Atkinson, Kendall.
Spherical Harmonics and Approximations on the Unit Sphere: An Introduction [electronic resource] / by Kendall Atkinson, Weimin Han. - Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2012. - IX, 244p. 19 illus., 11 illus. in color. online resource. - Lecture Notes in Mathematics, 2044 0075-8434 ; . - Lecture Notes in Mathematics, 2044 .
1 Preliminaries -- 2 Spherical Harmonics -- 3 Differentiation and Integration over the Sphere -- 4 Approximation Theory -- 5 Numerical Quadrature -- 6 Applications: Spectral Methods.
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.
9783642259838
10.1007/978-3-642-25983-8 doi
Mathematics.
Integral equations.
Differential equations, partial.
Functions, special.
Numerical analysis.
Physics.
Mathematics.
Numerical Analysis.
Special Functions.
Approximations and Expansions.
Integral Equations.
Partial Differential Equations.
Physics, general.
QA297-299.4
518
Spherical Harmonics and Approximations on the Unit Sphere: An Introduction [electronic resource] / by Kendall Atkinson, Weimin Han. - Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2012. - IX, 244p. 19 illus., 11 illus. in color. online resource. - Lecture Notes in Mathematics, 2044 0075-8434 ; . - Lecture Notes in Mathematics, 2044 .
1 Preliminaries -- 2 Spherical Harmonics -- 3 Differentiation and Integration over the Sphere -- 4 Approximation Theory -- 5 Numerical Quadrature -- 6 Applications: Spectral Methods.
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.
9783642259838
10.1007/978-3-642-25983-8 doi
Mathematics.
Integral equations.
Differential equations, partial.
Functions, special.
Numerical analysis.
Physics.
Mathematics.
Numerical Analysis.
Special Functions.
Approximations and Expansions.
Integral Equations.
Partial Differential Equations.
Physics, general.
QA297-299.4
518