Spherical Harmonics and Approximations on the Unit Sphere: An Introduction

✍ Scribed by Atkinson, Kendall E;Han, Weimin

Publisher: Springer Berlin Heidelberg
Year: 2012
Tongue: English
Leaves: 253
Series: Lecture Notes in Mathematics 2044
Edition: 2012
Category: Library

No coin nor oath required. For personal study only.

✦ Synopsis

These notes provide an introduction to the theory of spherical harmonics in an arbitrary dimension as well as an overview of classical and recent results on some aspects of the approximation of functions by spherical polynomials and numerical integration over the unit sphere. The notes are intended for graduate students in the mathematical sciences and researchers who are interested in solving problems involving partial differential and integral equations on the unit sphere, especially on the unit sphere in three-dimensional Euclidean space. Some related work for approximation on the unit disk in the plane is also briefly discussed, with results being generalizable to the unit ball in more dimensions.

✦ Table of Contents

Spherical Harmonics and Approximations on the Unit Sphere: An Introduction......Page 4
Preface......Page 6
Contents......Page 8
Chapter1 Preliminaries......Page 11
Chapter2 Spherical Harmonics......Page 20
Chapter3 Differentiation and Integration over the Sphere......Page 96
Chapter4 Approximation Theory......Page 140
Chapter5 Numerical Quadrature......Page 173
Chapter6 Applications: Spectral Methods......Page 219
References......Page 245
Index......Page 250

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