1st Edition
Geomathematically Oriented Potential Theory
PRELIMINARIES
Three-Dimensional Euclidean Space R3
Basic Notation
Integral Theorems
Two-Dimensional Sphere Ω
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 Ω
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.
Biography
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.
