Computer algebra recipes. A gourmet's guide to the mathematical models of science. Incl. 1 CD-ROM (Q5942926)

This textbook is a readable introduction to Maple, a computer algebra system. The authors present real life situations, describe them in the language of mathematics, and then use Maple to find or deduce conclusions, predictions and classifications of each of these situations. The book is divided into three parts. The first part contains a description of basic commands of Maple. The reader is introduced to the ways in which construct the graph representing given data, to linear correlation and linear regression, to the graph of an analytic function best-fitting the given data, to solving linear, trigonometric and logarithmic equations, coordinate transformations, numerical integration (by the Monte Carlo method), the random walk, and to matrix calculus. Practical recipes for analytic and numerical solution of ordinary differential and difference equations form the contents of the second part of the book, along with recipes for fractal geometry. The third part is devoted to investigations of the behaviour of nonlinear dynamical systems. Here the reader finds recipes for solving partial differential equations (Laplace transform, Fourier transform, separation of variables), for solving optimization problems and for investigation of Fourier series. Measures of confidence or tests of likelihood for functions computed from the given data are not discussed. The book studies numerous topics, but (with a few exceptions) neither the methods for mathematical description of a given situation nor mathematical methods for investigation of the models obtained are presented. The presentation contains many small inaccuracies; to an expert familiar with the topic these may be only inconsequential misprints, but to a student from another field they may well become real obstacles.