Symbolic Recipes

This book gives examples of symbolic manipulation in actual use, for senior students and researchers in other fields. The programs in the book are of intrinsic interest, but their main purpose is to exhibit a useful programming style in Maple. The book is organized into two main parts: part I deals with exact computation, and covers topics from linear algebra, polynomial manipulation, calculus, special functions, integral equations, and the calculus of variations. Part II deals with approximate analytical methods, such as numerical quadrature, the use of Chebyshev series, and Lanczos's tau method. A new symbolic study of the method of modified equations shows how computer algebra can aid in the numerical analysis of chaotic dynamical systems, and gives an example of solving a PDE arising in heat transfer.