Partial Differential Equations: An Introduction to Theory and Applications by Michael Shearer (PDF)

Description

An accessible yet rigorous introduction to partial differential equationsThis textbook provides beginning graduate students and advanced undergraduates with an accessible introduction to the rich subject of partial differential equations (PDEs). It presents a rigorous and clear explanation of the more elementary theoretical aspects of PDEs, while also drawing connections to deeper analysis and applications. The book serves as a needed bridge between basic undergraduate texts and more advanced books that require a significant background in functional analysis.Topics include first order equations and the method of characteristics, second order linear equations, wave and heat equations, Laplace and Poisson equations, and separation of variables. The book also covers fundamental solutions, Green’s functions and distributions, beginning functional analysis applied to elliptic PDEs, traveling wave solutions of selected parabolic PDEs, and scalar conservation laws and systems of hyperbolic PDEs.Provides an accessible yet rigorous introduction to partial differential equationsDraws connections to advanced topics in analysisCovers applications to continuum mechanicsAn electronic solutions manual is available only to professorsAn online illustration package is available to professors

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐To me, as a retired professor of mathematics, the most salient feature of this book is its brevity. In just 250 pages the authors introduce the basic theory of PDE and also sample some advanced topics. The advantages of such brevity are obvious—a thin book is much less intimidating for students, and the professor is not forced to skip over lots of peripheral material that cannot be squeezed into an introductory course. I think the book would work well as a text for a one-semester graduate course. In lecture the professor can flesh out difficult proofs, provide emphasis to make the important ideas stand out, and explain the context in which the problems arise, while the student has the book as a reference for studying carefully the core mathematical ideas.The layout of the book is attractive and easy to read. Each of its fifteen chapters includes an average of about ten problems, for which no solutions are given.

⭐The organization sucks. The book starts with lots of examples but doesn’t discuss systematically the methods for solving those equations. The exercises are poorly phrased which lead to obscure understanding of the questions. Moreover, instead of giving systematic practice of solving methods, the exercises concern too much too early on deep concepts and delicate details which are not supposed to be there for the first time readers. Hence I’d say please avoid this book at all cost!Try PDE book by Strauss!It’s concise and way clearer together with super helpful exercises which will sure help you learn necessary materials in PDE.

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