Introduction to asymptotics : a treatment using nonstandard analysis / D.S. Jones.

Format:

Book

Author/Creator:

Jones, D. S. (Douglas Samuel)

Language:

English

Subjects (All):

Asymptotic expansions.

Physical Description:

1 online resource (177 p.)

Place of Publication:

River Edge, N.J. : World Scientific, 1997.

Language Note:

English

Summary:

Many branches of science and engineering involve applications of mathematical analysis. An important part of applied analysis is asymptotic approximation which is, therefore, an active area of research with new methods and publications being found constantly. This book gives an introduction to the subject sufficient for scientists and engineers to grasp the fundamental techniques, both those which have been known for some time and those which have been discovered more recently. The asymptotic approximation of both integrals and differential equations is discussed and the discussion includes hy

Contents:

Preface; Contents; Chapter 1 BASIC THEORY; 1.1 Introduction; 1.2 Asymptotic sequences; 1.3 Asymptotic expansions; 1.4 Operations on asymptotic expansions; 1.5 Power series; 1.6 A generalisation; 1.7 An illustration; Exercises on Chapter 1; Chapter 2 INTEGRALS; 2.1 Stirling's formula; 2.2 Laplace integrals; 2.3 Laplace-type integrals; 2.4 Complex contours; 2.5 Fourier integrals; 2.6 Method of stationary phase; 2.7 Expansions; Exercises on Chapter 2; Chapter 3 SERIES; 3.1 General results; 3.2 Power series; 3.3 Partial sums; 3.4 Asymptotic behaviour of an entire function

3.5 Partial sums of integrals3.6 Maclaurin series; 3.7 Optimal remainders; Exercises on Chapter 3; Chapter 4 UNIFORM ASYMPTOTICS; 4.1 A simple example; 4.2 The function J; 4.3 Pole near a saddle point; 4.4 Saddle point near an endpoint; 4.5 Coalescing saddle points; Exercises on Chapter 4; Chapter 5 HYPERASYMPTOTICS; 5.1 Introduction; 5.2 A Laplace integral; 5.3 Extensions; 5.4 Stieltjes transforms; 5.5 Stokes' phenomenon; Exercises on Chapter 5; Chapter 6 DIFFERENTIAL EQUATIONS; 6.1 The WKB approximation; 6.2 An error bound for the WKB approximation; 6.3 Effect of a parameter

6.4 Solutions in series6.5 An error bound for the series; 6.6 Connection formulae; 6.7 Hyperasymptotics; 6.8 Parameter with zero; Exercises on Chapter 6; Appendix INTRODUCTION TO NONSTANDARD ANALYSIS; A.1 Basic ideas; A.2 Sequences; A.3 Continuity; A.4 The derivative; A.5 Integration; REFERENCES; INDEX

Notes:

Description based upon print version of record.

Includes bibliographical references (p. 159-160) and index.

ISBN:

9789812779373

981277937X