Mathematics for the Physical Sciences

Leslie Copley

Open Access Published by De Gruyter Open Poland 2015

Mathematics for the Physical Sciences

Leslie Copley

https://doi.org/10.2478/9783110409475

Overview
Contents

About this book

The book begins with a thorough introduction to complex analysis, which is then used to understand the properties of ordinary differential equations and their solutions. The latter are obtained in both series and integral representations. Integral transforms are introduced, providing an opportunity to complement complex analysis with techniques that flow from an algebraic approach. This moves naturally into a discussion of eigenvalue and boundary vale problems. A thorough discussion of multi-dimensional boundary value problems then introduces the reader to the fundamental partial differential equations and “special functions” of mathematical physics. Moving to non-homogeneous boundary value problems the reader is presented with an analysis of Green’s functions from both analytical and algebraic points of view. This leads to a concluding chapter on integral equations.

A text on advanced mathematical methods with numerous applications, detailed derivations and solutions, and a unique range of practical topics.

Author / Editor information

Leslie Copley, Professor Emeritus of Physics, Carleton University, Canada.

Topics

Frontmatter Publicly Available Download PDF	I
Contents Publicly Available Download PDF	V
Foreword Publicly Available Download PDF	X
1 Functions of a Complex Variable Publicly Available Download PDF	1
2 Cauchy’s Theorem Publicly Available Download PDF	46
3 The Calculus of Residues Publicly Available Download PDF	90
4 Dispersion Representations Publicly Available Download PDF	125
5 Analytic Continuation Publicly Available Download PDF	133
6 Asymptotic Expansions Publicly Available Download PDF	150
7 Padé Approximants Publicly Available Download PDF	163
8 Fourier Series and Transforms Publicly Available Download PDF	180
9 Ordinary Linear Differential Equations Publicly Available Download PDF	234
10 Partial Differential Equations and Boundary Value Problems Publicly Available Download PDF	279
11 Special Functions Publicly Available Download PDF	313
12 Non-Homogeneous Boundary Value Problems: Green’s Functions Publicly Available Download PDF	384
13 Integral Equations Publicly Available Download PDF	418
Bibliography Publicly Available Download PDF	434

(Deutsch)

Language: English
Publisher: De Gruyter Open Poland
Audience: Senior undergraduate and graduate students in the physical sciences and engineering.
Pages
- Main content: 446
Illustrations
- Illustrations: 54
- Coloured Illustrations: 6
- Tables: 6
Keywords: mathematical physics; boundary value problems

eBook

Published: December 15, 2014
ISBN: 9783110409475

Hardcover

Published: December 15, 2014
ISBN: 9783110409451