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  3. Ellipsoidal Harmonics
  • Cited by 67
Publisher:
Cambridge University Press
Online publication date:
August 2012
Print publication year:
2012
Online ISBN:
9781139017749
DOI:
https://doi.org/10.1017/CBO9781139017749
Subjects:
Mathematics (general), Mathematics, Differential and Integral Equations, Dynamical Systems and Control Theory, Mathematical Modeling and Methods
Series:
Encyclopedia of Mathematics and its Applications (146)
Information

Book description

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.

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Contents

Contents
References
Bibliography
References
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