Partial differential equations. Volume I, Basic theory / Michael E. Taylor.
2023
QA377
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Details
Title
Partial differential equations. Volume I, Basic theory / Michael E. Taylor.
Edition
Third edition.
ISBN
9783031338595 (electronic bk.)
3031338596 (electronic bk.)
9783031338588
3031338588
3031338596 (electronic bk.)
9783031338588
3031338588
Published
Cham : Springer, 2023.
Language
English
Description
1 online resource (712 pages) : illustrations (black and white).
Item Number
10.1007/978-3-031-33859-5 doi
Call Number
QA377
Dewey Decimal Classification
515/.353
Summary
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 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).
Note
Includes index.
Access Note
Access limited to authorized users.
Source of Description
Description based on print version record.
Series
Applied mathematical sciences (Springer-Verlag New York Inc.) ; v. 115.
Available in Other Form
Partial differential equations. Volume I, Basic theory.
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Table of Contents
Contents of Volumes II and III
Preface
1 Basic Theory of ODE and Vector Fields
2 The Laplace Equation and Wave Equation
3 Fourier Analysis, Distributions, and Constant-Coefficient Linear PDE
4 Sobolev Spaces
5 Linear Elliptic Equation
6 Linear Evolution Equations
A Outline of Functional Analysis
B Manifolds, Vector Bundles, and Lie Groups
Index.
Preface
1 Basic Theory of ODE and Vector Fields
2 The Laplace Equation and Wave Equation
3 Fourier Analysis, Distributions, and Constant-Coefficient Linear PDE
4 Sobolev Spaces
5 Linear Elliptic Equation
6 Linear Evolution Equations
A Outline of Functional Analysis
B Manifolds, Vector Bundles, and Lie Groups
Index.