Computer Simulation and Computer Algebra: Lectures for Beginners [Paperback]

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.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.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 Computerl“B