Asymptotic Expansions of Integrals

by Norman Bleistein, Richard A Handelsman

Asymptotic analysis, that branch of mathematics devoted to the study of the behavior of functions within chosen limits, was once thought of more as a specialized art than a necessary discipline. Now, a solid foundation in the theory and technique of asymptotic expansion of integrals is at the heart of the education of every student concentrating in applied mathematics. It is also an invaluable asset to scientists in many other fields.This excellent introductory text, written by two experts in the field, offers students of applied mathematics — and researchers and workers in other fields — a coherent and systematic presentation of the principles and methods of asymptotic expansions of integrals. Students will find each of the nine chapters useful and easy to comprehend; each begins with elementary material or informal introductions and concludes with an abundant selection of applicable problems and exercises. All that is needed is a basic understanding of calculus, differential equations, and complex variables.Practiced users of asymptotics will find the work a valuable reference with an extensive index locating all the functions covered in the text and every formula associated with the major techniques. Subjects include integration by parts, Watson's lemma, Laplace's method, stationary phase, and steepest descents. Also treated are the Mellin transform method and less elementary aspects of steepest descent. Each chapter is carefully illustrated with helpful diagrams and tables.Used for years as a text in classrooms throughout the country, the book has been revised and corrected for this inexpensive paperback edition. Any student or teacher looking for a suitable text for a year's or semester's course in asymptotics will value this affordable volume as the only comprehensive introduction available; scientists and researchers will undoubtedly refer to it again and again.

Genres: Mathematics

464 pages, Paperback

First published June 1, 1976

Reviews

[Mike Lisanke · Rating 1 out of 5]

This was not the book I was looking for. Far too much background was expected of the reader. I am an engineer and worked with a lot of mathematics and took graduate level courses in mathematics, but; I don't has encyclopedic knowledge of complex analysis; I did watch understandable videos on Asymptotic Expansions of Integrals and Perturbation Theory. I was expecting a textual representation with greater depth But seriously, many professors (esp. of math) love to bury the uninitiated in mounds of equations without clear step by step process in each example. This book has tons of these symbolic operations. Anyone who's enjoyed reading the book (taking the course from this book), please comment on the specific background required. Obtaining vales of functions at specific points without the ability to apply standard math seems very useful; but it appears I'll never know how! :-P