Computer Simulation and Computer Algebra
Lectures for Beginners
Published on 29. July 1988
Book
Paperback/Softback
IX, 155 pages
978-3-540-18909-1 (ISBN)
Description
Computers play an increasingly important role in many of today's activities, and correspondingly physicists find employment after graduation in computer related jobs, often quite remote from their physics education. The present lectures, on the other hand, emphasize how we can use computers for the purposes of fundamental research in physics. Thus we do not deal with programs designed for newspapers, banks, or travel agencies, i.e., word processing and storage of large amounts of data. Instead, our lectures concentrate on physics problems, where the computer often has to work quite hard to get a result. Our programs are necessarily 5 quite short, excluding for example quantum chemistry programs with 10 program lines. The reader will learn how to handle computers for well-defined purposes. Therefore, in the end, this course will also enable him to orient himself in computer-related jobs. The first chapter deals mainly with solutions of the Newtonian equation of motion, that force equals mass times acceleration, which is a precursor to the molecular dynamics method in statistical physics. The second chap ter considers, by means of several examples, another method for statistical physics, Monte Carlo simulation. These two chapters deal with numbers, the traditional territory of computers. In contrast, analytic formula manipulation, 3 5 4 3 such as (a+27b -4c)5 = a + 135a b - ... , is taught in the last chapter and is important, for instance, in analytic integration or for evaluating expressions in Einstein's general theory of relativity.
More details
Edition
Softcover reprint of the original 1st ed. 1988
Language
English
Place of publication
Heidelberg
Germany
Publishing group
Springer Berlin
Target group
College/higher education
Professional and scholarly
Dimensions
Height: 24.4 cm
Width: 17 cm
Weight
320 gr
ISBN-13
978-3-540-18909-1 (9783540189091)
DOI
10.1007/978-3-642-97091-7
Schweitzer Classification
Other editions
New editions
Dietrich Stauffer | Friedrich W. Hehl | Volker Winkelmann
Computer Simulation and Computer Algebra
Lectures for Beginners
Book
06/1989
2nd Edition
Springer
€85.55
Article exhausted; check for reprint
Content
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.- 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.- 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 mathematical 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 polynomials and rational functions.- 4.5 To make decisions with boolean operators.- 4.6 Writing messages.- 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.