LEADER 04631nam 22008535 450 001 9910360852403321 005 20240709094004.0 010 $a9783030314118 010 $a3-030-31411-1 024 7 $a10.1007/978-3-030-31411-8 035 $a(CKB)4100000009844896 035 $a(DE-He213)978-3-030-31411-8 035 $a(MiAaPQ)EBC5975561 035 $a(PPN)26914630X 035 $a(EXLCZ)994100000009844896 100 $a20191109d2019 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aGeometric multivector analysis $efrom Grassmann to Dirac /$fAndreas Rosén 210 1$aCham :$cSpringer International Publishing :$cImprint: Birkhäuser,$d[2019]. 210 4$d©2019 215 $a1 online resource (XIII, 465 pages, 29 illustrations., 8 illustrations. in color.) 225 1 $aBirkhäuser Advanced Texts Basler Lehrbücher,$x2296-4894 311 1 $a9783030314101 311 1 $a3-030-31410-3 327 $aPrelude: Linear algebra -- Exterior algebra -- Clifford algebra -- Mappings of inner product spaces -- Spinors in inner product spaces -- Interlude: Analysis -- Exterior calculus -- Hodge decompositions -- Hypercomplex analysis -- Dirac equations -- Multivector calculus on manifolds -- Two index theorems. 330 $aThis book presents a step-by-step guide to the basic theory of multivectors and spinors, with a focus on conveying to the reader the geometric understanding of these abstract objects. Following in the footsteps of M. Riesz and L. Ahlfors, the book also explains how Clifford algebra offers the ideal tool for studying spacetime isometries and Möbius maps in arbitrary dimensions. The book carefully develops the basic calculus of multivector fields and differential forms, and highlights novelties in the treatment of, e.g., pullbacks and Stokes?s theorem as compared to standard literature. It touches on recent research areas in analysis and explains how the function spaces of multivector fields are split into complementary subspaces by the natural first-order differential operators, e.g., Hodge splittings and Hardy splittings. Much of the analysis is done on bounded domains in Euclidean space, with a focus on analysis at the boundary. The book also includes a derivation of new Dirac integral equations for solving Maxwell scattering problems, which hold promise for future numerical applications. The last section presents down-to-earth proofs of index theorems for Dirac operators on compact manifolds, one of the most celebrated achievements of 20th-century mathematics. The book is primarily intended for graduate and PhD students of mathematics. It is also recommended for more advanced undergraduate students, as well as researchers in mathematics interested in an introduction to geometric analysis. 410 0$aBirkhäuser Advanced Texts Basler Lehrbücher,$x2296-4894 606 $aAlgebras, Linear 606 $aGlobal analysis (Mathematics) 606 $aManifolds (Mathematics) 606 $aDifferential equations 606 $aIntegral equations 606 $aGeometry, Differential 606 $aLinear Algebra 606 $aGlobal Analysis and Analysis on Manifolds 606 $aDifferential Equations 606 $aIntegral Equations 606 $aDifferential Geometry 606 $aAnàlisi global (Matemàtica)$2lemac 606 $aÀlgebra lineal$2lemac 606 $aGeometria diferencial$2lemac 606 $aEquacions diferencials$2lemac 606 $aEquacions integrals$2lemac 606 $aVarietats (Matemàtica)$2lemac 615 0$aAlgebras, Linear. 615 0$aGlobal analysis (Mathematics). 615 0$aManifolds (Mathematics). 615 0$aDifferential equations. 615 0$aIntegral equations. 615 0$aGeometry, Differential. 615 14$aLinear Algebra. 615 24$aGlobal Analysis and Analysis on Manifolds. 615 24$aDifferential Equations. 615 24$aIntegral Equations. 615 24$aDifferential Geometry. 615 7$aAnàlisi global (Matemàtica) 615 7$aÀlgebra lineal 615 7$aGeometria diferencial 615 7$aEquacions diferencials 615 7$aEquacions integrals 615 7$aVarietats (Matemàtica) 676 $a512.5 700 $aRosén$b Andreas$4aut$4http://id.loc.gov/vocabulary/relators/aut$0781339 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910360852403321 996 $aGeometric Multivector Analysis$91732489 997 $aUNINA