Custom cover image
Custom cover image

Ellipsoidal harmonics : theory and applications / George Dassios, University of Patras, Greece

By: Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: Encyclopedia of mathematics and its applications ; volume 146Publisher: Cambridge : Cambridge University Press, 2012Description: 1 Online-Ressource (xvi, 458 pages) : digital, PDF file(s)ISBN:
  • 9781139017749
Subject(s): Additional physical formats: 9780521113090 | 9780521113090. | Erscheint auch als: Ellipsoidal harmonics. Cambridge [u.a.] : Cambridge Univ. Press, 2012. XVI, 458 S. | Erscheint auch als: 9780521113090 Druck-AusgabeDDC classification:
  • 515/.53
MSC: MSC: *35-02 | 35J05 | 33E05 | 33C55 | 33-02 | 33E10 | 31B30LOC classification:
  • QA409
DOI: DOI: 10.1017/CBO9781139017749Online resources: 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, 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.Summary: 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 relationsOriginal version: Originalfassung: 2012PPN: PPN: 883377403Package identifier: Produktsigel: ZDB-20-CTM | ZDB-20-CBO
No physical items for this record

2012

KIT – The Research University in the Helmholtz Association                         Home | Impressum | Datenschutz | Barrierefreiheit | KIT