Geomathematically oriented potential theory
- Freeden, W.
- Boca Raton : CRC Press/Taylor & Francis Group, 
- Copyright notice
- Physical description
- xvi, 452 pages : illustrations ; 24 cm
- Monographs and textbooks in pure and applied mathematics ; 304.
QC178 .F66 2013
- Unknown QC178 .F66 2013
- Gerhards, Christian, 1982-
- Includes bibliographical references (pages 429-447) and index.
- PRELIMINARIES Three-Dimensional Euclidean Space R3 Basic Notation Integral Theorems Two-Dimensional 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 Boundary-Value 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 Boundary-Value 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 Higher-Order 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, sphere-oriented 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 three-dimensional 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 sphere-oriented potential theoretic methods as well as classical space potential theory.
(source: Nielsen Book Data)
- Publication date
- Copyright date
- Willi Freeden, University of Kaiserslautern, Germany, Christian Gerhards, University of Kaiserslautern, Germany.
- Pure and applied mathematics ; 304
- "A Chapman & Hall Book"