Computer Simulation and Computer Alegbra : Lectures for Beginners

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.