Ellipsoidal harmonics : theory and applications
 Author/Creator
 Dassios, G. (George)
 Language
 English.
 Imprint
 Cambridge, UK : Cambridge University Press, 2012, ©2012.
 Physical description
 xvi, 458 pages : illustrations ; 24 cm.
 Series
 Encyclopedia of mathematics and its applications ; v. 146.
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Contents/Summary
 Bibliography
 Includes bibliographical references (pages [436]452) and index.
 Contents

 Prologue 1. The ellipsoidal system and its geometry 2. Differential operators in ellipsoidal geometry 3. Lame functions 4. Ellipsoidal harmonics 5. The theory of Niven and Cartesian harmonics 6. Integration techniques 7. Boundary value problems in ellipsoidal geometry 8. Connection between spheroconal and ellipsoidal harmonics 9. The elliptic functions approach 10. Ellipsoidal biharmonic functions 11. Vector ellipsoidal harmonics 12. Applications to geometry 13. Applications to physics 14. Applications to lowfrequency scattering theory 15. Applications to bioscience 16. Applications to inverse problems Epilogue Appendix A. Background material Appendix B. Elements of dyadic analysis Appendix C. Legendre functions and spherical harmonics Appendix D. The fundamental polyadic integral Appendix E. Forms of the Lame equation Appendix F. Table of formulae Appendix G. Miscellaneous relations Bibliography Index.
 (source: Nielsen Book Data)
 Publisher's Summary
 The sphere is what might be called a perfect shape. Unfortunately nature is imperfect and many bodies are better represented by an ellipsoid. The theory of ellipsoidal harmonics, originated in the nineteenth century, could only be seriously applied with the kind of computational power available in recent years. This, therefore, is the first book devoted to ellipsoidal harmonics. Topics are drawn from geometry, physics, biosciences and inverse problems. It contains classical results as well as new material, including ellipsoidal biharmonic functions, the theory of images in ellipsoidal geometry and vector surface ellipsoidal harmonics, which exhibit an interesting analytical structure. Extended appendices provide everything one needs to solve formally boundary value problems. Endofchapter problems complement the theory and test the reader's understanding. The book serves as a comprehensive reference for applied mathematicians, physicists, engineers and for anyone who needs to know the current state of the art in this fascinating subject.
(source: Nielsen Book Data)
Subjects
 Subject
 Lamé's functions.
Bibliographic information
 Publication date
 2012
 Copyright date
 2012
 Responsibility
 George Dassios.
 Series
 Encyclopedia of mathematics and its applications ; 146
 ISBN
 9780521113090
 0521113091