| Hardcover ISBN: | 978-0-8218-5284-2 |
| Product Code: | GSM/123 |
| List Price: | $135.00 |
| MAA Member Price: | $121.50 |
| AMS Member Price: | $108.00 |
| eBook ISBN: | 978-1-4704-1184-8 |
| Product Code: | GSM/123.E |
| List Price: | $85.00 |
| MAA Member Price: | $76.50 |
| AMS Member Price: | $68.00 |
| Hardcover ISBN: | 978-0-8218-5284-2 |
| eBook: ISBN: | 978-1-4704-1184-8 |
| Product Code: | GSM/123.B |
| List Price: | $220.00 $177.50 |
| MAA Member Price: | $198.00 $159.75 |
| AMS Member Price: | $176.00 $142.00 |
| Hardcover ISBN: | 978-0-8218-5284-2 |
| Product Code: | GSM/123 |
| List Price: | $135.00 |
| MAA Member Price: | $121.50 |
| AMS Member Price: | $108.00 |
| eBook ISBN: | 978-1-4704-1184-8 |
| Product Code: | GSM/123.E |
| List Price: | $85.00 |
| MAA Member Price: | $76.50 |
| AMS Member Price: | $68.00 |
| Hardcover ISBN: | 978-0-8218-5284-2 |
| eBook ISBN: | 978-1-4704-1184-8 |
| Product Code: | GSM/123.B |
| List Price: | $220.00 $177.50 |
| MAA Member Price: | $198.00 $159.75 |
| AMS Member Price: | $176.00 $142.00 |
-
Book DetailsGraduate Studies in MathematicsVolume: 123; 2011; 410 ppMSC: Primary 35
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.
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 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
-
-
RequestsReview Copy – for publishers of book reviewsDesk Copy – for instructors who have adopted an AMS textbook for a courseExamination Copy – for faculty considering an AMS textbook for a coursePermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
- Book Details
- Table of Contents
- Additional Material
- Reviews
- Requests
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.
-
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 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
