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Invitation to partial differential equations / Mikhail Shubin ; edited by Maxim Braverman, Robert McOwen, Peter Topalov.
- Format:
- Book
- Author/Creator:
- Shubin, M. A. (Mikhail Aleksandrovich), 1944-2020, author.
- Series:
- Graduate studies in mathematics ; 205.
- Graduate studies in mathematics ; 205
- Language:
- English
- Russian
- Subjects (All):
- Differential equations, Partial--Textbooks.
- Differential equations, Partial.
- Differential equations, Partial--Problems, exercises, etc.
- Physical Description:
- 1 online resource (xvii, 319 pages) : illustrations
- Place of Publication:
- Providence, Rhode Island : American Mathematical Society, [2020]
- Language Note:
- Translated from Russian.
- Summary:
- 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
- Contents:
- Linear differential operators
- One-dimensional wave equation
- The Sturm-Liouville problem
- Distributions
- Convolution and Fourier transform
- Harmonic functions
- The heat equation
- Sobolev spaces. A generalized solution of Dirichlet's problem
- The eigenvalues and eigenfunctions of the Laplace operator
- The wave equation
- Properties of the potentials and their calculations
- Wave fronts and short-wave asymptotics for hyperbolic equations.
- Notes:
- Includes bibliographical references and index.
- Description based on print version record.
- ISBN:
- 9781470456979
- 1470456974
- OCLC:
- 1151233848
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