Partial Differential Equations II

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Beschreibung

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)

Über den Autor

Michael E. Taylor is a Professor at University of North Carolina in the Department of Mathematics.

Zusammenfassung

Three volumes offer complete reference to pde's

Includes both theory and applications

Lots of examples and exercises

Inhaltsverzeichnis

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.

Details

Erscheinungsjahr:	2023
Fachbereich:	Analysis
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Reihe:	Applied Mathematical Sciences
Inhalt:	xxiii 687 S. 14 s/w Illustr. 687 p. 14 illus.
ISBN-13:	9783031336997
ISBN-10:	3031336992
Sprache:	Englisch
Ausstattung / Beilage:	HC runder Rücken kaschiert
Einband:	Gebunden
Autor:	Taylor, Michael E.
Auflage:	3rd ed. 2023
Hersteller:	Springer International Publishing Springer International Publishing AG Applied Mathematical Sciences
Maße:	241 x 160 x 41 mm
Von/Mit:	Michael E. Taylor
Erscheinungsdatum:	07.12.2023
Gewicht:	1,35 kg

Artikel-ID: 126864906