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...
Main Authors: | , , , |
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Format: | eBook |
Language: | English |
Published: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1989, 1989
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Edition: | 2nd ed. 1989 |
Subjects: | |
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.