Articoli correlati a Partial Differential Equations: Analytical Solution...
Sinossi
A broad treatment of important partial differential equations, particularly emphasizing the analytical techniques. In each chapter the author raises various questions concerning the particular equations discussed, treats different methods for tackling these equations, gives applications and examples, and concludes with a list of proposed problems and a relevant bibliography. This new edition has been substantially updated to take account of the new techniques available, making it valuable for students and researchers in mathematics, physics and engineering.
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Recensione
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)
Contenuti
1. The Diffusion Equation.- 2. Laplace’s Equation.- 3. The Wave Equation.- 4. Linear Second-Order Equations with Two Independent Variables.- 5. The Scalar Quasilinear First-Order Equation.- 6. Nonlinear First-Order Equations.- 7. Quasilinear Hyperbolic Systems.- 8. Approximate Solutions by Perturbation Methods.- A.1. Review of Green’s Function for ODEs Using the Dirac Delta Function.- A.2. Review of Fourier and Laplace Transforms.- A.3. Review of Asymptotic Expansions.- References.
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