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Perturbation methods have always been an important tool for
treating nonlinear differential equations. Now the drudgery
associated with them has been eliminated! This book offers computer
algebra (MACSYMA) programs which implement the most popular
perturbation methods. Not only does this avoid the errors
associated with hand computation, but the increase in efficiency
permits more complicated problems to be tackled. This book is
useful both for the beginner learning perturbation methods for the
first time, as well as for the researcher. Methods covered include:
Lindstedt's method, center manifolds, normal forms, two variable
expansion method (method of multiple scales), averaging, Lie
transforms and Liapunov-Schmidt reduction. For each method the book
includes an introduction and some example problems solved both by
hand and by machine. The examples feature common bifurcations such
as the pitchfork and the Hopf. The MACSYMA code for each method is
given and suggested exercises are provided at the end of each
Chapter. An Appendix offers a brief introduction to MACSYMA.
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