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Invitation to partial differential equations. Edited by Maxim Braverman, Robert McOwen and Peter Topalov. (English) Zbl 1458.35001

Graduate Studies in Mathematics 205. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-3640-8/hbk; 978-1-4704-5697-9/ebook). xvii, 319 p. (2020).
The book under review is intended as an introduction to the classical theory of linear partial differential equations. This volume is designed for a one-semester course for graduate students in mathematics and applied mathematics.
The content of the book is rich but several classical topics are included, such as the Laplace, Poisson, heat and wave equations, as well as various applications to mathematical physics including waves and vibrating strings. Derivations of these equations are based primarily on physical and mechanical principles. The abstract framework includes distribution theory, Sobolev spaces, and theory of potentials.
All chapters and sections of the book take the reader from introductory material to more advanced topics. All of the usual topics of an introductory course at the graduate level are included. The volume includes several interesting examples, and most of them appear as exercises. Within each chapter the development is clear and easy to follow.
The book is highly recommended to graduate students and researchers in applied mathematics and mathematical physics.

MSC:

35-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to partial differential equations
35Jxx Elliptic equations and elliptic systems
35Kxx Parabolic equations and parabolic systems
35Lxx Hyperbolic equations and hyperbolic systems
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