Computer Simulation and Computer Algebra

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.

Diese dritte, erweiterte Auflage wurde aktualisiert und orientiert sich an der neuesten Reduce-Version (3.4.1) sowie an großangelegten Simulationen. Ein neues Kapitel über Vektor- und Parallelrechner wurde ergänzt. Daher wird diese Neuauflage sowohl von fortgeschrittenen Studenten der Physik und Mathematik als auch von Physikern begrüßt werden.

This enlarged third edition has been updated to the most recent version of Reduce (3.4.1) and large-scale simulations. A new chapter on vector and parallel computing has been added. Thus, this new edition will be welcomed by graduate physics and mathematics students and physicists as well.

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.- 4 Before and After the Vectorization.- 5 Parallel Computing.- IV REDUCE for Beginners - Seven Lectures on the Application of Computer-Algebra (CA).- First Lecture.- Second Lecture.- Third Lecture.- Fourth Lecture.- Fifth Lecture.- Sixth Lecture.- Seventh Lecture.- 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.