Separable Boundary-Value Problems in Physics / Edition 1

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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.

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Editorial Reviews

From the Publisher
“To the benefit of the reader, a summary presents aconvenient overview on all special functions covered. Thus thisbook can serve as a reference text for advanced undergraduatestudents.” (Zentralblatt MATH, 2012)

“They also consider a range of special functions that canresult, though they make clear this is not a text on specialfunctions. The fundamental material is suitable for a one-semestercourse in partial differential equations at the graduate or seniorlevel; the rest of the material can be used as self-study or moreadvanced courses.”  (Book News, 1 April 2012)

"The text is clear and direct with respect to the mathematicsand physics presented. Summing Up: Recommended. Upper-divisionundergraduates, graduate students, and researchers/faculty."(Choice, 1 December 2011)

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Product Details

  • ISBN-13: 9783527410200
  • Publisher: Wiley
  • Publication date: 6/7/2011
  • Edition number: 1
  • Pages: 398
  • Product dimensions: 6.70 (w) x 9.60 (h) x 0.90 (d)

Meet the Author

Morten Willatzen is Head of Research at the Center for ProductInnovation of the Mads Clausen Institute at the University ofSouthern Denmark. Having received his PhD from the Niels BohrInstitute at the University of Copenhagen, he held positions atAarhus University, Max-Planck-Institute for Solid State Research,Germany, and Senior Scientist at Danfoss A/S, DK. In 2000 he becameAssociate Professor, in 2004 Full Professor at the University ofSouthern Denmark. Morten Willatzen's research interests includesolid state physics, in particular quantum-confined structures andapplications to semiconductor laser amplifiers, flow acoustics, andmodelling of thermo-fluid systems.

L. C. Lew Yan Voon is Professor and Chair of the Department ofPhysics at Wright State University. Educated in Cambridge, England,and Vancouver, Canada, he received his PhD from WorcesterPolytechnic Institute, USA, where he held positions until 2004,with a stay at the Max-Planck-Institute for Solid State Research asan Alexander von Humboldt fellow. Dr. Lew Yan Voon was visitingscientist at the Air Force Research Laboratory, Hong KongUniversity of Science and Technology, Stanford University, and theUniversity of Southern Denmark. Professor Lew Yan Voon received theBalslev Award (Denmark) and the NSF CAREER award. His researchinterests are in semiconductor theory and mathematical physics andinvolve the study of band structure theory and applications tonanostructures.

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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 ofCurves
20. Quantum-mechanical Particle Confined to Surfaces ofRevolution
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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