Asymptotic Analysis of Differential Equations 1st Edition by Roscoe White 9781848166073 1848166079
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Product details:
ISBN 10: 1848166079
ISBN 13: 9781848166073
Author: Roscoe B White
The book gives the practical means of finding asymptotic solutions to differential equations, and relates WKB methods, integral solutions, Kruskal-Newton diagrams, and boundary layer theory to one another. The construction of integral solutions and analytic continuation are used in conjunction with the asymptotic analysis, to show the interrelatedness of these methods. Some of the functions of classical analysis are used as examples, to provide an introduction to their analytic and asymptotic properties, and to give derivations of some of the important identities satisfied by them. The emphasis is on the various techniques of analysis: obtaining asymptotic limits, connecting different asymptotic solutions, and obtaining integral representation.
Table of contents:
1 Dominant Balance
2 Exact Solutions
3 Complex Variables
4 Local Approximate Solutions
5 Phase-Integral Methods I
6 Perturbation Theory
7 Asymptotic Evaluation of Integrals
8 The Euler Gamma Function
9 Integral Solutions
10 Expansion in Basis Functions
11 Airy
12 Phase-Integral Methods II
13 Bessel
14 Weber and Hermite
15 Whittaker and Watson
16 Inhomogeneous Differential Equations
17 The Riemann Zeta Function
18 Boundary Layer Problems
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Tags: Roscoe White, Asymptotic, Analysis, Differential