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Partial differential equations.. II,...

Taylor, Michael E.

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Partial differential equations.. II,. Qualitative studies of linear equations

Record Type:	Electronic resources : Monograph/item
Title/Author:	Partial differential equations./ by Michael E. Taylor.
remainder title:	Qualitative studies of linear equations
Author:	Taylor, Michael E.
Published:	Cham :Springer International Publishing : : 2023.,
Description:	xxiii, 687 p. :ill., digital ;24 cm.
[NT 15003449]:	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.
Contained By:	Springer Nature eBook
Subject:	Differential equations, Partial. -
Online resource:	https://doi.org/10.1007/978-3-031-33700-0
ISBN:	9783031337000

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. 116..

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

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

518115
Differential equations, Partial.

LC Class. No.: QA377

Dewey Class. No.: 515.353

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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)
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