國立高雄大學圖資館 |

Language: English

Back

Geometric multivector analysisfrom G...

Rosen, Andreas.

Geometric multivector analysisfrom Grassmann to Dirac /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Geometric multivector analysisby Andreas Rosen.
Reminder of title:	from Grassmann to Dirac /
Author:	Rosen, Andreas.
Published:	Cham :Springer International Publishing :2019.
Description:	xiii, 465 p. :ill. (some col.), digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Algebras, Linear.
Online resource:	https://doi.org/10.1007/978-3-030-31411-8
ISBN:	9783030314118$q(electronic bk.)

Geometric multivector analysisfrom Grassmann to Dirac /
Rosen, Andreas.

Geometric multivector analysisfrom Grassmann to Dirac /[electronic resource] :by Andreas Rosen. - Cham :Springer International Publishing :2019. - xiii, 465 p. :ill. (some col.), digital ;24 cm. - Birkhauser advanced texts basler lehrbucher,1019-6242. - Birkhauser advanced texts basler lehrbucher..

Prelude: 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.

This 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 Mobius 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.

ISBN: 9783030314118$q(electronic bk.)

Standard No.: 10.1007/978-3-030-31411-8doiSubjects--Topical Terms:

183087
Algebras, Linear.

LC Class. No.: QA184.2 / .R67 2019

Dewey Class. No.: 512.5

Geometric multivector analysisfrom Grassmann to Dirac /
LDR:02878nmm a2200337 a 4500 001 569651
003 DE-He213
005 20191109180720.0
006 m d
007 cr nn 008maaau
008 200723s2019 gw s 0 eng d
020 $a 9783030314118$q(electronic bk.)
020 $a 9783030314101$q(paper)
024 7 $a 10.1007/978-3-030-31411-8 $2 doi
035 $a 978-3-030-31411-8
040 $a GP $c GP
041 0 $a eng
050 4 $a QA184.2 $b .R67 2019
072 7 $a PBF $2 bicssc
072 7 $a MAT002050 $2 bisacsh
072 7 $a PBF $2 thema
082 0 4 $a 512.5 $2 23
090 $a QA184.2 $b .R813 2019
100 1 $a Rosen, Andreas. $3 855745
245 1 0 $a Geometric multivector analysis $h [electronic resource] : $b from Grassmann to Dirac / $c by Andreas Rosen.
260 $a Cham : $b Springer International Publishing : $b Imprint: Birkhauser, $c 2019.
300 $a xiii, 465 p. : $b ill. (some col.), digital ; $c 24 cm.
490 1 $a Birkhauser advanced texts basler lehrbucher, $x 1019-6242
505 0 $a Prelude: 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.
520 $a This 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 Mobius 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.
650 0 $a Algebras, Linear. $3 183087
650 1 4 $a Linear and Multilinear Algebras, Matrix Theory. $3 274063
650 2 4 $a Global Analysis and Analysis on Manifolds. $3 273786
650 2 4 $a Partial Differential Equations. $3 274075
650 2 4 $a Integral Equations. $3 274836
650 2 4 $a Differential Geometry. $3 273785
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer eBooks
830 0 $a Birkhauser advanced texts basler lehrbucher. $3 760267
856 4 0 $u https://doi.org/10.1007/978-3-030-31411-8
950 $a Mathematics and Statistics (Springer-11649)