Ellipsoidal Harmonics

Theory and Applications

By: George Dassios

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Hardcover | 12 July 2012 | Edition Number 1

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476 Pages

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23.39 x 15.6 x 3.02

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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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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 sphero-conal and ellipsoidal harmonics
The elliptic functions approach
Ellipsoidal bi-harmonic functions
Vector ellipsoidal harmonics
Applications to geometry
Applications to physics
Applications to low-frequency scattering theory
Applications to bioscience
Applications to inverse problems
Epilogue
Background material
Elements of dyadic analysis
Legendre functions and spherical harmonics
The fundamental polyadic integral
Forms of the Lamé equation
Table of formulae
Miscellaneous relations
Bibliography
Index
Table of Contents provided by Publisher. All Rights Reserved.

Ellipsoidal Harmonics

Theory and Applications

At a Glance

Hardcover

Shipping

How to return your order

Defective items

You Can Find This Book In

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