Separable Boundary-Value Problems in Physics / Edition 1

Separable Boundary-Value Problems in Physics / Edition 1

by Morten Willatzen, Lok C. Lew Yan Voon
     
 

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ISBN-10: 3527410201

ISBN-13: 9783527410200

Pub. Date: 06/07/2011

Publisher: Wiley

Innovative developments in science and technology require a thorough knowledge of applied mathematics, particularly in the field of differential equations and special functions. These are relevant in modeling and computing applications of electromagnetic theory and quantum theory, e.g. in photonics and nanotechnology. The problem of solving partial differential

Overview

Innovative developments in science and technology require a thorough knowledge of applied mathematics, particularly in the field of differential equations and special functions. These are relevant in modeling and computing applications of electromagnetic theory and quantum theory, e.g. in photonics and nanotechnology. The problem of solving partial differential equations remains an important topic that is taught at both the undergraduate and graduate level.

Separable Boundary-Value Problems in Physics is an accessible and comprehensive treatment of partial differential equations in mathematical physics in a variety of coordinate systems and geometry and their solutions, including a differential geometric formulation, using the method of separation of variables. With problems and modern examples from the fields of nano-technology and other areas of physics.

The fluency of the text and the high quality of graphics make the topic easy accessible. The organization of the content by coordinate systems rather than by equation types is unique and offers an easy access.

The authors consider recent research results which have led to a much increased pedagogical understanding of not just this topic but of many other related topics in mathematical physics, and which like the explicit discussion on differential geometry shows - yet have not been treated in the older texts. To the benefit of the reader, a summary presents a convenient overview on all special functions covered. Homework problems are included as well as numerical algorithms for computing special functions. Thus this book can serve as a reference text for advanced undergraduate students, as a textbook for graduate level courses, and as a self-study book and reference manual for physicists, theoretically oriented engineers and traditional mathematicians.

Product Details

ISBN-13:
9783527410200
Publisher:
Wiley
Publication date:
06/07/2011
Pages:
398
Product dimensions:
6.70(w) x 9.60(h) x 0.90(d)

Table of Contents

Part I Preliminaries
1. Introduction
2. General Theory
Part II Two-Dimensional Coordinate Systems
3. Rectangular Coordinates
4. Circular Coordinates
5. Elliptic Coordinates
6. Parabolic Coordinates
Part III Three-Dimensional Coordinate Systems
7. Rectangular Coordinates
8. Circular Cylinder Coordinates
9. Elliptic Cylinder Coordinates
10. Parabolic Cylinder Coordinates
11. Spherical Polar Coordinates
12. Prolate Spheroidal Coordinates
13. Oblate Spheroidal Coordinates
14. Parabolic Rotational Coordinates
15. Conical Coordinates
16. Ellipsoidal Coordinates
17. Paraboloidal Coordinates
Part IV Advanced Formulations
18. Differential Geometric Formulations
19. Quantum-mechanical Particle Confined to Neighborhood of Curves
20. Quantum-mechanical Particle Confined to Surfaces of Revolution
21. Boundary Perturbation Theory
Appendices
A Hypergeometric Functions
B Baer Functions
C Bessel Functions
D Lamé
Functions
E Legendre Functions
F Mathieu Functions
G Spheroidal Wave Functions
H Weber Functions
I Elliptic Integrals and Functions
Index

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