Lecture Notes On Applied Analysis : Series In Analysis - Roderick S C Wong

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Lecture Notes On Applied Analysis

By: Roderick S C Wong

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Hardcover | 21 January 2010

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304 Pages

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15.8 x 23.0 x 1.9

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There are several subjects in analysis that are frequently used in applied mathematics, theoretical physics and engineering sciences, such as complex variable, ordinary differential equations, special functions, asymptotic methods, integral transforms and distribution theory. However, for graduate students or upper-level undergraduate students who are not going to specialize in these areas, there is no need for them to study these subjects in great depth. Instead, it would probably be more beneficial for them to have an introduction to these topics so that when the need arises, they know what approach to take. With this in mind, this set of lecture notes has been written for a one-semester course. Sufficient details have also been included to make it sufficiently adaptable for self-study. There are in total six chapters with each covering only a few topics. Furthermore, the chapters are all self-contained. The prerequisites for the readers of this book are advanced calculus, a first course in ordinary differential equations and elementary complex variable.

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Preface	p. vii
Complex Analysis	p. 1
Cauchy's theorm	p. 1
One-to-One and Analytic Functions	p. 9
Darboux's Method	p. 17
Riemann-Hilbert Problems	p. 26
Exercises	p. 35
Ordinary Differential Equations	p. 43
Regular Singularity	p. 43
Integral Representations	p. 54
Some Useful Transformations	p. 62
Boundedness, Oscillation and Stability	p. 70
Exercises	p. 80
Special Functions	p. 87
Hypergeometric Function	p. 87
Bessel Functions	p. 99
Legendre Functions	p. 115
Orthogonal Polynomials	p. 128
Exercises	p. 141
Asymptotic Expansions	p. 149
Fundamentals	p. 149
Method of Steepest Descents	p. 160
Irregular Singularities	p. 177
WKB Method and Turning Point	p. 186
Exercises	p. 197
Integral Transforms	p. 205
Fourier Transforms	p. 205
Laplace Transforms	p. 213
Hankel Transforms	p. 223
Mellin Transforms	p. 232
Exercises	p. 239
Distribution Theory	p. 247
The Dirac Delta Function	p. 247
Differentiation and Schwartz Space	p. 255
Asymptotic Expansions of Stieltjes Transforms	p. 262
Integral and Series Representations	p. 272
Exercises	p. 281
Index	p. 287
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Lecture Notes On Applied Analysis

At a Glance

Hardcover

Shipping

How to return your order

Defective items

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