Author	Atkinson, Kendall. author
Title	Spherical Harmonics and Approximations on the Unit Sphere: An Introduction [electronic resource] / by Kendall Atkinson, Weimin Han
Imprint	Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2012
Connect to	http://dx.doi.org/10.1007/978-3-642-25983-8
Descript	IX, 244p. 19 illus., 11 illus. in color. online resource

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

1 Preliminaries -- 2 Spherical Harmonics -- 3 Differentiation and Integration over the Sphere -- 4 Approximation Theory -- 5 Numerical Quadrature -- 6 Applications: Spectral Methods

1. Mathematics
2. Integral equations
3. Differential equations
4. partial
5. Functions
6. special
7. Numerical analysis
8. Physics
9. Mathematics
10. Numerical Analysis
11. Special Functions
12. Approximations and Expansions
13. Integral Equations
14. Partial Differential Equations
15. Physics
16. general