Author | Stauffer, Dietrich. author |
---|---|
Title | Computer Simulation and Computer Algebra [electronic resource] : Lectures for Beginners / by Dietrich Stauffer, Friedrich W. Hehl, Volker Winkelmann, John G. Zabolitzky |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1989 |
Edition | Second Edition |
Connect to | http://dx.doi.org/10.1007/978-3-642-97174-7 |
Descript | XI, 155 p. online resource |
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 -- 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 polynomials and rational functions -- 4.5 To make elecisions 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 lโHospitalโs 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