"This work explores and presents the principles of 'surface potential theory for the sphere,' in addition to those in the Euclidean space R3, and breaks new mathematical ground in dealing generically with potential theoretic aspects of gravitation and geomagnetism. The work covers a two-semester graduate course in the teaching cycle of geomathematics, but it can as well be used as a reference for researchers and aims at presenting the "state of the art" in three-dimensional Euclidean as well as two-dimensional spherical potential theory for applications in the geosciences"--
German mathematicians Freeden and Gerhards present a textbook for a two-semester graduate course within a geomathematics curriculum. They explain the theory of potentials concerned with the Laplace equation with a particular emphasis on the Earth's gravitational and magnetic field. Physics is required to understand the nature of gravitation or magnetics, they say, but their goal is to provide insight on how gravitation and magnetics can be geomathematically handled for the relevant observables, and how the resulting geopotential problems can be solved in a systematic, mathematically rigorous framework involving three-dimensional Euclidean space as well as spherical concepts. Annotation ©2012 Book News, Inc., Portland, OR (booknews.com)
PRELIMINARIES: Three-Dimensional Euclidean Space R3. Two-Dimensional
Sphere . POTENTIAL THEORY IN THE EUCLIDEAN SPACE R3: Basic Concepts.
Gravitation. Geomagnetism. POTENTIAL THEORY ON THE UNIT SPHERE : Basic
Concepts. Gravitation. Geomagnetics. Bibliography. Index.
Willi Freeden is a professor in the Geomathematics Group at the University of Kaiserslautern. Dr. Freeden is an editorial board member of seven international journals and was previously the editor-in-chief of the International Journal on Geomathematics. His research interests include special functions of mathematical (geo)physics, PDEs, constructive approximation, integral transforms, numerical methods, the use of mathematics in industry, and inverse problems in geophysics, geodesy, and satellite technology.
Christian Gerhards is a visiting postdoc researcher in the Department of Mathematics and Statistics at the University of New South Wales.
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