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Ellipsoidal Harmonics
Author: George Dassios
Publisher: Cambridge University Press
Published: 2012-07-12
Total Pages: 475
ISBN-13: 0521113091
DOWNLOAD EBOOK →The first book devoted to ellipsoidal harmonics presents the state of the art in this fascinating subject.
An Elementary Treatise on Fourier's Series and Spherical, Cylindrical, and Ellipsoidal Harmonics
An Elementary Treatise on Fourier's Series and Spherical, Cylindric, and Ellipsoidal Harmonics
Author: William Elwood Byerly
Publisher: Cosimo, Inc.
Published: 2007-01-01
Total Pages: 301
ISBN-13: 1602063052
DOWNLOAD EBOOK →First published in 1893, Byerly's classic treatise on Fourier's series and spherical, cylindrical, and ellipsoidal harmonics has been used in classrooms for well over a century. This practical exposition acts as a primer for fields such as wave mechanics, advanced engineering, and mathematical physics. Topics covered include: . development in trigonometric series . convergence on Fourier's series . solution of problems in physics by the aid of Fourier's integrals and Fourier's series . zonal harmonics . spherical harmonics . cylindrical harmonics (Bessel's functions) . and more. Containing 190 exercises and a helpful appendix, this reissue of Fourier's Series will be welcomed by students of higher mathematics everywhere. American mathematician WILLIAM ELWOOD BYERLY (1849-1935) also wrote Elements of Differential Calculus (1879) and Elements of Integral Calculus (1881).
An Elemenatary Treatise on Fourier's Series, and Spherical, Cylindrical, and Ellipsoidal Harmonics, with Applications to Problems in Mathematical Physics
The Theory of Spherical and Ellipsoidal Harmonics
Ellipsoidal Harmonics
Author:
Publisher:
Published: 2012
Total Pages: 440
ISBN-13: 9781107263420
DOWNLOAD EBOOK →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.
The Ultimate Image Singularities for External Spheroidal and Ellipsoidal Harmonics
Author: Touvia Miloh
Publisher:
Published: 1973
Total Pages: 32
ISBN-13:
DOWNLOAD EBOOK →The image system of singularities of an arbitrary exterior potential field within a tri-axial ellipsoid is derived. It is found that the image system consists of a source and doublet distribution over the fundamental ellipsoid. The present contribution is a generalization of previous theories on the image system of an exterior potential field within a sphere and spheroid. A proof of Havelock's spheroid theorem which apparently is not available in the literature is also given. The knowledge of the image system is required, for example, when hydrodynamical forces and moments acting on an ellipsoid immersed in a potential flow are computed by the Lagally theorem. The two examples given consider the image system of singularities of an ellipsoid in a uniform translatory motion and in pure rotation. (Author).
Handbook of Geomathematics
Author: Willi Freeden
Publisher: Springer Science & Business Media
Published: 2010-08-13
Total Pages: 1371
ISBN-13: 364201545X
DOWNLOAD EBOOK →During the last three decades geosciences and geo-engineering were influenced by two essential scenarios: First, the technological progress has changed completely the observational and measurement techniques. Modern high speed computers and satellite based techniques are entering more and more all geodisciplines. Second, there is a growing public concern about the future of our planet, its climate, its environment, and about an expected shortage of natural resources. Obviously, both aspects, viz. efficient strategies of protection against threats of a changing Earth and the exceptional situation of getting terrestrial, airborne as well as spaceborne data of better and better quality explain the strong need of new mathematical structures, tools, and methods. Mathematics concerned with geoscientific problems, i.e., Geomathematics, is becoming increasingly important. The ‘Handbook Geomathematics’ as a central reference work in this area comprises the following scientific fields: (I) observational and measurement key technologies (II) modelling of the system Earth (geosphere, cryosphere, hydrosphere, atmosphere, biosphere) (III) analytic, algebraic, and operator-theoretic methods (IV) statistical and stochastic methods (V) computational and numerical analysis methods (VI) historical background and future perspectives.
The Theory of Spherical and Ellipsoidal Harmonics
