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Graduate Studies in Mathematics
2011; 410 pp; hardcover
List Price: US$78
Member Price: US$62.40
Order Code: GSM/123
Partial Differential Equations: Second Edition - Lawrence C Evans
This book is a reader-friendly, relatively short introduction to the modern theory of linear partial differential equations. An effort has been made to present complete proofs in an accessible and self-contained form.
The first three chapters are on elementary distribution theory and Sobolev spaces with many examples and applications to equations with constant coefficients. The following chapters study the Cauchy problem for parabolic and hyperbolic equations, boundary value problems for elliptic equations, heat trace asymptotics, and scattering theory. The book also covers microlocal analysis, including the theory of pseudodifferential and Fourier integral operators, and the propagation of singularities for operators of real principal type. Among the more advanced topics are the global theory of Fourier integral operators and the geometric optics construction in the large, the Atiyah-Singer index theorem in \(\mathbb R^n\), and the oblique derivative problem.
Graduate students and research mathematicians interested in partial differential equations.
"This is a wonderful book, very well adapted to a graduate level, that covers not only 'classical' topics but also topics that are not so 'conventional', and gives, with a renewed vigor, a broad and unified knowledge of the theory of PDEs."
-- Mathematical Reviews
"This is a very good book for graduate students and for mathematicians interested in Fourier analysis and PDEs. The book is very well-written. I would recommend this book without reservations to anyone who wants an unambiguous and fast introduction to an eclectic selection of topics in linear PDEs."
-- MAA Reviews
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