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Author: Karl E. Gustafson
Publisher: Courier Corporation
Published: 2012-04-26
Total Pages: 500
ISBN-13: 0486140873
DOWNLOAD EBOOKEasy-to-use text examines principal method of solving partial differential equations, 1st-order systems, computation methods, and much more. Over 600 exercises, with answers for many. Ideal for a 1-semester or full-year course.
Author: Ralph E. Showalter
Publisher: Courier Corporation
Published: 2011-09-12
Total Pages: 226
ISBN-13: 0486135799
DOWNLOAD EBOOKThis graduate-level text opens with an elementary presentation of Hilbert space theory sufficient for understanding the rest of the book. Additional topics include boundary value problems, evolution equations, optimization, and approximation.1979 edition.
Author: Samuel S. Holland
Publisher: Courier Corporation
Published: 2012-05-04
Total Pages: 578
ISBN-13: 0486139298
DOWNLOAD EBOOKNumerous worked examples and exercises highlight this unified treatment. Simple explanations of difficult subjects make it accessible to undergraduates as well as an ideal self-study guide. 1990 edition.
Author: Avner Friedman
Publisher: Courier Corporation
Published: 2008-11-24
Total Pages: 276
ISBN-13: 0486469190
DOWNLOAD EBOOKLargely self-contained, this three-part treatment focuses on elliptic and evolution equations, concluding with a series of independent topics directly related to the methods and results of the preceding sections. 1969 edition.
Author: Haim Brezis
Publisher: Springer Science & Business Media
Published: 2010-11-02
Total Pages: 600
ISBN-13: 0387709142
DOWNLOAD EBOOKThis textbook is a completely revised, updated, and expanded English edition of the important Analyse fonctionnelle (1983). In addition, it contains a wealth of problems and exercises (with solutions) to guide the reader. Uniquely, this book presents in a coherent, concise and unified way the main results from functional analysis together with the main results from the theory of partial differential equations (PDEs). Although there are many books on functional analysis and many on PDEs, this is the first to cover both of these closely connected topics. Since the French book was first published, it has been translated into Spanish, Italian, Japanese, Korean, Romanian, Greek and Chinese. The English edition makes a welcome addition to this list.
Author: Joseph Wloka
Publisher: Cambridge University Press
Published: 1987-05-21
Total Pages: 536
ISBN-13: 9780521277594
DOWNLOAD EBOOKA rigorous introduction to the abstract theory of partial differential equations progresses from the theory of distribution and Sobolev spaces to Fredholm operations, the Schauder fixed point theorem and Bochner integrals.
Author: Michael Shearer
Publisher: Princeton University Press
Published: 2015-03-01
Total Pages: 287
ISBN-13: 140086660X
DOWNLOAD EBOOKAn accessible yet rigorous introduction to partial differential equations This 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 equations Draws connections to advanced topics in analysis Covers applications to continuum mechanics An electronic solutions manual is available only to professors An online illustration package is available to professors
Author: Karl E. Gustafson
Publisher: Courier Corporation
Published: 1999-01-01
Total Pages: 492
ISBN-13: 9780486612713
DOWNLOAD EBOOKThis volume offers an excellent undergraduate-level introduction to the main topics, methods, and applications of partial differential equations. Chapter 1 presents a full introduction to partial differential equations and Fourier series as related to applied mathematics. Chapter 2 begins with a more comprehensive look at the principal method for solving partial differential equations — the separation of variables — and then more fully develops that approach in the contexts of Hilbert space and numerical methods. Chapter 3 includes an expanded treatment of first-order systems, a short introduction to computational methods, and aspects of topical research on the partial differential equations of fluid dynamics. With over 600 problems and exercises, along with explanations, examples, and a comprehensive section of answers, hints, and solutions, this superb, easy-to-use text is ideal for a one-semester or full-year course. It will also provide the mathematically inclined layperson with a stimulating review of the subject's essentials.
Author: Paul Sacks
Publisher: Academic Press
Published: 2017-05-16
Total Pages: 322
ISBN-13: 0128114576
DOWNLOAD EBOOKTechniques of Functional Analysis for Differential and Integral Equations describes a variety of powerful and modern tools from mathematical analysis, for graduate study and further research in ordinary differential equations, integral equations and partial differential equations. Knowledge of these techniques is particularly useful as preparation for graduate courses and PhD research in differential equations and numerical analysis, and more specialized topics such as fluid dynamics and control theory. Striking a balance between mathematical depth and accessibility, proofs involving more technical aspects of measure and integration theory are avoided, but clear statements and precise alternative references are given . The work provides many examples and exercises drawn from the literature. - Provides an introduction to mathematical techniques widely used in applied mathematics and needed for advanced research in ordinary and partial differential equations, integral equations, numerical analysis, fluid dynamics and other areas - Establishes the advanced background needed for sophisticated literature review and research in differential equations and integral equations - Suitable for use as a textbook for a two semester graduate level course for M.S. and Ph.D. students in Mathematics and Applied Mathematics
Author: Françoise Demengel
Publisher: Springer Science & Business Media
Published: 2012-01-24
Total Pages: 480
ISBN-13: 1447128079
DOWNLOAD EBOOKThe theory of elliptic boundary problems is fundamental in analysis and the role of spaces of weakly differentiable functions (also called Sobolev spaces) is essential in this theory as a tool for analysing the regularity of the solutions. This book offers on the one hand a complete theory of Sobolev spaces, which are of fundamental importance for elliptic linear and non-linear differential equations, and explains on the other hand how the abstract methods of convex analysis can be combined with this theory to produce existence results for the solutions of non-linear elliptic boundary problems. The book also considers other kinds of functional spaces which are useful for treating variational problems such as the minimal surface problem. The main purpose of the book is to provide a tool for graduate and postgraduate students interested in partial differential equations, as well as a useful reference for researchers active in the field. Prerequisites include a knowledge of classical analysis, differential calculus, Banach and Hilbert spaces, integration and the related standard functional spaces, as well as the Fourier transformation on the Schwartz space. There are complete and detailed proofs of almost all the results announced and, in some cases, more than one proof is provided in order to highlight different features of the result. Each chapter concludes with a range of exercises of varying levels of difficulty, with hints to solutions provided for many of them.
