Asymptotic Expansions of Integrals (Dover Books on Mathematics)

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.