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

Format:

Book

Author/Creator:

Dassios, G. (George), author.

Series:

Encyclopedia of mathematics and its applications ; v. 146.

Encyclopedia of mathematics and its applications ; volume 146

Language:

English

Subjects (All):

Lamé's functions.

Physical Description:

1 online resource (xvi, 458 pages) : digital, PDF file(s).

Place of Publication:

Cambridge : Cambridge University Press, 2012.

Language Note:

English

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.

Contents:

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 relations.

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Includes bibliographical references (pages 436-452) and index.

ISBN:

1-107-22259-1

1-280-77379-0

9786613684561

1-139-51722-8

1-139-51465-2

1-139-01774-8

1-139-51372-9

1-139-51630-2

1-139-51815-1

OCLC:

796383833