Publisher Description

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. 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.

Author Biography

George Dassios is Professor of Applied Mathematics at the University of Patras, Greece and at ICE-FT/FORTH (a research institute in Greece).

Table of 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 sphero-conal and ellipsoidal harmonics; 9. The elliptic functions approach; 10. Ellipsoidal bi-harmonic functions; 11. Vector ellipsoidal harmonics; 12. Applications to geometry; 13. Applications to physics; 14. Applications to low-frequency 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.

Promotional "Headline"

The first book devoted to ellipsoidal harmonics presents the state of the art in this fascinating subject.

Description for Bookstore

The first book in the literature devoted to ellipsoidal harmonics includes topics drawn from geometry, physics, biosciences and inverse problems. It serves as a reference for applied mathematicians and for anyone else who needs to know the current state of the art in this fascinating subject.

Description for Library

The first book in the literature devoted to ellipsoidal harmonics includes topics drawn from geometry, physics, biosciences and inverse problems. It serves as a reference for applied mathematicians and for anyone else who needs to know the current state of the art in this fascinating subject.

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