Taylor

Partial Differential Equations I

Basic Theory

3., Third Edition 2023

Springer International Publishing

ISBN 978-3-031-33859-5

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auch verfügbar als Buch (Hardcover) für 80,24 €

Bibliografische Daten

eBook. PDF

3., Third Edition 2023. 2023

XXIV, 714 p. 40 illus..

In englischer Sprache

Umfang: 714 S.

Verlag: Springer International Publishing

ISBN: 978-3-031-33859-5

Weiterführende bibliografische Daten

Das Werk ist Teil der Reihe: Applied Mathematical Sciences

auch verfügbar als Buch (Hardcover) für 80,24 €

Produktbeschreibung

The first of three volumes on partial differential equations, this one introduces basic examples arising in continuum mechanics, electromagnetism, complex analysis and other areas, and develops a number of tools for their solution, in particular Fourier analysis, distribution theory, and Sobolev spaces. These tools are then applied to the treatment of basic problems in linear PDE, including the Laplace equation, heat equation, and wave equation, as well as more general elliptic, parabolic, and hyperbolic equations. 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. In includes new sectionson 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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