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Advanced Mathematical Methods for Scientists and Engineers I - Asymptotic Methods and Perturbation Theory (Paperback, Softcover reprint of hardcover 1st ed. 1999)
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Advanced Mathematical Methods for Scientists and Engineers I - Asymptotic Methods and Perturbation Theory (Paperback, Softcover reprint of hardcover 1st ed. 1999)
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A clear, practical and self-contained presentation of the methods
of asymptotics and perturbation theory for obtaining approximate
analytical solutions to differential and difference equations.
Aimed at teaching the most useful insights in approaching new
problems, the text avoids special methods and tricks that only work
for particular problems. Intended for graduates and advanced
undergraduates, it assumes only a limited familiarity with
differential equations and complex variables. The presentation
begins with a review of differential and difference equations, then
develops local asymptotic methods for such equations, and explains
perturbation and summation theory before concluding with an
exposition of global asymptotic methods. Emphasizing applications,
the discussion stresses care rather than rigor and relies on many
well-chosen examples to teach readers how an applied mathematician
tackles problems. There are 190 computer-generated plots and tables
comparing approximate and exact solutions, over 600 problems of
varying levels of difficulty, and an appendix summarizing the
properties of special functions.
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