**Graduate Studies in Mathematics**

Volume: 123;
2011;
410 pp;
Hardcover

MSC: Primary 35;

Print ISBN: 978-0-8218-5284-2

Product Code: GSM/123

List Price: $78.00

Individual Member Price: $62.40

**Electronic ISBN: 978-1-4704-1184-8
Product Code: GSM/123.E**

List Price: $78.00

Individual Member Price: $62.40

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#### Supplemental Materials

# Lectures on Linear Partial Differential Equations

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*Gregory Eskin*

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.

#### Readership

Graduate students and research mathematicians interested in partial differential equations.

#### Reviews & Endorsements

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

#### Table of Contents

# Table of Contents

## Lectures on Linear Partial Differential Equations

- Cover Cover11 free
- Title page iii4 free
- Contents vii8 free
- Preface xv16 free
- Theory of distributions 120 free
- Fourier transforms 3352
- Applications of distributions to partial differential equations 6988
- Second order elliptic equations in bounded domains 111130
- The scattering theory 141160
- Pseudodifferential operators 197216
- Elliptic boundary value problems and parametrices 263282
- Fourier integral operators 329348
- Bibliography 403422
- Index 407426 free
- Back Cover Back Cover1432