Partial Differential Equations: Analytical Solution Techniques (The Wadsworth & Brooks/Cole Mathematics Series)

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9780534122164: Partial Differential Equations: Analytical Solution Techniques (The Wadsworth & Brooks/Cole Mathematics Series)
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This is a text for a two-semester or three-quarter sequence of courses in partial differential equations. It is assumed that the student has a good background in vector calculus and ordinary differential equations and has been introduced to such elementary aspects of partial differential equations as separation of variables, Fourier series, and eigenfunction expansions. Some familiarity is also assumed with the application of complex variable techniques, including conformal map­ ping, integration in the complex plane, and the use of integral transforms. Linear theory is developed in the first half of the book and quasilinear and nonlinear problems are covered in the second half, but the material is presented in a manner that allows flexibility in selecting and ordering topics. For example, it is possible to start with the scalar first-order equation in Chapter 5, to include or delete the nonlinear equation in Chapter 6, and then to move on to the second­ order equations, selecting and omitting topics as dictated by the course. At the University of Washington, the material in Chapters 1-4 is covered during the third quarter of a three-quarter sequence that is part of the required program for first-year graduate students in Applied Mathematics. We offer the material in Chapters 5-8 to more advanced students in a two-quarter sequence.

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"This book contains a broad treatment of partial differential equations that arise in the sciences and engineering, particularly emphasizing the analytical solution techniques. In each chapter the author discusses the important applications that lead to the class of equations to be studied, presents different methods for tackling these equations, and concludes with a selection of instructive problems. A relevant bibliography has also been included at the end of this book."--BOOK JACKET. "Students and researchers in the sciences and engineering will find this book useful."--BOOK JACKET.

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From the reviews of the second edition:

"The book provides a well chosen collection of analytical solution techniques by applications to a wide class of problems of mathematical physics. It will be useful for the researchers in PDE-s, physicists, engineers and also for students with basic knowledge in vector calculus, ODE-s and PDE-s." (Jeno Hegedus, Acta Scientiarum Mathematicarum, Vol. 71, 2005)

"This is the revised and enlarged second edition of a text book on partial differential equations. ... the book gives a good overview of a large number of analytic solution techniques for both linear and nonlinear partial differential equations ... . In addition, the author always tries to include information on the applications that lead to a particular equation and to use an intuitive approach explaining the mechanisms behind the observed phenomena. ... it is definitely an interesting source for both students and teachers." (G. Teschl, Monatshefte für Mathematik, Vol. 133 (4), 2001)

"The text presents the classical, analytical techniques used by applied mathematicians, scientist, and engineers to solve problems. ... The Kevorkian text is an outstanding treatment of classical PDEs and applications suitable for beginning graduate students in mathematics and applied science. It represents what ‘everyone should know’ about PDE methods ... . If I had to recommend a single book to a research engineer who wanted to learn the basic, analytical tools of PDEs ... I might select this book." (J. David Logan, SIAM Review, Vol. 42 (3), 2000)

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