MARC Record from Library of Congress

LEADER: 03416cam a2200349 i 4500
001 2011051233
003 DLC
005 20130105083004.0
008 111212s2012 enka b 001 0 eng
010 $a 2011051233
020 $a9780521113090 (hardback)
040 $aDLC$beng$cDLC$erda$dDLC
042 $apcc
050 00 $aQA409$b.D37 2012
082 00 $a515/.53$223
084 $aMAT000000$2bisacsh
100 1 $aDassios, G.$q(George)
245 10 $aEllipsoidal harmonics :$btheory and applications /$cGeorge Dassios, University of Patras, Greece.
264 1 $aCambridge, UK :$bCambridge University Press,$c2012.
300 $axvi, 458 pages :$billustrations ;$c25 cm.
336 $atext$2rdacontent
337 $aunmediated$2rdamedia
338 $avolume$2rdacarrier
490 0 $aEncyclopedia of mathematics and its applications ;$v146
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.
504 $aIncludes bibliographical references (pages 436-452) and index.
505 8 $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.
650 0 $aLamé's functions.
650 7 $aMATHEMATICS / General.$2bisacsh
856 42 $3Contributor biographical information$uhttp://www.loc.gov/catdir/enhancements/fy1205/2011051233-b.html
856 42 $3Publisher description$uhttp://www.loc.gov/catdir/enhancements/fy1205/2011051233-d.html
856 41 $3Table of contents only$uhttp://www.loc.gov/catdir/enhancements/fy1205/2011051233-t.html