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Computer Simulation and Computer Algebra Lectures for Beginners

The chapter on statistical-physics simulations has been enlarged, mainly by a dis­ cussion of multispin coding techniques for the Ising model (bit-by-bit parallel oper­ ations). In the chapter about Reduce, some details of the presentation have been cor­ rected or clarified. The new operator MATEIGE...

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Bibliographic Details
Main Authors: Stauffer, Dietrich, Hehl, Friedrich W. (Author), Winkelmann, Volker (Author), Zabolitzky, John G. (Author)
Format: eBook
Language:English
Published: Berlin, Heidelberg Springer Berlin Heidelberg 1989, 1989
Edition:2nd ed. 1989
Subjects:
Applied Dynamical Systems
Computer Simulation
Computer Modelling
Nonlinear Theories
Computer Software
Mathematical Physics
Theoretical, Mathematical And Computational Physics
Mathematical Software
Mathematical Methods In Physics
Dynamics
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • 1.6 A Reduce program, a follow-up of commands
  • 1.7 Assign a temporary result to a variable
  • 1.8 Homework
  • Lecture 2
  • 2.1 Built-in operators
  • 2.2 Manipulating Reduce expressions amounts to manipulating formulae
  • 2.3 The process of evaluation in Reduce
  • 2.4 Repeatedly doing something: Loops
  • 2.5 Loops and lists
  • 2.6 Multidimensional objects: Arrays
  • 2.7 Homework
  • Lecture 3
  • 3.1 The conditional statement
  • 3.2 Combining several statements I: The group statement
  • 3.3 Combining several statements II: The compound statement
  • 3.4 Some elementary mathematieal functions
  • 3.5 Differentiation with DF
  • 3.6 Integration with INT
  • 3.7 Substitution with SUB
  • 3.8 Homework
  • Lecture 4
  • 4.1 Operators that act on lists
  • 4.2 Right and left-hand-side of an equation
  • 4.3 Solving (non-)linear equations
  • 4.4 Retrieving parts of polynomialsand rational functions
  • 4.5 To make elecisions with boolean operators
  • 4.6 Writing messages
  • 1. Computational Methods in Classical Physics
  • 1.1 Preface
  • 1.2 Motion of a Classical Point-Like Particle
  • 1.3 Short Course in FORTRAN Programming Methodology
  • 1.4 Methods of Higher Accuracy (and Efficiency)
  • 1.5 Finding Extremal Points of Motion
  • 1.6 Statics and Dynamics of Strings
  • 1.7 Dynamics of Strings
  • 1.8 Literature
  • 2. Monte Carlo Simulations in Statistical Physics
  • 2.1 Introduction
  • 2.2 Random Numbers
  • 2.3 Ising Model
  • 2.4 Cellular Automata (Q2R and Creutz)
  • 2.5 Diffusion and Percolation
  • 2.6 Eden Clusters
  • 2.7 Kauffman Model
  • 2.8 Summary
  • 2.9 Appendix: Principles of Vector Computing
  • 2.10 References
  • Notes Added to the Second Edition
  • 3. Reduce for Beginners. Six Lectures on the Application of Computer-Algebra (CA)
  • Lecture 1
  • 1.1 A first interactive Reduce session
  • 1.2 What can CA do for you?
  • 1.3 The Reduce character set
  • 1.4 Integers, rational and real numbers
  • 1.5 Variables named by identifiers
  • 4.7 How to define your own operators
  • 4.8 LET rules
  • 4.9 Homework
  • Lecture 5
  • 5.1 Extended LET rules
  • 5.2 Examples: Factorials and binomial coefficients
  • 5.3 Clearing LET rules
  • 5.4 Creating non-commutative algebras, symmetric and antisymmetric operators
  • 5.5 Procedures for repeated use of commands
  • 5.6 A procedure for l’Hospital’s rule and a caveat
  • 5.7 Homework
  • Lecture 6
  • 6.1 Linear algebra package: Matrices
  • 6.2 Calculus of exterior differential forms in EXCALC
  • 6.3 Turning switches on and off
  • 6.4 Reordering expressions
  • 6.5 On Reduce input and output
  • 6.6 Generating Fortran programs
  • 6.7 Concluding remarks
  • 6.8 Homework
  • References
  • A.1 Where can you buy Reduce?
  • A.2 Some additional exercises (preliminary)
  • 4. Appendix: A Short Introduction to FORTRAN.

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