**Graduate Studies in Mathematics**

Volume: 169;
2015;
281 pp;
Hardcover

MSC: Primary 35;

Print ISBN: 978-1-4704-1881-6

Product Code: GSM/169

List Price: $69.00

Individual Member Price: $55.20

**Electronic ISBN: 978-1-4704-2785-6
Product Code: GSM/169.E**

List Price: $69.00

Individual Member Price: $55.20

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#### Supplemental Materials

# Partial Differential Equations: An Accessible Route through Theory and Applications

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*András Vasy*

This text on partial differential equations is
intended for readers who want to understand the theoretical
underpinnings of modern PDEs in settings that are important for the
applications without using extensive analytic tools required by most
advanced texts. The assumed mathematical background is at the level of
multivariable calculus and basic metric space material, but the latter
is recalled as relevant as the text progresses.

The key goal of this book is to be mathematically complete without
overwhelming the reader, and to develop PDE theory in a manner that
reflects how researchers would think about the material. A concrete
example is that distribution theory and the concept of weak solutions
are introduced early because while these ideas take some time for the
students to get used to, they are fundamentally easy and, on the
other hand, play a central role in the field. Then, Hilbert spaces
that are quite important in the later development are introduced via
completions which give essentially all the features one wants without
the overhead of measure theory.

There is additional material provided for readers who would like to
learn more than the core material, and there are numerous exercises to
help solidify one's understanding. The text should be suitable for
advanced undergraduates or for beginning graduate students including
those in engineering or the sciences.

#### Table of Contents

# Table of Contents

## Partial Differential Equations: An Accessible Route through Theory and Applications

- Cover Cover11
- Title page iii4
- Contents v6
- Preface ix10
- Chapter 1. Introduction 112
- Chapter 2. Where do PDE come from? 1930
- Chapter 3. First order scalar semilinear equations 2940
- Chapter 4. First order scalar quasilinear equations 4556
- Chapter 5. Distributions and weak derivatives 5566
- Chapter 6. Second order constant coefficient PDE: Types and d’Alembert’s solution of the wave equation 8192
- Chapter 7. Properties of solutions of second order PDE: Propagation, energy estimates and the maximum principle 93104
- Chapter 8. The Fourier transform: Basic properties, the inversion formula and the heat equation 113124
- Chapter 9. The Fourier transform: Tempered distributions, the wave equation and Laplace’s equation 133144
- Chapter 10. PDE and boundaries 147158
- Chapter 11. Duhamel’s principle 159170
- Chapter 12. Separation of variables 169180
- Chapter 13. Inner product spaces, symmetric operators, orthogonality 179190
- Chapter 14. Convergence of the Fourier series and the Poisson formula on disks 201212
- Chapter 15. Bessel functions 221232
- Chapter 16. The method of stationary phase 235246
- Chapter 17. Solvability via duality 245256
- Chapter 18. Variational problems 263274
- Bibliography 277288
- Index 279290
- Back Cover Back Cover1295

#### Readership

Professors, graduate students, and others interested in teaching and learning partial differential equations.