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AuthorStauffer, Dietrich. author
TitleComputer Simulation and Computer Algebra [electronic resource] : Lectures for Beginners / by Dietrich Stauffer, Friedrich W. Hehl, Volker Winkelmann, John G. Zabolitzky
ImprintBerlin, Heidelberg : Springer Berlin Heidelberg, 1988
Connect tohttp://dx.doi.org/10.1007/978-3-642-97091-7
Descript IX, 155 p. online resource

SUMMARY

Computers play an increasingly important role in many of today's activities, and correspondingly physicists find employment after graduation in computerยญ related jobs, often quite remote from their physics education. The present lectures, on the other hand, emphasize how we can use computers for the purposes of fundamental research in physics. Thus we do not deal with programs designed for newspapers, banks, or travel agencies, i.e., word processing and storage of large amounts of data. Instead, our lectures concentrate on physics problems, where the computer often has to work quite hard to get a result. Our programs are necessarily 5 quite short, excluding for example quantum chemistry programs with 10 program lines. The reader will learn how to handle computers for well-defined purposes. Therefore, in the end, this course will also enable him to orient himself in computer-related jobs. The first chapter deals mainly with solutions of the Newtonian equation of motion, that force equals mass times acceleration, which is a precursor to the molecular dynamics method in statistical physics. The second chapยญ ter considers, by means of several examples, another method for statistical physics, Monte Carlo simulation. These two chapters deal with numbers, the traditional territory of computers. In contrast, analytic formula manipulation, 3 5 4 3 such as (a+27b -4c)5 = a + 135a b - ... , is taught in the last chapter and is important, for instance, in analytic integration or for evaluating expressions in Einstein's general theory of relativity


CONTENT

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 -- 3. Reduce for Beginners. Six Lectures on the Application of Computer-Algebra (CA) -- Lecture 1 -- Lecture 2 -- Lecture 3 -- Lecture 4 -- Lecture 5 -- Lecture 6 -- References -- 4. Appendix: A Short Introduction to FORTRAN


Mathematics Computer simulation Computer software Physics Mathematics Mathematical Software Simulation and Modeling Mathematical Methods in Physics Numerical and Computational Physics



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