Spherical Harmonics and Approximations on the Unit Sphere: An Introduction

✍ Scribed by Kendall Atkinson, Weimin Han (auth.)

Publisher: Springer-Verlag Berlin Heidelberg
Year: 2012
Tongue: English
Leaves: 253
Series: Lecture Notes in Mathematics 2044
Edition: 1
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

Front Matter....Pages i-ix
Preliminaries....Pages 1-9
Spherical Harmonics....Pages 11-86
Differentiation and Integration over the Sphere....Pages 87-130
Approximation Theory....Pages 131-163
Numerical Quadrature....Pages 165-210
Applications: Spectral Methods....Pages 211-236
Back Matter....Pages 237-244

✦ Subjects

Numerical Analysis;Special Functions;Approximations and Expansions;Integral Equations;Partial Differential Equations;Physics, general

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