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Partial Differential Equations and Boundary-Value Problems with Applications

ISBN-10: 0821868896
ISBN-13: 9780821868898
Edition: 3rd 2011 (Revised)
Authors: Mark A. Pinsky
List price: $83.00 Buy it from $27.97 Rent it from $30.65
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Description: Building on the basic techniques of separation of variables and Fourier series, the book presents the solution of boundary-value problems for basic partial differential equations: the heat equation, wave equation, and Laplace equation, considered in  More...

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Book details

List price: $83.00
Edition: 3rd
Copyright year: 2011
Publisher: American Mathematical Society
Publication date: 8/15/2011
Binding: Hardcover
Pages: 526
Size: 7.50" wide x 10.25" long x 1.50" tall
Weight: 2.706
Language: English

Building on the basic techniques of separation of variables and Fourier series, the book presents the solution of boundary-value problems for basic partial differential equations: the heat equation, wave equation, and Laplace equation, considered in various standard coordinate systems--rectangular, cylindrical, and spherical. Each of the equations is derived in the three-dimensional context; the solutions are organized according to the geometry of the coordinate system, which makes the mathematics especially transparent. Bessel and Legendre functions are studied and used whenever appropriate throughout the text. The notions of steady-state solution of closely related stationary solutions are developed for the heat equation; applications to the study of heat flow in the earth are presented. The problem of the vibrating string is studied in detail both in the Fourier transform setting and from the viewpoint of the explicit representation (d'Alembert formula). Additional chapters include the numerical analysis of solutions and the method of Green's functions for solutions of partial differential equations. The exposition also includes asymptotic methods (Laplace transform and stationary phase). With more than 200 working examples and 700 exercises (more than 450 with answers), the book is suitable for an undergraduate course in partial differential equations.

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