Partial Differential Equations and Boundary Value Problems With Applications - Hardcover

Pinsky, Mark A.

Hardcover

ISBN 10: 157766275X ISBN 13: 9781577662754

Publisher: Waveland Pr Inc, 2003

Synopsis

Now available from Waveland Press, this corrected version of a classic text offers a level of rigor and completeness that rivals any book of its kind. Building on the basic techniques of separation-of-variables and Fourier series-integral methods, the book contains the solution of boundary-value problems for the heat equation, wave equation, and Laplace's equation in the standard coordinate systems--rectangular, cylindrical, and spherical. Each of the basic equations is derived in the three-dimensional context; the solutions are organized according to the geometry of the coordinate system rather than by the type of the equation, which makes the mathematics especially clear. Bessel and Legendre functions are developed in their own right, and their use is specifically indicated, where appropriate. The notion of steady-state solution and the closely related stationary solutions are developed for the heat equation and applied to the problem of heat flow in the earth. The problem of the vibrating string is also studied in detail, both from the Fourier viewpoint and the viewpoint of the explicit representation (d'Alembert's formula). Additional chapters include the numerical analysis of solutions and the method of Green's functions for solutions of partial differential equations. Special features include more than 200 worked examples and 700 exercises, with nearly 450 answers; asymptotic methods (Laplace and stationary phase); and over 300 typographical cleanups from the previous publisher's versions!

About this title

From the Publisher

Title of interest from Waveland Press: Kirkwood, An Introduction to Analysis, Second Edition (ISBN 9781577662327).

From the Inside Flap

"I have taught from this very nice book. Both the students and I have been happy with it. It is an important and useful topic in math (both pure and applied), and it is especially relevant and central to the service courses offered by most math departments. Sample of topics: the Green function method; the equations of heat, waves, and the PDEs of Laplace and Poisson; Orthogonal functions and Fourier methods; the method of stationary phase; and the classical Sturm Liouvile problems. Pinsky's book is the best text for teaching these classical tools. A nice feature of the current edition is a section on the use of Mathematica in the study of PDEs. When students need to look up one of the classical formulas in the theory of boundary value problems, I often refer to Pinsky's book, which has always been on target.
-- Palle E. T. Jorgensen (Iowa City, Iowa)

Edition details

• Publisher: Waveland Pr Inc
• Publication date: 2003
• ISBN 10: 157766275X
• ISBN 13: 9781577662754
• Binding: Hardcover
• Language: English
• Number of pages: 544