Hardcover ISBN:  9780821852842 
Product Code:  GSM/123 
List Price:  $83.00 
MAA Member Price:  $74.70 
AMS Member Price:  $66.40 
Electronic ISBN:  9781470411848 
Product Code:  GSM/123.E 
List Price:  $78.00 
MAA Member Price:  $70.20 
AMS Member Price:  $62.40 

Book DetailsGraduate Studies in MathematicsVolume: 123; 2011; 410 ppMSC: Primary 35;
This book is a readerfriendly, 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 selfcontained 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 AtiyahSinger index theorem in \(\mathbb R^n\), and the oblique derivative problem.ReadershipGraduate students and research mathematicians interested in partial differential equations.

Table of Contents

Chapters

Chapter 1. Theory of distributions

Chapter 2. Fourier transforms

Chapter 3. Applications of distributions to partial differential equations

Chapter 4. Second order elliptic equations in bounded domains

Chapter 5. Scattering theory

Chapter 6. Pseudodifferential operators

Chapter 7. Elliptic boundary value problems and parametrices

Chapter 8. Fourier integral operators


Additional Material

Reviews

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 wellwritten. 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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 Book Details
 Table of Contents
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This book is a readerfriendly, 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 selfcontained 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 AtiyahSinger index theorem in \(\mathbb R^n\), and the oblique derivative problem.
Graduate students and research mathematicians interested in partial differential equations.

Chapters

Chapter 1. Theory of distributions

Chapter 2. Fourier transforms

Chapter 3. Applications of distributions to partial differential equations

Chapter 4. Second order elliptic equations in bounded domains

Chapter 5. Scattering theory

Chapter 6. Pseudodifferential operators

Chapter 7. Elliptic boundary value problems and parametrices

Chapter 8. Fourier integral operators

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 wellwritten. 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