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Ellipsoidal harmonics : theory and applications

Author: G Dassios
Publisher: Cambridge, UK : Cambridge University Press, 2012.
Series: Encyclopedia of mathematics and its applications, v. 146.
Edition/Format:   Book : EnglishView all editions and formats
Database:WorldCat
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,  Read more...
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Details

Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: G Dassios
ISBN: 9780521113090 0521113091
OCLC Number: 774016637
Description: xvi, 458 pages : illustrations ; 25 cm.
Contents: Prologue --
The ellipsoidal system and its geometry --
Differential operators in ellipsoidal geometry --
Lamé functions --
Ellipsoidal harmonics --
The theory of Niven and Cartesian harmonics --
Integration techniques --
Boundary value problems in ellipsoidal geometry --
Connection between harmonics --
The elliptic functions approach --
Ellipsoidal biharmonic functions --
Vector ellipsoidal harmonics --
Applications to geometry --
Applications to physics --
Applications to low-frequency scattering theory --
Applications to bioscience --
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 Lamé equation --
Appendix F. Table of formulae --
Appendix G. Miscellaneous relations.
Series Title: Encyclopedia of mathematics and its applications, v. 146.
Responsibility: George Dassios, University of Patras, Greece.

Abstract:

"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 bi-harmonic 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. End-of-chapter 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"--
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