Separable Boundary–Value Problems in Physics

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.
From the contents:Part I PreliminariesIntroductionGeneral TheoryPart II Two–Dimensional Coordinate SystemsRectangular CoordinatesCircular CoordinatesElliptic CoordinatesParabolic CoordinatesPart III Three–Dimensional Coordinate SystemsRectangular CoordinatesCircular Cylinder CoordinatesElliptic Cylinder CoordinatesParabolic Cylinder CoordinatesSpherical Polar CoordinatesProlate Spheroidal CoordinatesOblate Spheroidal CoordinatesParabolic Rotational CoordinatesConical CoordinatesEllipsoidal CoordinatesParaboloidal CoordinatesPart IV Advanced FormulationsDifferential–Geometric FormulationsQuantum–Mechanical Particle Confined to the Neighborhood of CurvesQuantum–Mechanical Particle Confined to Surfaces of RevolutionBoundary Perturbation TheoryAppendicesHypergeometric FunctionsBaer FunctionsBessel FunctionsLamé FunctionsLegendre FunctionsMathieu FunctionsSpheroidal Wave FunctionsWeber FunctionsElliptic Integrals and Functions

Spis treści:
Preface.
Part One Preliminaries.
1 Introduction.
2 General Theory.
Part Two Two–Dimensional Coordinate Systems.
3 Rectangular Coordinates.
4 Circular Coordinates.
5 Elliptic Coordinates.
6 Parabolic Coordinates.
Part Three Three–Dimensional Coordinate Systems.
7 Rectangular Coordinates.
8 Circular Cylinder Coordinates.
9 Elliptic Cylinde r 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 Four Advanced Formulations.
18 Differential–Geometric Formulation.
19 Quantum–Mechanical Particle Confined to the Neighborhood of Curves.
20 Quantum–Mechanical Particle Confined to Surfaces of Revolution.
21 Boundary Perturbation Theory.
Appendix A Hypergeometric Functions.
Appendix B Baer Functions 305
Appendix C Bessel Functions.
Appendix D Lamé Functions.
Appendix E Legendre Functions.
Appendix F Mathieu Functions.
Appendix G Spheroidal Wave Functions.
Appendix H Weber Functions.
Appendix I Elliptic Integrals and Functions.
References.
Index.

Nota biograficzna:
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.

Okładka tylna:
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.
From the contents:Part I PreliminariesIntroductionGeneral TheoryPart II Two–Dimensional Coordinate SystemsRectangular CoordinatesCircular CoordinatesElliptic CoordinatesParabolic CoordinatesPart III Three–Dimensional Coordinate SystemsRectangular CoordinatesCircular Cylinder CoordinatesElliptic Cylinder CoordinatesParabolic Cylinder CoordinatesSpherical Polar CoordinatesProlate Spheroidal CoordinatesOblate Spheroidal CoordinatesParabolic Rotational CoordinatesConical CoordinatesEllipsoidal CoordinatesParaboloidal CoordinatesPart IV Advanced FormulationsDifferential–Geometric FormulationsQuantum–Mechanical Particle Confined to the Neighborhood of CurvesQuantum–Mechanical Particle Confined to Surfaces of RevolutionBoundary Perturbation TheoryAppendicesHypergeometric FunctionsBaer FunctionsBessel FunctionsLamé FunctionsLegendre FunctionsMathieu Functions< li>Spheroidal Wave FunctionsWeber FunctionsElliptic Integrals and Functions