Advanced Mathematical Methods for Scientists and Engineers: Asymptotic
by Carl M. Bender, Steven A. Orszag
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Book Summary Information
Author: Carl M. Bender, Steven A. OrszagEdition: Hardcover
Audio: English (Original Language); English (Unknown); English (Published)
Published: 1999-10-29
ISBN: 0387989315
Number of pages: 593
Publisher: Springer
Accessories:
- Elementary Analysis: The Theory of Calculus
- Metric Spaces (Springer Undergraduate Mathematics Series)
- Mathematics and its History
Book Reviews of Advanced Mathematical Methods for Scientists and Engineers: Asymptotic
Book Review: Still the Best
Summary: 5 Stars
I used this book in grad school about 15 years ago and got it out again yesterday to learn more about sophisticated path deformations in the complex plane. This style of going through interesting examples, pointing out possible trouble and explaining the main ideas is perfect for physicists who need advanced math tools but hate typical math papers of the proof-lemma-proof-type.
It's not outdated, symbolic math software can do a lot, but often can't handle the full problem and you have to simplify by hand before starting the computer.
Summary of Advanced Mathematical Methods for Scientists and Engineers: Asymptotic
This book gives a clear, practical and self-contained presentation of the methods of asymptotics and perturbation theory and explains how to use these methods to obtain approximate analytical solutions to differential and difference equations. These methods allow one to analyze physics and engineering problems that may not be solvable in closed form and for which brute-force numerical methods may not converge to useful solutions. The objective of this book is to teaching the insights and problem-solving skills that are most useful in solving mathematical problems arising in the course of modern research. Intended for graduate students and advanced undergraduates, the book assumes only a limited familiarity with differential equations and complex variables. The presentation begins with a review of differential and difference equations; develops local asymptotic methods for differential and difference equations; explains perturbation and summation theory; and concludes with a an exposition of global asymptotic methods, including boundary-layer theory, WKB theory, and multiple-scale analysis. Emphasizing applications, the discussion stresses care rather than rigor and relies on many well-chosen examples to teach the reader 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.General Books
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