Ellipsoidal Harmonics

NOTE EDITORE

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.

SOMMARIO

Prologue; 1. The ellipsoidal system and its geometry; 2. Differential operators in ellipsoidal geometry; 3. Lamé 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 Lamé equation; Appendix F. Table of formulae; Appendix G. Miscellaneous relations; Bibliography; Index.

PREFAZIONE

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.

AUTORE

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

ALTRE INFORMAZIONI

• Condizione: Nuovo
• ISBN: 9780521113090
• Collana: Encyclopedia of Mathematics and its Applications
• Dimensioni: 240 x 28 x 160 mm Ø 860 gr
• Formato: Copertina rigida
• Illustration Notes: 32 b/w illus.
• Pagine Arabe: 474