Computer Simulation and Computer Algebra: Lectures for Beginners

ISBN-13: 9783540565307 / Angielski / Miękka / 1993 / 287 str.

Dietrich Stauffer; Friedrich W. Hehl; Nobuyasu Ito

Opis

Computer Simulation and Computer Algebra. Starting from simple examples in classical mechanics, these introductory lectures proceed to simulations in statistical physics (using FORTRAN) and then explain in detail the use of computer algebra (by means of Reduce). This third edition takes into account the most recent version of Reduce (3.4.1) and updates the description of large-scale simulations to subjects such as the 170000 X 170000 Ising model. Furthermore, an introduction to both vector and parallel computing is given.

Spis treści

I Computational Methods in Classical Physics.- 1 Motion of a Classical Point-Like Particle.- 2 Short Course in FORTRAN Programming Methodology.- 3 Methods of Higher Accuracy (and Efficiency).- 4 Finding Extremal Points of Motion.- 5 Statics and Dynamics of Strings.- 6 Dynamics of Strings.- 7 Literature.- II Monte Carlo Simulations in Statistical Physics.- 1 Random Numbers.- 2 Ising Model.- 3 Cellular Automata (Q2R and Creutz).- 4 Diffusion and Percolation.- 5 Eden Clusters.- 6 Kauffman Model.- 7 Summary.- 8 Appendix: A Short Introduction to FORTRAN.- 9 Literature.- III Principles of Vector and Parallel Computing.- 1 Basic Idea.- 2 An Example — Q2R.- 3 More About Vector Processing.- 3.1 IF-Statement.- 3.2 Initial Cost for the Vector-Processing.- 3.3 Bank Conflict.- 3.4 Library Routines.- 4 Before and After the Vectorization.- 5 Parallel Computing.- 5.1 Basic Ideas.- 5.2 Types of Parallel Computers and Algorithms.- IV REDUCE for Beginners — Seven Lectures on the Application of Computer-Algebra (CA).- First Lecture.- 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 Assigning Values to Variables.- 1.8 Access to Previous Input and Output.- 1.9 Homework.- Second Lecture.- 2.1 Built-in Operators.- 2.2 Reduce Expressions.- 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.- Third Lecture.- 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 and Rule Lists.- 3.8 Homework.- Fourth Lecture.- 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 Rule Lists and the LET-statement.- 4.9 Homework.- Fifth Lecture.- 5.1 Activate and Deactivate Rule Lists.- 5.2 More About Rule Lists.- 5.3 Examples: Factorials and Binomial Coefficients.- 5.4 Deactivating User-defined Rules.- 5.5 Non-commutative Algebras, Symmetric and Antisymmetric Operators.- 5.6 Procedures for Repeated Use of Commands.- 5.7 A Procedure for PHospitaPs Rule and a Caveat.- 5.8 Homework.- Sixth Lecture.- 6.1 Linear Algebra Package: Matrices.- 6.2 Turning Switches On and Off.- 6.3 Reordering Expressions.- 6.4 On Reduce Input and Output.- 6.5 Generating Fortran Programs.- 6.6 Concluding Remarks.- 6.7 Homework.- Seventh Lecture.- 7.1 Vector and Tensor Calculus.- 7.2 Packages for Three-dimensional Vector Calculus.- 7.3 Tensor Analysis, Christoffel Symbols, General Relativity.- 7.4 The EXCALC Package for Exterior Differential Forms.- 7.5 Graphics with GNUPLOT.- 7.6 Homework.- A Some Additional Exercises.- B Changes From Reduce 3.3 to Reduce 3.4.1.- C Further Information on Reduce.- C.1 Where Can You Buy Reduce?.- C.2 Execution Times for the Reduce Standard Test.- D Literature.- Joint Index.