Geomathematically Oriented Potential Theory

ISBN: 9781439895429 出版年：2012 页码：466 Freeden, Willi Gerhards, Christian CRC Press

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.