03978nam 22007695 450 99646662950331620200701015058.03-642-25983-910.1007/978-3-642-25983-8(CKB)3360000000365821(SSID)ssj0000630009(PQKBManifestationID)11393320(PQKBTitleCode)TC0000630009(PQKBWorkID)10731542(PQKB)10389040(DE-He213)978-3-642-25983-8(MiAaPQ)EBC3070403(PPN)159086329(EXLCZ)99336000000036582120120216d2012 u| 0engurnn|008mamaatxtccrSpherical Harmonics and Approximations on the Unit Sphere: An Introduction[electronic resource] /by Kendall Atkinson, Weimin Han1st ed. 2012.Berlin, Heidelberg :Springer Berlin Heidelberg :Imprint: Springer,2012.1 online resource (IX, 244 p. 19 illus., 11 illus. in color.) Lecture Notes in Mathematics,0075-8434 ;2044Bibliographic Level Mode of Issuance: Monograph3-642-25982-0 Includes bibliographical references and index.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.Lecture Notes in Mathematics,0075-8434 ;2044Numerical analysisSpecial functionsApproximation theoryIntegral equationsPartial differential equationsPhysicsNumerical Analysishttps://scigraph.springernature.com/ontologies/product-market-codes/M14050Special Functionshttps://scigraph.springernature.com/ontologies/product-market-codes/M1221XApproximations and Expansionshttps://scigraph.springernature.com/ontologies/product-market-codes/M12023Integral Equationshttps://scigraph.springernature.com/ontologies/product-market-codes/M12090Partial Differential Equationshttps://scigraph.springernature.com/ontologies/product-market-codes/M12155Physics, generalhttps://scigraph.springernature.com/ontologies/product-market-codes/P00002Numerical analysis.Special functions.Approximation theory.Integral equations.Partial differential equations.Physics.Numerical Analysis.Special Functions.Approximations and Expansions.Integral Equations.Partial Differential Equations.Physics, general.518Atkinson Kendallauthttp://id.loc.gov/vocabulary/relators/aut54021Han Weiminauthttp://id.loc.gov/vocabulary/relators/autBOOK996466629503316Spherical Harmonics and Approximations on the Unit Sphere: An Introduction2831483UNISA