This book is based on notes from a beginning graduate course on partial differential equations. Prerequisites for using the book are a solid undergraduate course in real analysis. There are more than 100 exercises in the book. Some of them are just exercises, whereas others, even though they may require new ideas to solve them, provide additional important information about the subject.It is a great pleasure to see this book—written by a great master of the subject—finally in print. This treatment of a core part of mathematics and its applications offers the student both a solid foundation in basic calculations techniques in the subject, as well as a basic introduction to the more general machinery, e.g., distributions, Sobolev spaces, etc., which are such a key part of any modern treatment. As such this book is ideal for more advanced undergraduates as well as mathematically inclined students from engineering or the natural sciences. Shubin has a lovely intuitive writing style which provides a gentle introduction to this beautiful subject. Many good exercises (and solutions) are provided!—Rafe Mazzeo, Stanford UniversityThis text provides an excellent semester's introduction to classical and modern topics in linear PDE, suitable for students with a background in advanced calculus and Lebesgue integration. The author intersperses treatments of the Laplace, heat, and wave equations with developments of various functional analytic tools, particularly distribution theory and spectral theory, introducing key concepts while deftly avoiding heavy technicalities.—Michael Taylor, University of North Carolina, Chapel Hill

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Yes, you can access Invitation to Partial Differential Equations by Mikhail Shubin, Maxim Braverman, Robert McOwen, Peter Topalov in PDF and/or ePUB format, as well as other popular books in Mathematics & Mathematics General. We have over one million books available in our catalogue for you to explore.

Information

Publisher

American Mathematical Society

Year

2020

ISBN

9781470456979

Topic

Mathematics

Subtopic

Mathematics General

Index

Mathematics

Cover
Title page
Foreword
Preface
Selected notational conventions
Chapter 1. Linear differential operators
Chapter 2. One-dimensional wave equation
Chapter 3. The Sturm-Liouville problem
Chapter 4. Distributions
Chapter 5. Convolution and Fourier transform
Chapter 6. Harmonic functions
Chapter 7. The heat equation
Chapter 8. Sobolev spaces. A generalized solution of Dirichlet’s problem
Chapter 9. The eigenvalues and eigenfunctions of the Laplace operator
Chapter 10. The wave equation
Chapter 11. Properties of the potentials and their computation
Chapter 12. Wave fronts and short-wave asymptotics for hyperbolic equations
Chapter 13. Answers and hints. Solutions
Bibliography
Index
Back Cover