國立高雄大學圖資館 |

登入

回首頁

Partial differential equations.II,Qualitative studies of linear equations

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Partial differential equations.by Michael E. Taylor.
其他題名:	Qualitative studies of linear equations
作者:	Taylor, Michael E.
出版者:	Cham :Springer International Publishing :2023.
面頁冊數:	xxiii, 687 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
標題:	Differential equations, Partial.
電子資源:	https://doi.org/10.1007/978-3-031-33700-0
ISBN:	9783031337000$q(electronic bk.)

Partial differential equations.II,Qualitative studies of linear equations
Taylor, Michael E.

Partial differential equations.II,Qualitative studies of linear equations[electronic resource] /Qualitative studies of linear equationsby Michael E. Taylor. - Third edition. - Cham :Springer International Publishing :2023. - xxiii, 687 p. :ill., digital ;24 cm. - Applied mathematical sciences,v. 1162196-968X ;. - Applied mathematical sciences ;v.176..

Preface -- 7 Pseudodifferential Operators -- 8 Spectral Theory -- 9 Scattering by Obstacles -- 10 Dirac Operators and Index Theory -- 11 Brownian Motion and Potential Theory -- 12 The ∂-Neumann Problem -- C Connections and Curvature -- Index.

This second in the series of three volumes builds upon the basic theory of linear PDE given in volume 1, and pursues more advanced topics. Analytical tools introduced here include pseudodifferential operators, the functional analysis of self-adjoint operators, and Wiener measure. The book also develops basic differential geometrical concepts, centered about curvature. Topics covered include spectral theory of elliptic differential operators, the theory of scattering of waves by obstacles, index theory for Dirac operators, and Brownian motion and diffusion. The book is targeted at graduate students in mathematics and at professional mathematicians with an interest in partial differential equations, mathematical physics, differential geometry, harmonic analysis, and complex analysis. The third edition further expands the material by incorporating new theorems and applications throughout the book, and by deepening connections and relating concepts across chapters. It includes new sections on rigid body motion, on probabilistic results related to random walks, on aspects of operator theory related to quantum mechanics, on overdetermined systems, and on the Euler equation for incompressible fluids. The appendices have also been updated with additional results, ranging from weak convergence of measures to the curvature of Kahler manifolds. Michael E. Taylor is a Professor of Mathematics at the University of North Carolina, Chapel Hill, NC. Review of first edition: "These volumes will be read by several generations of readers eager to learn the modern theory of partial differential equations of mathematical physics and the analysis in which this theory is rooted." (Peter Lax, SIAM review, June 1998)

ISBN: 9783031337000$q(electronic bk.)

Standard No.: 10.1007/978-3-031-33700-0doiSubjects--Topical Terms:

189753
Differential equations, Partial.

LC Class. No.: QA377

Dewey Class. No.: 515.353

Partial differential equations.II,Qualitative studies of linear equations
LDR:03119nmm a2200361 a 4500 001 653416
003 DE-He213
005 20231206233053.0
006 m d
007 cr nn 008maaau
008 240426s2023 sz s 0 eng d
020 $a 9783031337000$q(electronic bk.)
020 $a 9783031336997$q(paper)
024 7 $a 10.1007/978-3-031-33700-0 $2 doi
035 $a 978-3-031-33700-0
040 $a GP $c GP
041 0 $a eng
050 4 $a QA377
072 7 $a PBKJ $2 bicssc
072 7 $a MAT007000 $2 bisacsh
072 7 $a PBKJ $2 thema
082 0 4 $a 515.353 $2 23
090 $a QA377 $b .T244 2023
100 1 $a Taylor, Michael E. $3 509366
245 1 0 $a Partial differential equations. $n II, $p Qualitative studies of linear equations $h [electronic resource] / $c by Michael E. Taylor.
246 3 $a Qualitative studies of linear equations
250 $a Third edition.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2023.
300 $a xxiii, 687 p. : $b ill., digital ; $c 24 cm.
490 1 $a Applied mathematical sciences, $x 2196-968X ; $v v. 116
505 0 $a Preface -- 7 Pseudodifferential Operators -- 8 Spectral Theory -- 9 Scattering by Obstacles -- 10 Dirac Operators and Index Theory -- 11 Brownian Motion and Potential Theory -- 12 The ∂-Neumann Problem -- C Connections and Curvature -- Index.
520 $a This second in the series of three volumes builds upon the basic theory of linear PDE given in volume 1, and pursues more advanced topics. Analytical tools introduced here include pseudodifferential operators, the functional analysis of self-adjoint operators, and Wiener measure. The book also develops basic differential geometrical concepts, centered about curvature. Topics covered include spectral theory of elliptic differential operators, the theory of scattering of waves by obstacles, index theory for Dirac operators, and Brownian motion and diffusion. The book is targeted at graduate students in mathematics and at professional mathematicians with an interest in partial differential equations, mathematical physics, differential geometry, harmonic analysis, and complex analysis. The third edition further expands the material by incorporating new theorems and applications throughout the book, and by deepening connections and relating concepts across chapters. It includes new sections on rigid body motion, on probabilistic results related to random walks, on aspects of operator theory related to quantum mechanics, on overdetermined systems, and on the Euler equation for incompressible fluids. The appendices have also been updated with additional results, ranging from weak convergence of measures to the curvature of Kahler manifolds. Michael E. Taylor is a Professor of Mathematics at the University of North Carolina, Chapel Hill, NC. Review of first edition: "These volumes will be read by several generations of readers eager to learn the modern theory of partial differential equations of mathematical physics and the analysis in which this theory is rooted." (Peter Lax, SIAM review, June 1998)
650 0 $a Differential equations, Partial. $3 189753
650 0 $a Differential equations, Linear. $3 185864
650 1 4 $a Differential Equations. $3 285983
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer Nature eBook
830 0 $a Applied mathematical sciences ; $v v.176. $3 557779
856 4 0 $u https://doi.org/10.1007/978-3-031-33700-0
950 $a Mathematics and Statistics (SpringerNature-11649)