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Multiple Scale and Singular Perturbation Methods (Paperback, Softcover reprint of the original 1st ed. 1996)
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Multiple Scale and Singular Perturbation Methods (Paperback, Softcover reprint of the original 1st ed. 1996)
Series: Applied Mathematical Sciences, 114
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Total price: R5,376
Discovery Miles: 53 760
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This book is a revised and updated version, including a substantial
portion of new material, of our text Perturbation Methods in
Applied Mathematics (Springer Verlag, 1981). We present the
material at a level that assumes some familiarity with the basics
of ordinary and partial differential equations. Some of the more
advanced ideas are reviewed as needed; therefore this book can
serve as a text in either an advanced undergraduate course or a
graduate-level course on the subject. Perturbation methods, first
used by astronomers to predict the effects of small disturbances on
the nominal motions of celestial bodies, have now become widely
used analytical tools in virtually all branches of science. A
problem lends itself to perturbation analysis if it is "close" to a
simpler problem that can be solved exactly. Typically, this
closeness is measured by the occurrence of a small dimensionless
parameter, E, in the governing system (consisting of differential
equations and boundary conditions) so that for E = 0 the resulting
system is exactly solvable. The main mathematical tool used is
asymptotic expansion with respect to a suitable asymptotic sequence
of functions of E. In a regular perturbation problem, a
straightforward procedure leads to a system of differential
equations and boundary conditions for each term in the asymptotic
expansion. This system can be solved recursively, and the accuracy
of the result improves as E gets smaller, for all values of the
independent variables throughout the domain of interest. We discuss
regular perturbation problems in the first chapter."
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