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008 120606t2012 enk f 001 0 eng d
020 _a9780521113090
039 9 _a201301141236
_basmadi
_y201206061209
_zsafura
040 _aUMP
090 _aQA409 .D37 2012
100 1 _aDassios, George
245 1 0 _aEllipsoidal harmonics :
_btheory and applications /
_cGeorge Dassios
260 _aCambridge, UK :
_bCambridge University Press,
_c2012
300 _axvi, 458 p. :
_bill. ;
_c25 cm.
490 1 _aEncyclopedia of mathematics and its applications ;
_v146
504 _aIncludes bibliographical references (pages 436-452) and index
505 0 _aMachine generated contents note: 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
520 _a"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"--
_cProvided by publisher
650 0 _aLamé’s functions
830 0 _aEncyclopedia of mathematics and its applications ;
_v146
999 _aVIRTUA40
_c63127
_d63133
999 _aVTLSSORT0080*0200*0400*0900*1000*2450*2600*3000*4900*5040*5050*5200*6500*8300*9992