Description

Book Synopsis
A survey of asymptotic methods set in the applied research context of wave propagation. It stresses rigorous analysis in addition to formal manipulations. It is suitable for a beginning graduate course on asymptotic analysis in applied mathematics and is aimed at students of pure and applied mathematics as well as science and engineering.

Table of Contents
Fundamentals: Themes of asymptotic analysis The nature of asymptotic approximations Asymptotic analysis of exponential integrals: Fundamental techniques for integrals Laplace's method for asymptotic expansions of integrals The method of steepest descents for asymptotic expansions of integrals The method of stationary phase for asymptotic analysis of oscillatory integrals Asymptotic analysis of differential equations: Asymptotic behavior of solutions of linear second-order differential equations in the complex plane Introduction to asymptotics of solutions of ordinary differential equations with respect to parameters Asymptotics of linear boundary-value problems Asymptotics of oscillatory phenomena Weakly nonlinear waves Appendix: Fundamental inequalities Bibliography Index of names Subject index.

Applied Asymptotic Analysis

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    A Hardback by Peter D. Miller

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      Book details

      Publisher American Mathematical Society
      Published 6/30/2006 12:00:00 AM
      ISBN-13 9780821840788
      978-0821840788
      ISBN-10 0821840789
      Also in:
      Mathematics Calculus and mathematical analysis Quantum physics

      Description

      Book Synopsis
      A survey of asymptotic methods set in the applied research context of wave propagation. It stresses rigorous analysis in addition to formal manipulations. It is suitable for a beginning graduate course on asymptotic analysis in applied mathematics and is aimed at students of pure and applied mathematics as well as science and engineering.

      Table of Contents
      Fundamentals: Themes of asymptotic analysis The nature of asymptotic approximations Asymptotic analysis of exponential integrals: Fundamental techniques for integrals Laplace's method for asymptotic expansions of integrals The method of steepest descents for asymptotic expansions of integrals The method of stationary phase for asymptotic analysis of oscillatory integrals Asymptotic analysis of differential equations: Asymptotic behavior of solutions of linear second-order differential equations in the complex plane Introduction to asymptotics of solutions of ordinary differential equations with respect to parameters Asymptotics of linear boundary-value problems Asymptotics of oscillatory phenomena Weakly nonlinear waves Appendix: Fundamental inequalities Bibliography Index of names Subject index.

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