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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Vector & tensor analysis
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Introduction to Asymptotic Methods (Paperback)
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Introduction to Asymptotic Methods (Paperback)
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Among the theoretical methods for solving many problems of applied
mathematics, physics, and technology, asymptotic methods often
provide results that lead to obtaining more effective algorithms of
numerical evaluation. Presenting the mathematical methods of
perturbation theory, Introduction to Asymptotic Methods reviews the
most important methods of singular perturbations within the scope
of application of differential equations. The authors take a
challenging and original approach based on the integrated
mathematical-analytical treatment of various objects taken from
interdisciplinary fields of mechanics, physics, and applied
mathematics. This new hybrid approach will lead to results that
cannot be obtained by standard theories in the field. Emphasizing
fundamental elements of the mathematical modeling process, the book
provides comprehensive coverage of asymptotic approaches, regular
and singular perturbations, one-dimensional non-stationary
non-linear waves, Pade approximations, oscillators with negative
Duffing type stiffness, and differential equations with
discontinuous nonlinearities. The book also offers a method of
construction for canonical variables transformation in parametric
form along with a number of examples and applications. The book is
applications oriented and features results and literature citations
that have not been seen in the Western Scientific Community. The
authors emphasize the dynamics of the development of perturbation
methods and present the development of ideas associated with this
wide field of research.
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