are the characteristic values or eigenvalues of the matrix A.
They can be distinct, or repeated, and the complex roots must appear in conjugate pairs. The set of roots containing the complex-conjugate roots is said to be self-conjugate.
(I add, in a computer program it is best to store and process complex-conjugate as such. Doing these specially increases the accuracy. You know that the imaginary parts have to cancel, so you make it work that way.)
So this characteristic equation for the matrix A is denoted as Q(lambda) and it can be factored.
The product of the eigenvalues of a matrix A is equal to its determinant, and the sum of the eigenvalues, is equal to the sum of the elements on the main diagonal (the trace) of A.
Now to evaluate this State Transition Matrix, STM, Phi(t) there are several methods.
One uses the Caley-Hamiton Theorem, and this is proving to be beyond my current comprehension level. I am going to need another source, one which more carefully develops this. And D'Azzo and Houpis do not really develop Caley-Hamilton, and they certainly do not prove it.
You can do it with the Laplace Transform, and this does require finding the eigenvalues and then doing partial fraction expansion, and then this last they are attributing to Oliver Heaviside.
I would say that this is the most common way if you want an analytic solution. Though it still helps to have suitable computer software. You don't want to be re-entering 10 digit floating point values.
Now the Laplace Transform does not work with non-linearities or with a time varying matrix A. So the other way is a computer numerical solution, which really just amounts to integrating, and this does work just fine with non-linearity and time variance. And this is the most common kind of simulation for systems described by differential equations. But there are no analytic design methods which come out of this, just more and more simulation runs. You could do this with some multivariable Newton-Raphson method, and just make the machines do the work, until you get what you want.
https://en.wikipedia.org/wiki/Newton%27s…
But often you will see a herd think effect, simulating things which would depend on far more accuracy than is present in the component models or in the system description. It becomes just a busy box.
******************************
Now, because most of the Conventional Controls stuff and Modern Controls stuff which follows is pretty standardized, I am going to jump way ahead in the book to something which I think was added to this 1988 3rd edition, Liapunov's Second Method.
This is the place where this gets to be like Nonlinear Dynamic Systems Theory, or Chaos Theory.
So Lipunov's Second requires dermination of a scalar function V, called the Liapunov Function.
"
This function must approach an equilibrium point along a trajectory as time increases. A Liapunov function is readily determined for linear time-invariant systems; however, the determination is difficult for nonlinear and for time-variable systems. Despite these limitations, the Liapunov method provides a generalized approach to stability that is needed by the control engineer.
"
Vladimir M. Lipunov, Russian Astrophysicist, born 1952, still living, at Professor of the Moscow State University, Doctor of Physical and Mathematical Sciences
https://en.wikipedia.org/wiki/Vladimir_M…
https://ieeexplore.ieee.org/abstract/doc…
5 page pdf
https://math.okstate.edu/people/binegar/…
https://en.wikipedia.org/wiki/Lyapunov_s…
http://www.open-science-repository.com/l…
SJG
A good movie about Marquis De Sade, using improvised pens to write on rolls in cloth to be smuggled out of prison.
https://www.imdb.com/title/tt0180073/?re…
Joe Bonamassa Official - "I'll Play The Blues For You" - Live At The Greek Theatre
https://www.youtube.com/watch?v=qoX0Olfq…
Midnight Blues (note the 5 string bass)
https://www.youtube.com/watch?v=8z74lr3t…
Norah Jones - Something
https://www.youtube.com/watch?v=KC42CJoB…
doesn't seem to be the same person:
https://www.linkedin.com/in/vladimirlipu…
Differential equations for engineers and scientists / C.G. Lambe and C.J. Tranter. 2018, 372 pages
*
Classical Mathematical Physics
Dynamical Systems and Field Theories
Thirring, Walter E., 1927- Springer
+
Introduction to Dynamical Systems
Brin, Michael (2002)
Introduction to dynamical systems / Michael Brin, Garrett Stuck(Cambridge 2002, 240 pages)
*
SJG
I know the frequency domain and Laplace transform stuff backwards and forwards. And the takes up the first half of the book.
But the second half is Modern Controls, and primarily time domain. It also introduces a number of new concepts, and then Modern Controls has continued to evolve since this book was published.
So I need now to go to other sources.
From this:
Takahashi, Y. et al "Control and Dynamic Systems 1970
D'Azzo and Houpis lift some spacey looking 3d Phase Diagrams, worthy of the Chaos Theory movement.
Control and dynamic systems [by] Yasundo Takahashi, Michael J. Rabins [and] David M. Auslander. (1970, 800 pages!)
*
D and H go onto talk about discrete time systems and the Z-transform. But they also introduce something I have never heard of before, the Tustin transform and they reference a 1947 paper by A. Tustin.
Okay, this is just another name for the Bilinear Transform, and of course I know all about that.
https://en.wikipedia.org/wiki/Bilinear_t…
10 page pdf, MIT
https://ocw.mit.edu/courses/mechanical-e…
another 10 page pdf
http://web.cecs.pdx.edu/~tymerski/ece452…
page 69 of 520 page pdf, The Art of VA Filter Design, by Vadim Zavalishin (this might be an online only book, as I cannot find anything else of it)
https://www.native-instruments.com/filea…
^ this might be audio oriented
Vadim Zavalishin - “The art of VA filter design” – A different kind of digital filter theory ( hour long talk)
https://www.youtube.com/watch?v=zPzCLqkQ…
Interview, almost 2 hours
https://www.adsrsounds.com/useful-articl…
SJG
Wave of Bomb Threats Terrorizing Historically Black Colleges Continues During Black History Month (shows importance of Black Colleges)
https://www.democracynow.org/2022/2/18/s…
Filmmaker Stanley Nelson on Police Brutality, Black History & His First Oscar Nomination for “Attica” (has that surreal phone call between Richard Nixon and Nelson Rockefeller)
https://www.democracynow.org/2022/2/18/s…
*
Optimal control with aerospace applications / James M. Longuski, Jose J. Guzman, John E. Prussing.(2014)
*
Feedback control for computer systems / Philipp K. Janert. (2013)
*
Functional analysis, calculus of variations and optimal control / Francis Clarke (2013)
*
Calculus of variations and optimal control theory : a concise introduction / Daniel Liberzon
*
Control theory and its applications / Vito G. Massari, editor. (2011)
0
Nonlinear model predictive control : theory and algorithms / Lars Grüne and Jürgen Pannek (2011)
*
**** Nonlinear power flow control design : utilizing exergy, entropy, static and dynamic stability, and Lyapunov analysis / Rush D. Robinett III, David G. Wilson (2011)
*
Optimization using personal computers : with applications to electrical networks / Thomas R. Cuthbert, Jr. (1987)
These books have stupid titles. But then not everyone that easily transitioned from FORTRAN and mainframes to PCs.
There is good mathematics in these books and it is broadly applicable today.
SJG
X - Burning House of Love
https://www.youtube.com/watch?v=LInxU2dW…
Circuit design using personal computers / Thomas R. Cuthbert, Jr. (1983)
https://www.abebooks.com/servlet/BookDet…
Don't know that much about buying books used, but I need to learn because I want to collect so many of these.
Title is stupid. But what Cuthbert means is the use of microcomputers and hand held calculators. Cuthbert is using a Commodore PET. He acknowledges the arrival of the IBM PC, giving microcomputers a new legitimacy.
He also uses HP-67 and 97. He talks about HP-41. And about HP-9815. I think this had cost close to $1000, full QWERTY keyboard, but undersized buttons. 1 or 2 line by 80 character LCD display and BASIC.
Cuthbert quotes R. W. Hamming, saying that the best programs for a designer to use, are his own.
Thomas R. Cuthbert, Jr.
Director, Advanced Tehnology
Collins Transmission Systems Division
Rockwell International Corporation
Dallas, Texas
He signs his preface as Plano Texas, December 1982
SJG
Firmly sits on the the throne for this topic.
Matthaei, Young, and Jones (1964) Microwave Filters, Impedance-Matching Networks, and Coupling Structures.
Hamming, R. W. (1973) Numerical Methods for Scientists and Engineers
Ley, B. J. (1970) Computer Aided Analysis and Design for Electrical Engineers
McCalla, T. R. (1967) Introduction to Numerical Methods and FORTRAN Programming
Murdock, B. K. (1979) Handbook of Electronic Design and Analysis Procedures Using Programmable Calculators
Noble, B. (1969) Applied Linear Algebra
Terman, F. E. (1943) Radio Engineers' Handbook
Van Valeknburg, M. E. (1960) Introduction to Modern Network Synthesis ( he had many editons of many books )
Zverev, A. I. (1967) Handbook of Fiter Synthesis
Acton, F. S. (1970) Numerical Methods That Work
Aoki, M. (1971) Introduction to Optimization
Bandler, J. W. (1973) in "Modern Filter Theory and Design" (G.C. Temes and S.K. Mitra eds)
Beale, E. M. L. (1972) in "Numerical Methods for Non-Linear Optimization (F. A. Lootsma, ed.)
Beveridge, G. S. and R. S. Schechter (1970) Optimization: Theory and Practice
Blinchikoff, H. J. and A. I. Zverev (1976) Filtering in the Time and Frequencey Domain
Bode H. W. (1945) Network Analysis and Feedback Amplifier Design
Box, M. J., D. Davies, and W. H. Swann (1969) Non-linear Optimization Techniques
Churchill, R. V. (1960) Complex Variables and Applications
Daniels, R. W. (1974) Approximation Methods for Electronic Filter Design
Dixon, L. C. W. (1971) in Numerical Methods for Nonlinear Optimization (F. A. Lootsma, ed.)
SJG
Ralston, A. (1965) A First Course in Numerical Analysis
Ramo, S., and J. R. Whinnery (1953) Fields and Waves in Modern Radio. I think the Vanduzer author was added for a later edition.
Saal, R. (1979) Handbook of Filer Design
Seshu, S., and N. Balabanian (1959) Linear Network Analysis
Spence R. (1970) Linear Active Networks
FILSYN a general purpose filter synthesis program, 1977
Temes, G. C., and S. K. Mitra (1973) Modern Filter Theory and Design
Taub, F. J. (1964) Interactive Method of Solution of Equations
Turnbull H. W. (1952) Theory of Equations
*******************
Now I am emphasizing books because they are easier to get. But there are still a few other things I need to chronicle here anyway.
Besser, L., and S. Swenson (1977) trade article about FET amp design.
Hewlett-Packard (1968) S-parameters ... App note 95, September 1968
(1972) S-parameter design, app note 154 April
Kotzebue, K. L. (1976) and (1979) papers in IEEE Trans. Microwave Theory. A quasi-linear approach to the design of microwave transistor power amplifiers. And in Cuthbert's text he talks of Kotzebue saying that with common emitter BJT's, the input saturates first.
also an article by K. S. Shanmugan
Simulation of communication systems / Michel C. Jeruchim, Philip Balaban, K. Sam Shanmugan (1992), Shanmugan has earlier books about digital communications
SJG
The Shanmugam book I could not find. Availability today may be limited:Shanmugam, K. Sam
Digital and analog communication systems / K. Sam Shanmugam ( 1979 ) but has other books too.
And then Cuthbert deals a lot with filtering and ladder networks:
Lam, Harry Y. F., 1944-
Analog and digital filters : design and realization / Harry Y-F. Lam
Englewood Cliffs, N.J. : Prentice-Hall, c1979
https://www.amazon.com/Analog-Digital-Fi…
Analog and digital filters : design and realization / Harry Y-F. Lam (1979)
* and available for used purchase
Ralph J. Smithhttps://www.amazon.com/Circuits-Devices-Systems-…
Charles A. Holt
https://www.amazon.com/Electronic-Circui…
Good book. He also has an electromagnetism book
William Hayt, also good
https://www.amazon.com/Engineering-Elect…
Newer one than what Cuthbert references: Ramo, Whinnery, and Van Duzer, this is also very good, 1975
Johnk, Carl T. A. (Carl Theodore Adolf), 1919-
Engineering electromagnetic fields and waves / [by] Carl T. A. Johnk.
Communication systems : an introduction to signals and noise in electrical communication / A. Bruce Carlson ( 1986, but goes back further and up to 2002 )
Frederick, Dean K., 1934-
Title Linear systems in communication and control / Dean K. Frederick and A. Bruce Carlson ( goes back far like 1971 )
Oppenheim, Alan V., 1937-
Signals and systems / Alan V. Oppenheim, Alan S. Willsky with Ian T. Young
and his other book about Digital Filtering
Lyons, Richard G., 1948-
Understanding digital signal processing / Richard G. Lyons.
This is a bit of an overview, lighter on math, kind of book.
Simon Haykin, Active Network Theory, his 5th book. Read through
chapter 4. Has formal matrix theory for going from element lists and
then having matrix descriptions to indicate what connects to what.
Extensive formal theory for this!
So in the Haykin book I am ready to start chapter 5. More 2 port
network properties. It's going to talk about reciprocity. Then there
will be a chapter about scattering parameters.
The book does deal with gyrators, negative impedance converters, and
inverse negative impedance converters. These, along with mutually
coupled inductors are the 4 unusual type of matrix two ports.
Active network theory / [by] S. S. Haykin. (1970)
*
Deals with node and loop equations. But this book is not really using
standard terminology. Haykin is at McMaster Univ.
Then also State Variables approach!
Charles A. Holt book, and M. E. Vanvalkenberg
Active and passive analog filter design : an introduction / Lawrence P. Huelsman. (1993) This guy had written a huge number of books, but Cuthbert does not mention him
SJG
AC/DC - It's A Long Way To The Top (If You Wanna Rock 'N' Roll)
https://www.youtube.com/watch?v=a-MVuqh8…
Thin Lizzy - The Boys Are Back In Town - Live At Rockpalast.avi
https://www.youtube.com/watch?v=Ta3YkTdI…
X - Live at The Teragram, DTLA 12/19/2019
https://www.youtube.com/watch?v=hxjLyppF…
https://www.youtube.com/watch?v=fTGGfvrW…
https://www.youtube.com/watch?v=lGf6YG_O…
https://www.youtube.com/watch?v=Exs-mcKA…
https://www.youtube.com/watch?v=iJ5RaPj7…
He was born 1928
On this business of fitting polynomials to data, it looks simple. You can solve n+1 equations with n+1 unknowns and make a nth order polynomial fit n+1 data points. But the results are useless. You get something that swings wildly, like about 100x the span of the data points.
So how can your really do it? Well it is a complex subject.
Cuthbert cites one Levy, E. C.. And he is working with rational polynomial functions. Both numerator and denominator are polynomials. I hope that somewhere else, in a newer book this is worked out.
But Cuthbert cites:
Levy, E. C. (1959) Complex-Curve Fitting, IRE Trans, Auto. Control May pp.37-43
And then Fano, R. M. did work in 1950 on broadband impedance matching.
This is probably him:
Transmission of information; a statistical theory of communications, Robert Fano, 1961
*
What Cuthbert cites though is just a paper.
Fano extended the work of Bode,
Bode, H. W. 1945 book.
Here:
Fano, R. M. (1950) Theoretical Limitations on the broadband matching of arbitrary impedances. J. Franking Inst, Feb pp 139-145
and I have no idea what the above ^ journal is.
THis is Bode:
Network analysis and feedback amplifier design, by Hendrik W. Bode (1945)
*
SJG
Best of Acid Jazz and Funky Grooves
https://www.youtube.com/watch?v=QK2mtWjt…
This might not have been bipolar. It could have been FET. But for maximum power gain it would have to be common emitter or common source.
He found that the inputs saturated first.
So I am underwhelmed by this work. It just shows that you can't design RF power amps based on small signal modelling. Gee Whiz!
SJG
This develops some great statistical distributions about intestinal distributions.
Also details effects of various inputs on output, highlighting corn, cabbage and dairy.
Quite an old book:
Semiconductor-diode parametric amplifiers / Lawrence A. Blackwell [and] Kenneth L. Kotzebue. (1961)
*
Matthaei, Young, and Jones, known in some quarters as "The Bible" was invoked a couple of times, and then finally pertaining to 'printed circuit edge coupled filters'.
SJG
Numerical Recipes in FORTRAN, 2nd edition.
Numerical Recipes in FORTRAN
by W. H. Press (Author), B. P. Flannery (Author), S. A. Teukolsky (Author), W. T. Vetterling (Author)
There are newer versions of this, for the newer versions of FORTRAN. But what I want o look at now is this list of authors. It seems to be some kind of a corporate body. So are the other books with such titles written by this same team, and how far forward does it go?
SJG
http://numerical.recipes/
SJG
*
This newest version does not list a computer language. All the better.
Allowing for some fund raising, you can read this online.
Now, a bit more about Thomas Remy Cuthbert. His is a book about circuit design algorithms. Only secondarily is it about numerical analysis. But he does talk about an algorithm and software which can solve polynomials up to 20th degree.
I had bought and used a program, it may have been the same one. But why only up to 20th degree I do not know.
Never needed to go beyond that, but today with things more computer based, maybe.
SJG
Hamming, R. W. 1962 Numerical Methods for Engineers and Scientists, 1988 Dover reprint. And the stuff Dover reprints is always good.
Ralston, A. and Rabinowitz P. 1978 First Course in Numerical Analysis.
Sedgewick, R. 1988 Algorithms
Knuth, Donald E.
and talk about Gauss-Jordan Elimination, and also about pivots, additional right hand column matrices, and compact notation, LU decomposition, Spase, S.I.A.M., commerical packages, LINPACK, IMSL, NAGFortran library, Simulated Annealing.
FFT, from midsixtys. J. W. Cooley, J. W. Turkey, and done by power of 2 or by power of 4
And this nitwit:
E. O. Brigham, 1974 he Fast Fourier Transform
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Talk about Square Window, Welch window, Bartlett window, Hann window
Deming W. E. 1943 Statistical Adjustment of Data, DOVER
Runge-Kutta Method
Rice, J. R. 1983 Numerical Methods
Actior, F. S. 1970, 1990 Numberical Methods that Work, Mathematical Association of America
Strang G. and Fix G., 1973, An Analysis of the Finite Element Method
OPpenheim, A. V. and Schafer, R. W. 1989 Discrete-Time Signal Processing
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WOW! Burma Food
https://www.youtube.com/watch?v=djqAKV1H…
Miles Davis and Thelonious Monk
https://www.youtube.com/watch?v=O7zaUceG…
His first book, "Design of Amplifiers and Oscillators by the S-Parameter Method" was published in 1982. He later joined with two colleagues and published "Microwave Circuit Design Using Linear and NonLinear Techniques" in 1990 (1st ed.), 2005 (2nd ed.) and 2021 (3rd ed.).
https://www.amazon.com/Microwave-Circuit…
Microwave circuit design using linear and nonlinear techniques / George D. Vendelin, Anthony M. Pavio, Ulrich L. Rohde.
*
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The designer's guide to SPICE and Spectre / by Kenneth S. Kundert ; [with foreword by Paul Gray]. (1995)
0
He also wrote a chapter in a book about sparse matrix analysis back when he was at UCB.
And I would draw attention to Rhode Schwartz because of the Vendelin book:
https://www.rohde-schwarz.com/us/home_48…
And then there is Stephen A. Maas
Nonlinear microwave circuits / Stephen A. Maas. (1997)
*
Nonlinear microwave and RF circuits / Stephen A. Maas.
0
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Antenna engineering handbook / edited by Richard C. Johnson and Henry Jasik.
https://www.amazon.com/Antenna-Engineeri…
And writing a forward for Ken Kundert:
https://en.wikipedia.org/wiki/Paul_E._Gr…
Physical electronics and circuit models of transistors / Paul E. Gray [and others]. (1964)
This is a different Paul Gray, Paul R. Gray from UCB
https://ccst.us/people/uncategorized/pau…
SJG
https://tuscl.net/photo.php?id=10346
X- Live At The Whisky A Go Go
https://www.youtube.com/watch?v=LInxU2dW…
Have Nots
https://www.youtube.com/watch?v=idXpvk_T…
Signals and systems in electrical engineering [by] William A. Lynch [and] John G. Truxal (1962)
Introductory system analysis: signals and systems in electrical engineering / [by] William A. Lynch [and] John G. Truxal. (1961)
*
Linear systems in communication and control / [by] Dean K. Frederick and A. Bruce Carlson. (1971)
*
Feedback circuit analysis / [by] S. S. Hakim. (1966) wrote many books covering a very broad range
*
SJG
Veruca Salt Live
https://www.youtube.com/watch?v=z7hONwIi…
Active network theory / [by] S. S. Haykin. (1970)
Detection and estimation : applications to radar / edited by Simon S. Haykin. (1976)
and there is more!
SJG
Detection and estimation : applications to radar / edited by Simon S. Haykin. (1976)
Communication systems / Simon Haykin. (1978)
Array processing : applications to radar / edited by Simon Haykin. (1980)
Introduction to adaptive filters / Simon Haykin. (1984)
Adaptive filter theory / Simon Haykin. (1986)
An introduction to analog and digital communications / Simon Haykin. (1989)
Advances in spectrum analysis and array processing / Simon Haykin, editor. (1995) but only vol 2 of the 3 volumes is available
Adaptive filter theory / Simon Haykin (1996 3rd edition)
Signals and systems / Simon Haykin, Barry Van Veen. (1998)
Neural networks : a comprehensive foundation / Simon Haykin (1999) and it goes forward too!
Let me look now to Alan Oppenheimer
but first:
Digital signal processing with kernel methods / José Luis Rojo-Álvarez, Manel Martínez-Ramón, Jordi Muñoz-Marí, Gustau Camps-Valls (2018)
Digital signal processing : a computer based approach / Sanjit K. Mitra (2006)
0
Analysis and synthesis of linear active networks. Sanjit K. Mitra (1969)
Active inductorless filters / Edited by Sanjit K. Mitra. (1971)
Modern filter theory and design. Editors: Gabor C. Temes and Sanjit K. Mitra (1973)
Understanding delta-sigma data converters / Richard Schreier, Gabor C. Temes (2005)
0
SJG
https://en.wikipedia.org/wiki/Eliahu_I._…
Inners and stability of dynamic systems [by] E. I. Jury (1974)
0
Theory and application of the z-transform method / [by] E. I. Jury (1973)
*
Sampled-data control systems / Eliahu I. Jury (1977)
*
R. W. Hamming
Coding and information theory / Richard W. Hamming (1986)
Introduction to applied numerical analysis / [by] Richard W. Hamming (date not known)
Numerical methods for scientists and engineers / R. W. Hamming. (1962)
Calculus and the computer revolution [by] Richard W. Hamming. (1968, only 72 pages)
Computers and society / [by] R. W. Hamming. (1971)
and more follows.
Richard Wesley Hamming (February 11, 1915 – January 7, 1998) was an American mathematician whose work had many implications for computer engineering and telecommunications. His contributions include the Hamming code (which makes use of a Hamming matrix), the Hamming window, Hamming numbers, sphere-packing (or Hamming bound), and the Hamming distance.
Born in Chicago, Hamming attended University of Chicago, University of Nebraska and the University of Illinois at Urbana–Champaign, where he wrote his doctoral thesis in mathematics under the supervision of Waldemar Trjitzinsky (1901–1973). In April 1945 he joined the Manhattan Project at the Los Alamos Laboratory, where he programmed the IBM calculating machines that computed the solution to equations provided by the project's physicists. He left to join the Bell Telephone Laboratories in 1946. Over the next fifteen years he was involved in nearly all of the Laboratories' most prominent achievements. For his work he received the Turing Award in 1968, being its third recipient.
After retiring from the Bell Labs in 1976, Hamming took a position at the Naval Postgraduate School in Monterey, California, where he worked as an adjunct professor and senior lecturer in computer science, and devoted himself to teaching and writing books. He delivered his last lecture in December 1997, just a few weeks before he died from a heart attack on January 7, 1998.
https://en.wikipedia.org/wiki/Richard_Ha…
SJG
https://mathgenealogy.org/id.php?id=4556
Oliver Heaviside
Heaviside operational calculus : an elementary foundation / [by] Douglas H. Moore. (1971)
Lectures on Seiberg-Witten invariants / John Douglas Moore born 1943
0
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https://web.math.ucsb.edu/~moore/selecte…
https://web.math.ucsb.edu/~moore/researc…
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With Applications to Electrical Networks
John Wily and Sons 1987
Thomas R. Cuthbert Jr., his second book, and he is now
Director, Digital Signal Processing
Collins Transmission System Division
Rockwell International Corporation
Dallas Texas
Thomas Remy Cuthbert, born 1928
Now this book, like his prior, has a really stupid title. But never mind the math in this is really good and I have long wanted to read it.
SJG
How Often Do You Use Algebra
https://tuscl.net/discussion.php?id=7896…
Hope You're Feeling Better ~ Santana
https://www.youtube.com/watch?v=P_vJBz2_…
Lots of references, but different from his other book.
SJG
first of all Knuth 1968, Art of Computer Programming. And matrix types, Vandermonde, Combinatorial, Cauchy, Hilbert
and then Nash 1979 Compact Numerical Methods for Computers: Linear Algebra and Function Administration
matrix types: Hilbert, Ding Dong, Moler, Bordered, Diagonal, Wilkinson W+, Ones
Dongarra, J. J., C B. Moler etal (1979) LINPACK User's Guide, SIAM
Smith (1976) and Garbow (1977) document the EISPACK eigensystem
Hopper (1981) Harwell Subroutine Library. United Kingdom Atomic Energy Authority
Compact numerical methods for computers : linear algebra and function minimisation / J.C. Nash. (1990 2nd edition)
*
SJG
Smith, Boyle, Dongarra, Garbow, Ikebe, Kelma etal
Matrix Eigensystem Routines, Springer-Verlag, 1976
Matrix eigensystem routines : EISPACK guide / B. T. Smith [and others] 1976
*
also available is a 1977 extension guide
And Cuthbert's book:
Optimization Using Personal Computers: With Applications to Electrical Networks Hardcover – January 1, 1987
by Thomas R. Cuthbert
https://www.amazon.com/gp/product/B000IB…
SJG
Differential and integral calculus / by R. Courant ; translated by E. J. McShane. (1937 2nd edition)
*
And he has other books too.
I like old books like this because I can see how they likely explained things differently.
SJG
X - Burning House of Love (Live at Farm Aid 1985)
https://www.youtube.com/watch?v=7kbDuaio…
Optimization Using Personal Computers
With Applications to Electrical Networks
John Wily and Sons 1987
Cuthbert p14
He sites:
Acton, F. S. (1970) Numerical Methods That Work
Numerical methods that work / Forman S. Acton. (Mathematical Association of America 1990)
* widely disseminated
Cuthbert quotes Acton:
"
minimum-seeking methods are often used when a modicum of thought would disclose more appropriate techniques. They are the first refuge of the computational scoundrel, and one feels at times that the world would be a better place if they were quietly abandoned. ... The unpleasant fact that the approach can well require 10 to 100 times as much computation as methods more specific to the problem is ignored -- for who can tell what is being done by the computer?
"
I have seen this first hand. Curthbert is writing in 1987. A lot of this correlates to the popularity of personal computers and to the rise of some software vendors who's names I will not speak.
They promote idiocy. And wasting computer cycles is not by itself that important. The problem is that the entire approach to the problem at hand is completely wrong headed. And then the simulation program becomes a child's busy box, a video game. And the well paid people who are running this are just glorified script files. The simulation program serves as a division of labor, as there will be one pit boss who gives the orders, and then minions who carry it out. Very very little smarts is being used, and what results is usually completely appropriate, but they will never understand this.
I am embarrassed to admit that I know how many millions of dollars a company can blow through doing this. And I know there are large sectors of industry which are entirely like this.
I have seen things like this in human behavior all along. But this specific kind of stuff pertaining to computer simulations I first learned of reading discussion way way back about the race for the 64k DRAM chips. The US firms lost and Japan won. One analysis explained that in the US modelling and simulations some wrong assumptions had been made. But 95% of those doing the design and simulations were not even aware that there were such assumptions.
These people, they just know that if they continue being good frat boys, then they will continue to get paid and continue to have social approval. This is about all they are good for. They understand things in terms of buzz words, but they don't have an in depth understanding of how the ideas developed, what really is at issue, or of what the limitations are in the analysis. They don't understand the assumptions behind the buzz words.
SJG
X Burning House of Love
https://www.youtube.com/watch?v=7kbDuaio…
So he gives us a function F in the variables x and y. So he shows a graph of F rising over the x and y plane. There are 4 local maxima and 3 saddle points.
The function he gives us in that that complex, but it seems to be just an example to give us the idea.
So he talks about partial derivates and then he talks about approximating the maxima by a parabola in two variables.
Not sure why you really need to do this here, and he does not go into the math to do this, but he has 33 BASICA programs to do it.
I think if the function F were something for which each point required lengthy simulations, then by using the 2d parabolic approximation you might be able to get a satisfactory result more quickly.
Himmelblau, D. M. (1972) Applied Nonlinear Programming, McGraw Hill
SJG
X Burning House of Love
https://www.youtube.com/watch?v=LInxU2dW…
*
Himmelblau has other books oriented towards numerics for Chemical Engineering.
And Nonlinear Programming is the description of all this preferred by Cuthbert.
Gilbert Strang, Linear Algebra 1976, read just a couple of months ago.
And Cuthbert idenfies himself as being with Collins Radio Company, Texas Instruments, and Rockwell International and he signs his preface as being in Plano Texas.
He acknowledges Karl R. Varan. Our local Varian?
Davidson, W. C. (1959) wrote books about this, but not standard publishing.
In 1847 Cauchy described the method of steepest ascent.
Traub, J. F. (1964) Iterative Method for the Solution of Equations
Iterative methods for the solution of equations / [by] J.F. Traub. (1964)
*
and also note:
Information, uncertainty, complexity / J.F. Traub, G.W. Wasilkowski, H. Woźniakowski (1983)
*
SJG
X- Live At The Whisky A Go Go
https://www.youtube.com/watch?v=LInxU2dW…
Numerical methods for non-linear optimization : Conference sponsored by the Science Research Council, University of Dundee, Scotland, 1971 / Edited by F. A. Lootsma.
* a conference digest
Vlach J. and K. Singhal(1983) Computer Methods for Circuit Analysis and Design
Computer methods for circuit analysis and design / Jiří Vlach, Kishore Singhal (1983)
*
Dixon, L. C. W. (1972) Nonlinear Optimization
0
Practical methods of optimization / R. Fletcher (1980) 2 volumes
*
Selected applications of nonlinear programming / [by] Jerome Bracken and Garth P. McCormick.
Imprint New York : Wiley, [1968]
*
Compact numerical methods for computers : linear algebra and function minimisation / J.C. Nash. (1990 second edition)
*
Methods for solving systems of nonlinear equations / Werner C. Rheinboldt (1998 2nd ed)
*
SJG
X
https://www.youtube.com/watch?v=LInxU2dW…
Forsythe, G. E. (1970) mention of an article about pitfalls in computation, why a math book is not enough
Maron (1982) Numerical Analysis a Practical Approach
Numerical analysis : a practical approach / Melvin J. Maron, Robert J. Lopez (1991 2nd ed)
* widely distributed
Traub (1964) Iterative Methods for the Solution of Equations
widely distributed
Wilkinson (1963) Rounding Errors in Algebraic Processes
*
article
Kelma V. C., and A. J. Laub (1980) about the singular value decomposition...
Noble B. (1969) Applied Linear Algebra
Applied linear algebra / Ben Noble and James W. Daniel. (1988 3rd edition)
*
Murray (1972) Numerical Methods for Unconstrained Optimization
Numerical methods for unconstrained optimization / edited by W. Murray (1972)
* widely disseminated
Nash (1979) Compact Numerical Methods for Computers
Compact numerical methods for computers : linear algebra and function minimisation / J.C. Nash. (1990)
*
Gill, P. E., and Murry and Wright (1981) Practical Optimization
Numerical methods for constrained optimization / edited by P. E. Gill and W. Murray. (1974)
*
Bellman (1960)
Introduction to matrix analysis / Richard Bellman. (SIAM 1997 2nd edition)
*
Jennings (1977) Matrix Computations for Engineers and Scientists
Matrix computation for engineers and scientists / Alan Jennings (1977)
*
Introduction to matrices and linear transformations, by Daniel T. Finkbeiner, II (1966 2nd ed)
* widely disseminated
McCalla, T. R. (1967) Introduction to Numerical Methods and FORTRAN
0
Computational methods in elementary numerical analysis / J. Ll Morris (1983)
* widely disseminated
Solving least squares problems / [by] Charles L. Lawson [and] Richard J. Hanson. (1974)
*
A first course in numerical analysis / Anthony Ralston, Philip Rabinowitz (1978 2nd ed)
*
Nonlinear programming : sequential unconstrained minimization techniques / Anthony V. Fiacco, Garth P. McCormick. (SIAM 1990 2nd ed)
*
Matrix computations / Gene H. Golub, Charles F. Van Loan (2013 4th ed)
*
Advanced calculus / Wilfred Kaplan. (1973 2nd ed, has other books too)
*
Nonlinear and dynamic programming / by G. Hadley. (1964)
* widely disseminated
Foundations of optimization [by] Douglass J. Wilde [and] Charles S. Beightler (1967)
*
The art of computer programming / [by] Donald E. Knuth. (1968 3 volumes)
*
Practical methods of optimization / R. Fletcher. (1987 2 volumes)
*
Himmelblau, D. M. , Applied Nonlinear Programming (1972)
Applied nonlinear programming [by] David M. Himmelblau (1972)
*
also note
Numerical linear algebra with applications : using MATLAB / by William Ford. (2015)
0 now
Foundations of optimization / Osman Güler (2010)
*
SJG
Fitting treatment given the author's surname is pronounced "excrete".
So I didn't have it.
And Founder is going to give us complete mathematical notation in the post box, but it is not ready yet.
So I had to resort to ball point pen on paper.
Reading Thomas Cuthbert it made me think about things I had done long ago.
I decided to figure out the equations for least squares straight line fit to data.
Not hard, I'd followed it in books before and I had done it myself.
Just set up the square error term and the sum, and the use FOIL to evaluate the square. Pull she sum signs outside. Then differentiate for both variables, and then solve for when they are zero.
I set it up with Cramer's rule, so I can inspect for the possibility of a singular matrix. And I check the second derivatives, and I am done!
We use what math we want to. Now sure, lots of guys turn into Homer Simpson. But I for one am not going to let that happen. Well into middle age I am committed to learning much more than I ever have before, and to staying current in quite a few different areas.
SJG
X-Burning House of Love
https://www.youtube.com/watch?v=LInxU2dW…
+
https://www.amazon.com/Introduction-Algo…
4th ed, 1312 pages
SJG
Ain't No Mountain High Enough
https://www.youtube.com/watch?v=ABfQuZqq…
Courant, Richard, 1888-1972. (1937, 1961) Old old calculus book, translated from French.
SJG
Sex Slave Uni
https://tuscl.net/photo.php?id=10885
Claudette Colbert
https://tuscl.net/photo.php?id=10893
The Rolling Stones - Gimme Shelter - 2013 School of Rock AllStars Team 4
https://www.youtube.com/watch?v=we-3Y3vh…
The book of his I have seems to be the first of 2 volumes. And it is different from modern texts. I read these old books to see this. It is not so much what they really convey. It is more how they talk about it, what they feel they need to explain, and what they feel that they can just assume people will understand.
This book was originally written in French too.
https://en.wikipedia.org/wiki/Richard_Co…
Courant also wrote with David Hilbert.
SJG
Yeah, this is good. Probably written in German originally, not French.
More words than formulas or graphs.
Reads a bit more like a book of Analysis, than just a book of Calculus.
Talks about a lot of stuff which I probably take for granted because I grew up learning about these ideas.
like:
The Continuum of Numbers
The Conept of Function
SJG
Linda Ronstadt - You're No Good - 2016 School of Rock AllStars Team 6
https://www.youtube.com/watch?v=tMM5bjkK…
https://en.wikipedia.org/wiki/Cauchy%E2%…
https://mathworld.wolfram.com/SchwarzsIn…
https://brilliant.org/wiki/cauchy-schwar…
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Linda Ronstadt - You're No Good - 2016 School of Rock AllStars Team 6
https://www.youtube.com/watch?v=tMM5bjkK…
about geometric series
first and second definition of convergence, and geometric series.
He gets into logarithms and then different number bases. Says Babylonians used base 60. Less repeating decimals that way, more terminating. That makes sense, 60 has so many factors.
SJG
Linda Ronstadt - You're No Good - 2016 School of Rock AllStars Team 6
https://www.youtube.com/watch?v=tMM5bjkK…
SJG
Linda Ronstadt - You're No Good - 2016 School of Rock AllStars Team 6
https://www.youtube.com/watch?v=tMM5bjkK…
Then he gets to parametric representation!
SJG
Linda Ronstadt - You're No Good - 2016 School of Rock AllStars Team 6
https://www.youtube.com/watch?v=tMM5bjkK…
Courant, Richard, 1888-1972. (1937, 1961) Old old calculus book, translated from French.
Richard Courant (January 8, 1888 – January 27, 1972)
This is more similar to modern calculus text books than I had expected. And given the choice, I would put time into carefully following the newer books instead of this.
He has a second volume which I will read.
He actually has quite a few interesting looking books.
Going thru this, and cognizant of how long ago it was written, one thing comes to me.
I guess I when to school in the era of New Math. While it could have been better, I still got exposed to a lot of the concepts of advanced mathematics at an early age. I think it was much better than what those of my parent's generation got.
Courant talks a lot about power series and taylor series. And the modern books do this too.
To me this is related but peripheral to differential and integral calculus, but yet it is always associated.
Another old book talks about Cantor Dust. It is the idea that there are always numbers between numbers. And I guess the most extreme of this are the irrational numbers.
For people without much math experience irrational numbers are a challenging concept.
You get the terminating and repeating decimals when you do long division. But how do you get irrational numbers? Well you get them from a power series.
The kind of math and the uses of math which calculus is about requires a continuum of numbers which irrational numbers are the core of.
Today with floating point calculators we don't really think much about repeating decimals or irrational numbers. We just work within the precision we have and let that be sufficient.
HP Prime, 16 byte floating point, 33 decimal digits and 3 digit exponents.
Well if you do the long division yourself and look for the repeating decimal, that is an exact answer.
Calculus is more for the scientific calculator way, and of course allowing for the even more common irrational numbers.
Differential and integral calculus / by R. Courant ... translated by E.J. McShane volume 2
SJG
Sex Slave Initiation Uniform
https://tuscl.net/photo.php?id=10885
The Rolling Stones - Gimme Shelter - 2013 School of Rock AllStars Team 4
https://www.youtube.com/watch?v=we-3Y3vh…
Do kids chose to Major in business because they think it’s an easy path to wealth?
Sure, it covers some topics not typically taught in high school but many kids just think it’s “so hard”
I thought it was almost too easy. Maybe because I wasn’t a business major
Finite Math can get into a lot of things.
Usually there is one Calculus book for the Math, Physical Science and Engineering majors. Then there is one for Social Science, Biology, and Business majors, and it is a softer book.
Finite Math
https://sciencing.com/difference-between…
https://en.wikipedia.org/wiki/Finite_mat…
I took a Business Law Class during a summer at a Community College. Our instructor had been county DA. He was very smart. He was very complimentary and encouraging of me in class when he saw that I could challenge the way things were being presented in the text books examples, and he put down some of the Business Majors.
I got the highest exam score in the class and he complimented me, and I let him know that I was not a Business Major or a regular student at that school.
In my opinion, Business Majors are very outer directed people, responding to the social expectation that they graduate from college, but not really wanting to learn anything they don't have to.
So no, they aren't very bright.
I remember the first time I went to buy a new car. Once the deal was mostly done, they had me talk to this guy who's job it was to try and convince me that I can't work on the car myself, and that even though it came with a manufacturer's warranty, that it was worth it for me to buy the extended warranty.
Now I mean, what is the mathematical expectation of costs I will incur in car maintenance, versus the cost of the insurance. Which is higher? I mean someone could sell you an insurance policy for when light bulbs burn out, or for when it rains.
Then I looked at his hand, a very prominent ring, "San Jose State School of Business".
I think there are lots of more worthwhile things one could be learning in school, things which involve much more critical thinking, than Business. Business programs could be made much more critical thinking oriented.
SJG
The Rolling Stones - Gimme Shelter - 2013 School of Rock AllStars Team 4
https://www.youtube.com/watch?v=we-3Y3vh…
https://math.libretexts.org/Courses/Moun…
https://mathworld.wolfram.com/CubicSplin…
People do cubic splines. Never seen anyone do quintic splines, but it seems like it would work.https://www.sciencedirect.com/science/ar…
https://link.springer.com/article/10.100…
https://en.wikipedia.org/wiki/Spline_(ma…
Now when you only have certain data points, and you use one of these methods, you don't really know how well it is working because you don't have other data.
If what you want though is to integrate a continuous function, like say the notorious gaussian. You could use certain points to apply your method, and then look at how well you method comes up with something which fits the original function.
And then what is the benefit of a very sophisticated method, as opposed to just using smaller intervals?
SJG
Pleaser
https://pleasershoes.com/products/deligh…
https://pleasershoes.com/collections/all…
The Kinks - Till the End of the Day (1965) ( like the images of the neat old cars )
https://www.youtube.com/watch?v=mQw7wLvJ…
THE BYRDS Greatest Hits - The Best Of THE BYRDS | HD/HQ
https://www.youtube.com/watch?v=tAz2uS1I…
Yardbirds Anderson Theatre 1968
https://www.youtube.com/watch?v=8QncmVs7…
And with this new Chaos Theory, you need computers to even be able to visualize it.
SJG
Catie Reviews Pleaser Red 5 Inch Single Sole Sling Back High Heel Shoes with Nurse Costume Try On.
https://www.youtube.com/watch?v=5dZ7KQVF…
Some years back I read though most of a book by this team:
Thomas' calculus : early transcendentals / based on the original work by George B. Thomas, Jr., Massachusetts Institute of Technology ; as revised by Maurice D. Weir, Naval Postgraduate School, Joel Hass, University of California, Davis ; with the assistance of Christopher Heil, Georgia Institute of Technology
Calculus.
Weir, Maurice D. (2014)
Finite element exterior calculus / Douglas N. Arnold, University of Minnesota, Minneapolis, Minnesota
Arnold, Douglas N., 1954- author (2018)
Linear models and time-series analysis : regression, ANOVA, ARMA and GARCH / Marc S. Paolella, Department of Banking and Finance, University of Zurich, Switzerland (2019)
Understanding Maple / Ian Thompson, University of Liverpool (2017)
Interesting stuff, but not really what I was looking for
SJG
Babyface - Change the World (MTV Unplugged, NYC, 1997) (Clapton plays his electric Fender Stratocaster)
https://www.youtube.com/watch?v=jR7kekXB…
Kaitlyn Tries Pleaser KISS-254 Black 6 Inch High Heel Shoes With Black Stockings And Velvet Skirt (not the highest but an extremely sexy and totally CFM heel back design)
https://www.youtube.com/watch?v=FlgQRbjH…
https://pleasershoes.com/products/kiss-2…
Goodson, G. R. (Geoffrey Ross), 1948-
(2017)
*
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Differential and integral calculus / by R. Courant ; translated by E. J. McShane. 2nd volume, 1948 printing.
References H. W. Turnbull, The Theory of Determinants, Matrices, and INvariants, 1929
The theory of determinants, matrices, and invariants / by H. W. Turnbull (1945)
*
SJG
https://en.wikipedia.org/wiki/Affine_tra…
https://mathworld.wolfram.com/AffineTran…
SJG
The old books are very interesting and worthwhile, but you need to avail yourself of the new books to make sure you can follow the development.
Principles of mathematical analysis / Walter Rudin
Rudin, Walter, 1921-2010
*
The theory of determinants, matrices, and invariants / by H. W. Turnbull (1945)
*
curious
https://celebratio.org/Rudin_Mary/bibf/7…
Maxwell's equations in periodic structures / Gang Bao, Peijun Li
Bao, Gang, author (2022)
SJG
Turnbull, H. W. (Herbert Westren), 1885-1961 (1960 3rd edition)
This is a Dover republishing of a 1929 edition. Dover stuff is always good.
But here is a 1945 2nd edition:
The theory of determinants, matrices, and invariants / by H. W. Turnbull
Turnbull, H. W. (Herbert Westren), 1885-1961
*
SJG
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by H. W. Turnbull
first issued 1928, based on lectures given in 1926
second edition 1945, reprinted 1948
Starts off talking about homogeneous linear equations
ANd then the various ways to notate the determinants.
SJG
Uvalde and Buffalo testimony before US House, quite disturbing
https://www.youtube.com/watch?v=bC7zG9F_…
This book does emphasize determinants, and it starts out with simultaneous equations.
If you are going to have computers do the computations, gaussian elimination is faster to the the inverse than determinants. But I agree, determinants is more interesting.
Relationship between determinants and permutations and combinations, and hence factorials.
Now this does get into the characteristic equation, using Lambda and an Identity Matrix.
And the Caley Hamilton Thm.
SJG
https://en.wikipedia.org/wiki/Quaternion
LOL!
Yeah, I need newer math books. What math is used today has changed because of computers.
Principles of mathematical analysis / Walter Rudin
Rudin, Walter, 1921-2010
*
3 editions, 1st edition was 1953
SJG
Rudin, Walter, 1921-2010, 1st edition, 1953
mentions in the series, Bellman - Stability Theory of Differential Equations.
Stability theory of differential equations / R. E. Bellman 1953
Introduction to matrix analysis / Richard Bellman (1970)
Definitely a new kind of thinking comes in with going to calculus.
SJG
Livibaby
https://tuscl.net/photo.php?id=9446
Wicker Park School of Rock
https://www.youtube.com/watch?v=717EvZJb…
Newshour Today
https://www.youtube.com/watch?v=oVMa1jBj…
It isn't. But for example testing people for employment applications with things that are not a bona vide occupational requirement could be considered discriminatory.
SJG
Some of Rudin's refs, and of those in the pubisher's series
Rudin's first:
Graves, L. M. "The Theory of Functions of Real Variables" 1946
Hardy, G. H. "Pure Mathematics" 9th ed 1947
Hardy, G. H. and W. Rogosinski "Fourier Series" 2nd ed 1950
Kamke, E. "Theory of Sets" Dover 1950 (the stuff Dover reprints is always good!)
Theory of sets / Translated [from the 2d German ed.] by Frederick Bagemihl
Kamke, E. (Erich), 1890-1961. (1950 2nd German ed)
***
Landau, E. G. H. "Foundations of Analysis" 1951
Titchmarsh, E. C. "The Theory of Functions" 2nd ed 1939
Mathematics for the General Reader (2017)
Titchmarsh, E. C. (Edward Charles), 1899-1963,
+
The theory of functions / by E. C. Titchmarsh (1968 end ed)
* and other works too.
SJG
Ahlfors - Complex Analysis
Buck - Advanced Calculus
Codington and Levinson - Theory of Ordinary Differential Equations
Golomb and Shanks - Elements of Ordinary Differential Equations
Graves - The Theory of Functions of Real Variables
Griffin - Elementary Theory of Numbers
Hildebrand - INtroduction to Numberical Analysis
Householder - Principles of Numerical Analysis
Lass - Elements of PUre and Applied Mathematics
Lass - Vector and Tensor Analysis
Leighton - An Introduction to the Theory of Differential Equation
Nehari - Conformal Mapping
Newell - Vector Analysis
Rosser - Logic for Mathematicians
Rudin - Principles of Mathematical Analysis
Sneddon - Elements of Partial Differential Equations
Sneddon - Fourier Transforms
Stoll - Linear Algebra and Matrix Theory
Weinstock - Calculus of Variations
SJG
Rudin, Walter, 1921-2010, 1st edition, 1953
More of what is in the book:
Talks about Dedekind cuts, Metric Spaces, Compact Sets, Perfect Sets, Cauchy Criterion, Natural Log Base 'e', Legesque Theory, Riemann-Sieltjes Integral, Stone-Weierstrass thm, a couple of mean value thms, and L'Hopital's Rule, and Taylor's Thm, Curves and Length of a Curve, lub= least upper bound, glb= greatest lower bound
more of Rudin's refs.
Burkill, J. C. "The Lebesque Integral, 1951
Kestelman, H. "Modern Theories of Integration" 1937
Knoppm, K. "Theory and Application of INfinite Series 1928
SJG
Vanilla Fudge - Keep Me Hanging On - Chicago School of Rock Show Team (this girl's voice is what really makes this go)
https://www.youtube.com/watch?v=o9CU_5a6…
0
Foundations of analysis : the arithmetic of whole, rational, irrational, and complex numbers: a supplement to textbooks on the differential and integral calculus / by Edmund Landau ; translated by F. Steinhardt
Landau, Edmund, 1877-1938.
*
SJG
Nothing. You can't cross a vector and a scalar.
You can multiply a vector by a scalar.
Real good!
https://www.amazon.com/DIV-Grad-Curl-All…
Foundations of analysis; the arithmetic of whole, rational, irrational, and complex numbers. A supplement to textbooks on the differential and integral calculus / Translated by F. Steinhardt
Landau, Edmund, 1877-1938. (1960 but I think from originally a 1951 text) only 136 pages
SJG
Landau, Edmund, 1877-1938. (1960 but I think from originally a 1951 text) only 136 pages
his preface he dates 1929.
Book never talks about Calculus.
Lists lots of stuff from this publisher:
Chelsea Scientific Books
still around?
I think no.
Books by
S. Banach, George Boole, F. R. Gantmacher and David Hilbert and other books by E. Landau
SJG
Landau, Edmund, 1877-1938. (1960 but I think from originally a 1951 text) only 136 pages
Deals mostly with four function math, and a lot of stuff I would consider to be number theory. Makes me thing some.
He talks about Cuts and Dedekind's Theorem
A form of the continuity axiom for the real number system in terms of Dedekind cuts. It states that for any cut A|B of the set of real numbers there exists a real number α which is either the largest in the class A or the smallest in the class B.
https://encyclopediaofmath.org/wiki/Dede….
Richard Dedekind, "Essays on the Theory of Numbers" (tr. W.W.Beman) Dover (1963) [1901]
Anyway, Landau also talks about irrational and complex numbers.
***********************************
Hildebrand - Introduction to Numerical Analysis
Introduction to numerical analysis / [by] F. B. Hildebrand
Hildebrand, Francis Begnaud (1973, seems to be originally 1956) a very old book for the subject, lets see what they thought.
https://en.wikipedia.org/wiki/Francis_B.…
Francis Begnaud Hildebrand (1915 – 29 November 2002) was an American mathematician. He was a Professor of mathematics at the Massachusetts Institute of Technology (MIT) from 1940 until 1984. Hildebrand was known for his many influential textbooks in mathematics and numerical analysis.
https://mathgenealogy.org/id.php?id=6276…
David Hildebrand
https://www.thriftbooks.com/a/david-k-hi…
David Hilbert a totally unrelated person
https://en.wikipedia.org/wiki/David_Hilb…
SJG
Jefferson Starship - Jane - 2018 School of Rock AllStars Team 6 (really good!)
https://www.youtube.com/watch?v=BdWq4w8D…
Holy Diver
https://www.youtube.com/watch?v=kJ1Uu5vM…
MIT
Princeton
Harvard
Stanford
Berkeley
U of Chicago
Cal Tech
Columbia
NYU
UCLA
U Michigan
Interesting list. Only non coastal school on Top 10 is Chicago
Michigan missed top 10 but pretty good for state school
Source US NEWS
U of Chicago
Columbia
NYU
UCLA
U Michigan
In this Internet era I think we all can learn much more than would have been likely in past times. So in in depth knowledge of mathematics is within reach for those who want it. And then with computers we can bring much more math into applications then we otherwise could have.
SJG
PBS News Weekend live episode, July 2, 2022, Abortion and Guns
https://www.youtube.com/watch?v=x_Ti2Ssa…
Introduction to numerical analysis / [by] F. B. Hildebrand
Hildebrand, Francis Begnaud (1974, seems to be originally 1956) a very old book for the subject, lets see what they thought.
An old book, for the subject, but this is part of why I want to read it.
In his bibliography he lists some from R. W. Hamming
This is published as part of the McGraw Hill International Series in Pure and Applied Mathematics.
Some from the list:
Ahlfors: Complex Analysis
Buck: Advanced Calculus
Chester: Techniques in Partial Differential Equations
Cohn: Conformal Mapping on Riemann Surfaces
Dennemeyer: Introduction to Partial Differential Equations and Boundary Value Problems
Dettman: Mathematical Methods in Physics and Engineering
Golomb and Shanks: Elements of Ordinary Differential Equations
Hamming: Numerical Methods for Scientists and Engineers
Householder: The Numerical Treatment of a Single Nonlinear Equation
Kalman, Falb, and Arbib: Topics in Mathematical Systems Theory
Lass: Vector and Tensor Analysis
Lepage: Complex Variables and the Laplace Transform for Engineers
Monk: Introduction to Set Theory
Moore: Elements of Linear Algebra and Matrix Theory
TBC
SJG
Busacker and Saaty: Finite Graphs and Networks
Cheney: Introduction to Approximation Theory
Coddington and Levinson: Theory of Ordinary Differential Equations
Conte and de Boor: Elementary Numerical Analysis: An Algorithmic Approach
Epstein: Partial Differential Equations
Greenspan: Introduction to Partial Differential Equations
McCarty: Topology: An Introduction with Applications to Topological Groups
Mostow and Sampson: Linear Algebra
Moursund and Duris: Elementary Theory and Application of Numerical Analysis
Pearl: Matrix Theory and Finite Mathematics
Pipes and Harvill: Applied Mathematics for Engineers and Physicists
Ralston: A First Course in Numerical Analysis
Ritger and Rose: Differential Equations with Applications
Ritt: Fourier Series
Rossier: Logic for Mathematicians
Rudin: Principles of Mathematical Analysis
Simmons: Differential Equations with Applications and Historical Notes
Simmons: Introduction to Topology and Modern Analysis
Sneddon: Elements of Partial Differential Equations
Sturble: Nonlinear Differential Equations
Weinstock: Calculus of Variations
SJG
Introduction to numerical analysis / [by] F. B. Hildebrand
Hildebrand, Francis Begnaud (1974, seems to be originally 1956) a very old book for the subject, lets see what they thought.
So in 1974 access to computers was still limited, and programmable calculators were still pretty new.
And then back in 1956, not sure what people had, and it would only have been a few people, like large institutions and Military - NASA.
The book does talk about the use of slide rules.
So book talks about numerical solution to equations. Multiple equations and unknowns.
Talks about a coefficient matrix, and having a column matrix, and putting them together to make a rectangular augmented matrix.
They talk about using Cramer's Rule and Determinants. BUt then they explain that this is very slow. And I can attest to this.
And then they talk about Gaussian Elimination.
This is Gauss Reduction.
Then there is another wrinkle added for Gauss-Jordan Reduction, but this goes a little bit slower.
You do need to have some stuff in there to minimize the loss of accuracy when you have a broad spread of number absolute values in the coefficient matrix.
And then you have to be on watch for singular matrix, or rank being lower than the dimension. And it is not just a literal determinant of zero. You need to watch for overflow and underflow of your floating point scheme, and really you want to interdict things which compromise your accuracy.
He talks about Crout Reduction. And he has an appendix to develop it.
Came in 1941 , P. D. Crout in Trans AIEE.
Talks about Tridiagonal Sets of Equations.
https://en.wikipedia.org/wiki/Crout_matr…
Also this book has nothing in it like computer code.
SJG
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School of Rock 10 year reunion
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School of Rock Musical - Teachers Pet Combination
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Keep Me Hanging On
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Jefferson Starship - Jane - 2018 School of Rock AllStars Team 6, awesom lead singer
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Strange Kind of Women - Perfect Strangers - live at La Grande Ourse Concert Hall
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VANILLA FUDGE_You Keep Me Hanging On_BB Kings_6-22-13
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Chambers Brothers - Time Has Come Today - Cleveland School of Rock
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Linda Ronstadt - You're No Good - 2016 School of Rock AllStars Team 6
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School of Rock Reunion Concert - Jack Black - BEST QUALITY
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Electric Light Orchestra - Telephone Line - Chicago School of Rock
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Janis Joplin - Down On Me - School of Rock All-Stars Team 2
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Dio - Holy Diver - 2015 School of Rock AllStars Team 4 - Wicker Park Fest
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The Flamin' Groovies - Shake Some Action - Cleveland School of Rock
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Introduction to numerical analysis / [by] F. B. Hildebrand
Hildebrand, Francis Begnaud (1974, seems to be originally 1956) a very old book for the subject, lets see what they thought.
So it talks a lot about inherent errors and round off errors, as it has to.
References W. E. Milne Numerical Calculus (1949)
Numerical calculus : approximations, interpolation, finite differences, numerical integration and curve fitting
**
Talks about iterative methods and relaxation and iterative methods for nonlinear equations
Newton-Raphson Method
Higher order nonlinear, sets of nonlinear, and the Jacobian Determinant.
SJG
Nora Jones, Something
https://www.youtube.com/watch?v=KC42CJoB…
As I know you always want the roots, or at least for partial fraction expansion, and it talks about how to get these and to allow for quadratics. AIK you always want to deal with the complex roots in conjugate pairs to maintain accuracy.
ref:
Wilkinson, J. H.
1Book CoverRounding errors in algebraic processes
Wilkinson, J. H. (James Hardy)
Englewood Cliffs, N.J. : Prentice-Hall, [1964, c1963]
vi, 161 pages ;
*
and many other books and papers
SJG
Eric Clapton - Beware of Darkness at the Concert For George
https://www.youtube.com/watch?v=oRoo0-hw…
SJG
Introduction to numerical analysis / [by] F. B. Hildebrand
Hildebrand, Francis Begnaud (1974, seems to be originally 1956) a very old book for the subject, lets see what they thought.
So we've got a lot of stuff in the above. Talks about:
Linear Interpolation, Divided Differences, Second-degree Interpolation, Newton's Fundamental Formula, and lots of other things about interpolation.
Lagrangian Methods
I think the terminology has changed some:
https://en.wikipedia.org/wiki/Lagrange_m…
Here:
https://en.wikipedia.org/wiki/Lagrange_p…
^ and also Newton-Cotes Integration
Richardson Extrapolation, Romberg Integration
SJG
Jefferson Starship - Jane - 2018 School of Rock AllStars Team 6
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And we have Runge-Kutta Methods of Higher Order
A a whole lot of stuff about Least Squares Polynomial Approximation
SJG
Jefferson Starship - Jane - 2018 School of Rock AllStars Team 6
https://www.youtube.com/watch?v=BdWq4w8D…
Concepts of the calculus.
Boyer, Carl B. (Carl Benjamin), 1906-1976.
Books & Journals | Dover | [1959]
Very widely disseminated
1959 Dover reprint, and these are always good.
SJG
Jefferson Starship - Jane - 2018 School of Rock AllStars Team 6
https://www.youtube.com/watch?v=BdWq4w8D…
Originally a 1949 manuscript, but preface says 1939, so that is probably when the text was written. And mostly text, like a novel. Not formulas or graphs, mostly.
Talks about Newton and Leibniz, and whole lot of other historical stuff.
SJG
https://tuscl.net/photo.php?id=9418
Jan 6th
https://www.youtube.com/watch?v=48HH4LVn…
Concepts of the calculus.
Boyer, Carl B. (Carl Benjamin), 1906-1976.
Books & Journals | Dover | [1959]
So the newest references I see in this are 1936. There are lots from the decades before that, then a lot from the 1800's, and some going back even furhter.
Mostly they start off talking about infintesimal things, delta(s)/delta(t).
I guess math was not really developed to talk about stuff like that thousands of years ago.
And as I know, in modern calculus texts they talk about this kind of stuff as limits, and they have people work all sorts of problems dealing with limits, and when functions go non-existent or indeterminant because of dividing by zero.
And then it says, "The Pre-Hellenic peoples are usually regarded as pre-scientific in their attitude toward nature, inasmuch as they palpably lack the Greek confidence in its essential reasonableness, as well as the associated feeling that beneath the perplexing heterogeneity and ceaseless flux of events would be found elements of uniformity and permanence."
They say that Babalonians and Egyptians were not looking for these eternal universals in the same way as the Greeks. And so it is with the Greeks that you find the earliest idea of calculus.
So they say the Egyptian mathematical high point was the volume of the frustum of a square pyramid.
?? Does this mean volume of a pyramid? AIK it is 1/3 the area of the base times the height.
Frustum means truncated.
https://study.com/learn/lesson/frustum-o….
okay.
But Boyer is saying this uses something like calculus??
I kinda think it just comes down to Thm of Pythagoras, like are of a triangle.
volume
https://en.wikipedia.org/wiki/Tetrahedro…
Talk about Proclus and Pythagoras
SJG
But I remember when I decided that it was a bummer to have to use English rulers which read out in fractions. I had one 50ths of an inch ruler, and that was nice. But best is metric.
Anyway, Carl B. Boyer says that Ancient Egyptians really only thought integers. With fractions they did not see them as single numbers.
Now there was one exception 2/3. For some reason they saw that as a single number.
With 3/5 they saw that as the sum of 1/2 and 1/10.
Today we have calculators with so many digits that there is no reason to distinguish between terminating and repeating decimals, and no reason to keep special track of the later. We don't need exact answers. And then we have buttons for all manner of transindental funcion.
And then on the back cover of the book they list some of the greatest mathematicians, Newton, Leibnitz, Taylor, Descartes, Euler, Lagrange, Cantor, Weierstrass, Zeno, Pythagoras, and Euclid.
Of books listed by the publisher, Dover, this is a 1959 edition. But lets post a few of them. I like to read old books in this kind of an area to see how people used to think, as that helps me to better understand where we are at today.
Mathematical Methods for Scientists and Engineers, L. P. Smith, 435 pages
Mathematical methods for scientists and engineers / Preston Lloyd Smith. (1961 and lots of other books with similar titles)
*
I take note of this:
Mathematical methods for scientists and engineers : linear and nonlinear systems / Peter B. Kahn
Imprint New York : Wiley, [1990, 469 pages]
**
Algebras and Their Arithmetics, Leonard E. Dickson 241 pages
Algebras and their arithmetics / by Leonard Eugene Dickson. (1938, originally 1923)
*
Advanced Calculus, Edwin B. Wilson, 556 pages
Advanced calculus; a text upon select parts of differential calculus, differential equations, integral calculus, theory of functions, with numerous exercises.(1958, originally 1912)
*
A Treatise on Advanced Calculus, Philip Franklin, 595pp
A treatise on advanced calculus : including those parts of the theory of functions of real and complex variables which form the logical basis of the infinitesimal analysis and its applications to geometry and physics / by Philip Franklin. (1964, originally 1940, 595pp)
**
SJG
The Pretenders - Hard Rock - 1998 ( quite good and they added a keyboardist)
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Concepts of the calculus.
Boyer, Carl B. (Carl Benjamin), 1906-1976.
Books & Journals | Dover | [1959]
So he talks about the paradoxes of Zeno. Like say in a time interval, you move half of the distance between yourself and a fixed point. And then in the next interval, half of what remained, etc.
When do you finally get to the point?
This had come up in a conversation with someone who was ticketed for not coming to a complete stop at a stop sign. How slow is slow enough to be stopped?
But Boyer speaks of another Zeno formulation. Say Achilles runs a race with a tortoise and Achilles runs twice as fast as the tortoise, and so we give the tortoise a lead.
So when does Achilles catch up with the tortoise?
Well for the ancients they were not really accustomed to finding limits for infinite series. It gets too confusing.
For me, I would set it up as an algebra problem
Say Achilles runs at velocity Va.
The lead given the tortoise is Lt.
So the time when Achilles catches up with the tortoise will be Tc. And the distance Achilles has run will be Da.
Da = Tc * Va
Da = Lt + Tc * Va /2
So then we can eliminate Da:
Tc * Va = Lt + Tc * Va /2
So then:
Tc * Va - Tc * Va/2 = Lt
Tc * (Va -Va/2) =
Tc * Va/2 = Lt
So say the velocity of Achilles is 10 ft/sec, then the velocity of the Tortoise is 5 ft /sec.
So say the lead we gave the Tortoise was 100 ft.
So Tc = 2 * Lt / Va
So Tc = 2 * 100 / 10 = 20 seconds.
So Achilles will have run 200 ft
The Tortoise will have run 100 ft and then be 200 feet from the starting line.
Now this kind of approach does not get into convergence of infinite series or into calculus. It just uses algebra. But I guess it is a way of using algebra that has developed in a world where our understanding of time and motion has been shaped by calculus. And I have learned from years in school, having to do homework problems with word problems like this, and also by regularly solving similar kinds of problems on my own. You cut through the confusion by defining variables and laying out the relations.
Now Calculus is about infinitesimals. And I guess this is what has changed in thinking. And people learn math in school and from books today, and it is set up to facilitate Calculus.
So I would introduce here, Meditaitons and the Tarot and its Unknown Author, who says that Calculus with its concepts and notation, is a part of Hermeticism.
https://www.amazon.com/Meditations-Tarot…
I've always felt this about Calculus. But now reading this Carl Boyer and seeing how it developed, now I can much better appreciate that.
Newton and Leibniz certainly held occult views, they just wrote about them other places. And Boyer shows that originally Calculus was not well received and it took the work of a lot of other people going into the 18th century to more rigorously develop it.
And then one name that comes up is Hoene Wroński going into the 19th century. He was a Polish mathematician in exile in Paris. And it was he who is believed to have initiated the occultist Eliphas Levi. And Wroński is the originator of the dark gnosis practiced by Fraternitas Saturni.
Wroński took some exception to the work of Lagrange.
https://en.wikipedia.org/wiki/J%C3%B3zef….
I read all of this and consider. I am not really one to challenge the theoretical basis of calculus.
Rather I am more interested in how to apply it. And how much math you can use in a situation now depends on how you are using computers to implement it. The application of computers make it possible to use vastly more math.
SJG
Pretenders, My City Was Gone
https://www.youtube.com/watch?v=thu8DWsi…
Jane, School of Rock
https://www.youtube.com/watch?v=BdWq4w8D…
Dover 1958, but originally 1912. By far the oldest math book I have ever looked at.
Always what is interesting is what does the author feel they need to carefully explain, versus what do they feel is already fully understood. And then what might be dropped out of newer books.
SJG
Dover 1958, but originally 1912 and 1911 by Edwin Bidwell Wilson MIT
This is surprisingly to me like modern calculus text books. Now this is the advanced course, so some understanding presumed.
Of what jumps out at me, it talks about integration by parts and integrating factors, but it does not really explain them. And they don't explain it in the context of doing integrals, they explain it in the context of solving differential equations.
Got everything about Taylor Series and Maclaurin Series. Overall I would say the new books are better.
Lots about complex numbers and vectors. New books better.
Lots about multiple variables and partial derivatives.
Calculus of Variations
The modern books are more wordy, and there are more of them. But I think they are better and more worth putting time into.
SJG
Los Angeles, quite good!
https://www.youtube.com/watch?v=D-scKQr9…
PBS Newshour
https://www.youtube.com/watch?v=SW-8BjCG…
SJG
Both authors at University of Maryland
Dynamics Group at the University of Maryland
Brin is an editor of Forum Mathematicum
Garrett Stuck was professor mathematics at University of Maryland. Wrote "The Mathematica Primer (1998)
He is also founder of Chalkfree Inc, a software company.
I see one thing which I do understand. These dynamic systems are deterninistic.
Often there is confusion coming from the popularity of chaos theory, thinking that chaotic behavior comes from noise, round off error, or from the Heisenberg Uncertainty Principle.
It does not, it is simply the product of multiple non-linearities interacting.
And then when it comes to observing real systems, the issue is that you never do have an accurate enough mathematical model, and because you can never know the starting conditions to enough accuracy.
I have much to learn here I can see.
SJG
Vanilla Fudge - School of Rock
https://www.youtube.com/watch?v=o9CU_5a6…
Oxford University Press (2014)
This is special series of very small fine print books they have.
Holland's Refs:
Herbert A. Simon, The Sciences of the Artificial. MIT Press 1981
Arthur W. Burks, Essays in Cellular Automata. University of Illinois Press (1970)
Mitchell M. Waldrop, Complexity, (1972)
Melanie Mitchell. Complexity: A Guided Tour (2009)
Donald O. Hebb. The Organization of Behavior (1949)
Simon A. Levin, Fragile Dominion (199)
William Feller, Probability Theory and its Applications (1950)
Paul A. Samuelson, Economics 1948
SJG
Free - Wishing Well w/ British Leyland 3 axle dump truck
https://www.youtube.com/watch?v=eKy_puDD…
Complex Systems
* Self-organization
* Chaotic Behavior
* fat-tailed behaviour, rare events (mass extinctions, market crashes) occur more often than would be predicted by a normal bell-curve distribution.
* adaptive interaction
TWO KINDS OF COMPLEXITY
Complex Physical Systems (CPS)
Complex Adaptive Systems (CAS)
CAS deals with entities which are not fixed, usually called agents.
Navier Stokes Equations,
https://en.wikipedia.org/wiki/Navier%E2%…
Partial Differential Equations, extending from Maxwell's Equations for Electromagnetism, but for fluid flow.
Complex Physical Systems are almost always modelled by PDEs ( Partial Differential Equations )
SJG
Complex Adaptive System, CAS, more just in the computer, not really working by a summation rule and much more changeability in the Agents.
Network Theory, more forlmally known as graph theory. Denes Koing, early 20th centruy.
Then Duncan Watts and Mark Newman, and now Mitchell's "Complexity".
Then talking about fractals, scale-free networks.
Going to talk about Dynamics.
SJG
Gimme Shelter, Portland School of Rock
https://www.youtube.com/watch?v=XVnnXeER…
Dynamics, Physicist's concept of state.
But now we talk about bar magnets lining up in alternating orientations. And then of Ising's model.
http://star-www.dur.ac.uk/~tt/MSc/Lectur…
https://physics.stackexchange.com/questi…
https://farside.ph.utexas.edu/teaching/3…
https://phys.libretexts.org/Bookshelves/…
SJG
School of Rock
https://www.youtube.com/watch?v=eQp1RJtC…
1. Performance
2. Credit Assignment
3. Rule Disco
SJG
music which is more edgy
https://www.youtube.com/watch?v=eQp1RJtC…
Oxford University Press (2014)
CAS is all about Markov Chains, Markov Processes, Markov Matrices.
https://brilliant.org/wiki/markov-chains….
Lotka-Volterra equations, about Lynx Hare problems.
Gated Urn problems are like Markov Matrices.
Adaptation in natural and artificial systems : an introductory analysis with applications to biology, control, and artificial intelligence / by John H. Holland (1975)
*
I've read most of John H. Holland, and I have to say that most of the applications are hard for me to envision. But not read^
SJG
Mathematics
A Very Short Introduction
Timothy Gowers
https://csul.iii.com/search~S0?/Xmathema…,
*!
Free - Wishing Well
https://www.youtube.com/watch?v=eKy_puDD…
references: R. Bellman 1961, Adaptive Control Processes
Bellman, Richard, 1920-1984
Title Adaptive control processes : a guided tour
Imprint Princeton, N. J. : Princeton University Press, 1961
*
^ a very early book bridging from controls, to adaptive controls, to complexity and self-organization.
and in Holland's previous book everything runs on Markov Chains:
Adaptive Markov control processes / O. Hernández-Lerma
Imprint New York : Springer-Verlag, [1989]
*
SJG
Emily Williams-I Say a Little Prayer For You
https://www.youtube.com/watch?v=HX00cSNw…
21st Century Schizoid Man, School of Rock
https://www.youtube.com/watch?v=4_BEZJ1S…
Title Adaptive control processes : a guided tour
Imprint Princeton, N. J. : Princeton University Press, 1961
^ a very early book bridging from controls, to adaptive controls, to complexity and self-organization. So old that what this must mean is a lot different from what it would mean today.
Dedicated to A. Lyapunov, H. Poincare, and S. Lefschetz
And Bellman was with Rand Corporation
talks about Norbert Wiener and "cybernetics".
SJG
Perfect Strangers (Deep Purple cover)
https://www.youtube.com/watch?v=GMLgAvCM…
School of Rock AllStars perform "Highway Star" by Deep Purple
https://www.youtube.com/watch?v=-oGjZRe1…
Richard E. Bellman, an Applied Mathematician
https://en.wikipedia.org/wiki/Richard_E.…
Worked with Stuart Dreyfus. I am very familiar with Stuart and his bother Hubert.
Applied dynamic programming / by Richard E. Bellman and Stuart E. Dreyfus. (1962)
**
Credits Robert E. Kalaba
Robert E. Kalaba, an applied mathematician associated with USC for almost half a century and internationally renowned for his analytical and computational solutions to problems in physics, engineering, operations analysis and biology, died Sept. 29, following a brief illness. He was 78.
https://news.usc.edu/24478/USC-Professor…
Numerical inversion of the Laplace transform: applications to biology, economics, engineering, and physics / by Richard Bellman, Robert E. Kalaba, and Jo Ann Lockett. (1966)
*
Analytical dynamics : a new approach / Firdaus E. Udwadia and Robert E. Kalaba (1996)
*
SJG
<img src="https://i.etsystatic.com/35284413/r/il/c…">
https://www.etsy.com/listing/1226849587/…
<iframe width="560" height="315" src="https://www.youtube.com/embed/eQp1RJtCn2…" title="YouTube video player" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe>
https://en.wikipedia.org/wiki/Richard_E.…
studied mathematics at Brooklyn College where he earned a BA in 1941
He later earned an MA from the University of Wisconsin. During World War II he worked for a Theoretical Physics Division group in Los Alamos. In 1946 he received his Ph.D at Princeton under the supervision of Solomon Lefschetz.[8] Beginning 1949 Bellman worked for many years at RAND corporation and it was during this time that he developed dynamic programming.
p27, talks about how difficult 2 point boundary problem cases are.
Talks about Euler Equation and those of Sturm-Liouville type, and Terminal Control and Implicit Variational Problems.
Talks about bang-bang control, things which shift from one binary state to another.
pg34
Talks about Linearity and how some problems are make intractable because of complete linearity.
Norbert Wiener, Cybernetics 1948
S. Lefschetz
SJG
<iframe width="560" height="315" src="https://www.youtube.com/embed/W-fFHeTX70…" title="YouTube video player" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe>
Title Adaptive control processes : a guided tour
Imprint Princeton, N. J. : Princeton University Press, 1961
Many references to L. A. Zadeh, known for Fuzzy Sets and Fuzzy Logic. But this book was before much of that was known.
https://en.wikipedia.org/wiki/Lotfi_A._Z…
R. Bellman, Matrix Analysis 1960.
References R. Kalman, D. Hilbert
G. A. Bliss, Calculus of Variations, 1925
https://en.wikipedia.org/wiki/Lagrange_m…
In mathematical optimization, the method of Lagrange multipliers is a strategy for finding the local maxima and minima of a function subject to equality constraints (i.e., subject to the condition that one or more equations have to be satisfied exactly by the chosen values of the variables).[1] It is named after the mathematician Joseph-Louis Lagrange.
Overall I would say that this book treats too much to be useful. There is a well developed theory today for deterministic and stochastic controls, and a lot of work done on adaptive controls.
But this all came about after this book.
This author is also treating control of stuff which is not continuous at all, the stuff of game theory. Much less theory for that, and this book is real abstract.
Oh well, I wanted to see something very early.
SJG
by Joel R. Hass (Author), Maurice D. Weir (Author), George B. Thomas Jr. (Author)
Thomas' calculus : early transcendentals / based on the original work by George B. Thomas, Jr. ; as revised by Joel Hass, Christopher Heil, Maurice D. Weir (Pearson 2018)
a fairly new calculus book, and clearly quite good.
0?
https://www.amazon.com/University-Calcul…
And then going real far back:
Applied dynamic programming / by Richard E. Bellman and Stuart E. Dreyfus. (1962)
SJG
Very Good, Music Getting More Eclectic
<iframe width="560" height="315" src="https://www.youtube.com/embed/tVMjygPdBI…" title="YouTube video player" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe>
All of these people have since passed away now. Stuart Dreyfus taught Industrial Engineering at UC Berkeley, while his brother Hubert, an expert on Martin Heidegger taught philosophy. They were always antagonists to the MIT Artificial Intelligence Lab, starting with when it was run by Marvin Minsky, someone who in my opinion was an idiot.
https://www.amazon.com/What-Computers-St…
SJG
School of Rock
https://www.youtube.com/watch?v=4_BEZJ1S…
"In the period following World War II, it began to be recognized that there were a large number of interesting and significant activities which could be classified as multistage decision processes. It was soon seen that the mathematical problems that arose in their study stretched the conventional confines of analysis, and required new methods for their successful treatment. The classical techniques of calculus and the calculus of variations were occasionally valuable and useful in these areas, but were clearly limited in range and versatility, and were definitely lacking as far as furnishing numerical answers was concerned."
So the previous book dealth with the same stuff, but only on the very surface. Control theory is entirely based on calculus. They problems which can't be worked that way get into mathematical heuristics, "artificial intelligence", or this new Dynamic Programming.
A book which starts with a commonality to this will be very good.
SJG
Modern Controls Theory was developing at this time, and they do make reference to Rudolph Kalman, a NASA big wig.
But controls theory requires things which are continuous, or at least continuous in their digital representation. Most problems in scheduling, cargo loading, or resource allocation are completely discontinuous, so that their can you fall back on.
Both kinds of problems should connect, and this book is based on the premise that they do.
Dynamic Programming is mainly an optimization over plain recursion. Wherever we see a recursive solution that has repeated calls for same inputs, we can optimize it using Dynamic Programming. The idea is to simply store the results of subproblems, so that we do not have to re-compute them when needed later. This simple optimization reduces time complexities from exponential to polynomial.
For example, if we write simple recursive solution for Fibonacci Numbers, we get exponential time complexity and if we optimize it by storing solutions of subproblems, time complexity reduces to linear.
https://www.geeksforgeeks.org/dynamic-pr…
Dynamic programming is both a mathematical optimization method and a computer programming method. The method was developed by Richard Bellman in the 1950s and has found applications in numerous fields, from aerospace engineering to economics.
In both contexts it refers to simplifying a complicated problem by breaking it down into simpler sub-problems in a recursive manner. While some decision problems cannot be taken apart this way, decisions that span several points in time do often break apart recursively. Likewise, in computer science, if a problem can be solved optimally by breaking it into sub-problems and then recursively finding the optimal solutions to the sub-problems, then it is said to have optimal substructure.
If sub-problems can be nested recursively inside larger problems, so that dynamic programming methods are applicable, then there is a relation between the value of the larger problem and the values of the sub-problems.[1] In the optimization literature this relationship is called the Bellman equation.
https://en.wikipedia.org/wiki/Dynamic_pr…
Heinz Pagels: The cosmic code : quantum physics as the language of nature / Heinz R. Pagels. (1982)
SJG
The Rock Orchestra performs Genesis - The Lamb Lies Down on Broadway
https://www.youtube.com/watch?v=E5nZheA_…