This highly applied text is ideal where an informal approach to partial differential equations is desired (i.e. where theorem-proof approach is not necessary.) Most chapters start with physical examples. A unified treatment of linear problems is provided, plus a comprehensive discussion of nonlinear theory that includes the effect of shock waves. Perturbation method is given a thoroughly up-to-date treatment in Chapter Eight. Furthermore each chapter concludes with problems and references.
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)