<p>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.</p>

Advanced Mathematical Methods for Scientists and Engineers (International Series in Pure and Applied Mathematics)

Science & Math

Bender, Carl M.

Orszag, Steven A.

Mathematics

Mcgraw-Hill College

Advanced Mathematical Methods for Scientists and Engineers: Asymptotic Methods and Perturbation Theory

Springer

<p>A unified discussion of the formulation and analysis of special methods of mixed initial boundary-value problems. The focus is on the development of a new mathematical theory that explains why and how well spectral methods work. Included are interesting extensions of the classical numerical analysis.</p>

Numerical Analysis of Spectral Methods: Theory and Applications (CBMS-NSF Regional Conference Series in Applied Mathematics, Series Number 26)

Gottlieb, David

Society for Industrial and Applied Mathematics

Advanced Mathematical Methods for Scientists and Engineers I: Asymptotic Methods and Perturbation Theory

Bender, Carl M. M.

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