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

<p>“To the benefit of the reader, a summary presents a convenient overview on all special functions covered. Thus this book can serve as a reference text for advanced undergraduate students.” (<i>Zentralblatt MATH</i>, 2012)</p> <p>“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.”  (<i>Book News</i>, 1 April 2012)</p> <p>"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)</p> <p> </p>

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.<br> <br> 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.<br>

<i>Separable Boundary-Value Problems in Physics</i> 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. <p><b>From the contents:</b></p> <ul> <li> <div>Part I Preliminaries</div> </li> <li> <div>Introduction</div> </li> <li> <div>General Theory</div> </li> <li> <div>Part II Two-Dimensional Coordinate Systems</div> </li> <li> <div>Rectangular Coordinates</div> </li> <li> <div>Circular Coordinates</div> </li> <li> <div>Elliptic Coordinates</div> </li> <li> <div>Parabolic Coordinates</div> </li> <li> <div>Part III Three-Dimensional Coordinate Systems</div> </li> <li> <div>Rectangular Coordinates</div> </li> <li> <div>Circular Cylinder Coordinates</div> </li> <li> <div>Elliptic Cylinder Coordinates</div> </li> <li> <div>Parabolic Cylinder Coordinates</div> </li> <li> <div>Spherical Polar Coordinates</div> </li> <li> <div>Prolate Spheroidal Coordinates</div> </li> <li> <div>Oblate Spheroidal Coordinates</div> </li> <li> <div>Parabolic Rotational Coordinates</div> </li> <li> <div>Conical Coordinates</div> </li> <li> <div>Ellipsoidal Coordinates</div> </li> <li> <div>Paraboloidal Coordinates</div> </li> <li> <div>Part IV Advanced Formulations</div> </li> <li> <div>Differential-Geometric Formulations</div> </li> <li> <div>Quantum-Mechanical Particle Confined to the Neighborhood of Curves</div> </li> <li> <div>Quantum-Mechanical Particle Confined to Surfaces of Revolution</div> </li> <li> <div>Boundary Perturbation Theory</div> </li> <li> <div>Appendices</div> </li> <li> <div>Hypergeometric Functions</div> </li> <li> <div>Baer Functions</div> </li> <li> <div>Bessel Functions</div> </li> <li> <div>Lamé Functions</div> </li> <li> <div>Legendre Functions</div> </li> <li> <div>Mathieu Functions</div> </li> <li> <div>Spheroidal Wave Functions</div> </li> <li> <div>Weber Functions</div> </li> <li> <div>Elliptic Integrals and Functions</div> </li> </ul>

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