Separable Boundary-Value Problems in Physics
(Sprache: Englisch)
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...
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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.
Klappentext zu „Separable Boundary-Value Problems in Physics “
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.
Inhaltsverzeichnis zu „Separable Boundary-Value Problems in Physics “
Part I Preliminaries1. Introduction2. General TheoryPart II Two-Dimensional Coordinate Systems3. Rectangular Coordinates4. Circular Coordinates5. Elliptic Coordinates6. Parabolic CoordinatesPart III Three-Dimensional Coordinate Systems7. Rectangular Coordinates8. Circular Cylinder Coordinates9. Elliptic Cylinder Coordinates10. Parabolic Cylinder Coordinates11. Spherical Polar Coordinates12. Prolate Spheroidal Coordinates13. Oblate Spheroidal Coordinates14. Parabolic Rotational Coordinates15. Conical Coordinates16. Ellipsoidal Coordinates17. Paraboloidal CoordinatesPart IV Advanced Formulations18. Differential Geometric Formulations19. Quantum-mechanical Particle Confined to Neighborhood of Curves20. Quantum-mechanical Particle Confined to Surfaces of Revolution21. Boundary Perturbation TheoryAppendicesA Hypergeometric FunctionsB Baer FunctionsC Bessel FunctionsD Lamé FunctionsE Legendre FunctionsF Mathieu FunctionsG Spheroidal Wave FunctionsH Weber FunctionsI Elliptic Integrals and FunctionsIndex
Autoren-Porträt von Morten Willatzen, Lok C. Lew Yan Voon
Morten Willatzen is Head of Research at the Center for Product Innovation of the Mads Clausen Institute at the University of Southern Denmark. Having received his PhD from the Niels Bohr Institute at the University of Copenhagen, he held positions at Aarhus University, Max-Planck-Institute for Solid State Research, Germany, and Senior Scientist at Danfoss A/S, DK. In 2000 he became Associate Professor, in 2004 Full Professor at the University of Southern Denmark. Morten Willatzen's research interests include solid state physics, in particular quantum-confined structures and applications to semiconductor laser amplifiers, flow acoustics, and modelling of thermo-fluid systems.L. C. Lew Yan Voon is Professor and Chair of the Department of Physics at Wright State University. Educated in Cambridge, England, and Vancouver, Canada, he received his PhD from Worcester Polytechnic Institute, USA, where he held positions until 2004, with a stay at the Max-Planck-Institute for Solid State Research as an Alexander von Humboldt fellow. Dr. Lew Yan Voon was visiting scientist at the Air Force Research Laboratory, Hong Kong University of Science and Technology, Stanford University, and the University of Southern Denmark. Professor Lew Yan Voon received the Balslev Award (Denmark) and the NSF CAREER award. His research interests are in semiconductor theory and mathematical physics and involve the study of band structure theory and applications to nanostructures.
Bibliographische Angaben
- Autoren: Morten Willatzen , Lok C. Lew Yan Voon
- 2011, 1. Auflage., XXI, 377 Seiten, 60 Schwarz-Weiß-Abbildungen, 60 Abbildungen, Maße: 17,7 x 24,6 cm, Gebunden, Englisch
- Verlag: Wiley-VCH
- ISBN-10: 3527410201
- ISBN-13: 9783527410200
- Erscheinungsdatum: 06.04.2011
Sprache:
Englisch
Rezension zu „Separable Boundary-Value Problems in Physics “
"They also consider a range of special functions that can result, though they make clear this is not a text on special functions. The fundamental material is suitable for a one-semester course in partial differential equations at the graduate or senior level; the rest of the material can be used as self-study or more advanced courses." ( Book News , 1 April 2012) "The text is clear and direct with respect to the mathematics and physics presented. Summing Up: Recommended. Upper-division undergraduates, graduate students, and researchers/faculty." (Choice, 1 December 2011)
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