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Ellipsoidal Harmonics
Theory and Applications


Part of Encyclopedia of Mathematics and its Applications

  • Date Published: July 2012
  • availability: Available
  • format: Hardback
  • isbn: 9780521113090

£ 126.00

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About the Authors
  • 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.

    • Up to date with brand new results and material
    • Ideal for engineers and applied scientists who need to solve particular problems
    • May be used as a textbook for advanced undergraduate courses, graduate courses or special research topics
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    Product details

    • Date Published: July 2012
    • format: Hardback
    • isbn: 9780521113090
    • length: 474 pages
    • dimensions: 240 x 160 x 28 mm
    • weight: 0.86kg
    • contains: 32 b/w illus.
    • availability: Available
  • Table of Contents

    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
    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

  • Author

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

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