Geomathematically oriented potential theory
 Author/Creator
 Freeden, W.
 Language
 English.
 Publication
 Boca Raton : CRC Press/Taylor & Francis Group, [2013]
 Copyright notice
 ©2013
 Physical description
 xvi, 452 pages : illustrations ; 24 cm
 Series
 Monographs and textbooks in pure and applied mathematics ; 304.
Access
Available online

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QC178 .F66 2013

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QC178 .F66 2013
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Contributors
 Contributor
 Gerhards, Christian, 1982
Contents/Summary
 Bibliography
 Includes bibliographical references (pages 429447) and index.
 Contents

 PRELIMINARIES ThreeDimensional Euclidean Space R3 Basic Notation Integral Theorems TwoDimensional Sphere OMEGA Basic Notation Integral Theorems (Scalar) Spherical Harmonics (Scalar) Circular Harmonics Vector Spherical Harmonics Tensor Spherical Harmonics POTENTIAL THEORY IN THE EUCLIDEAN SPACE R3 Basic Concepts Background Material Volume Potentials Surface Potentials BoundaryValue Problems Locally and Globally Uniform Approximation Gravitation Oblique Derivative Problem Satellite Problems Gravimetry Problem Geomagnetism Geomagnetic Background Mie and Helmholtz Decomposition Gauss Representation and Uniqueness Separation of Sources Ionospheric Current Systems POTENTIAL THEORY ON THE UNIT SPHERE OMEGA Basic Concepts Background Material Surface Potentials Curve Potentials BoundaryValue Problems Differential Equations for Surface Gradient and Surface Curl Gradient Locally and Globally Uniform Approximation Gravitation Disturbing Potential Linear Regularization Method Multiscale Solution Geomagnetics Mie and Helmholtz Decomposition HigherOrder Regularization Methods Separation of Sources Ionospheric Current Systems Bibliography Index Exercises appear at the end of each chapter.
 (source: Nielsen Book Data)
 Publisher's Summary
 As the Earth's surface deviates from its spherical shape by less than 0.4 percent of its radius and today's satellite missions collect their gravitational and magnetic data on nearly spherical orbits, sphereoriented mathematical methods and tools play important roles in studying the Earth's gravitational and magnetic field. Geomathematically Oriented Potential Theory presents the principles of space and surface potential theory involving Euclidean and spherical concepts. The authors offer new insight on how to mathematically handle gravitation and geomagnetism for the relevant observables and how to solve the resulting potential problems in a systematic, mathematically rigorous framework. The book begins with notational material and the necessary mathematical background. The authors then build the foundation of potential theory in threedimensional Euclidean space and its application to gravitation and geomagnetism. They also discuss surface potential theory on the unit sphere along with corresponding applications. Focusing on the state of the art, this book breaks new geomathematical grounds in gravitation and geomagnetism. It explores modern sphereoriented potential theoretic methods as well as classical space potential theory.
(source: Nielsen Book Data)
Subjects
Bibliographic information
 Publication date
 2013
 Copyright date
 2013
 Responsibility
 Willi Freeden, University of Kaiserslautern, Germany, Christian Gerhards, University of Kaiserslautern, Germany.
 Series
 Pure and applied mathematics ; 304
 Note
 "A Chapman & Hall Book"
 ISBN
 9781439895429
 1439895422