Partial Differential Equations and Boundary-Value Problems with Applications (Pure and Applied Undergraduate Texts) - Tapa dura

Pinsky, Mark A.

 
9780821868898: Partial Differential Equations and Boundary-Value Problems with Applications (Pure and Applied Undergraduate Texts)
Tapa dura
ISBN 10: 0821868896 ISBN 13: 9780821868898
Editorial: American Mathematical Society, 2011

Sinopsis

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.

"Sinopsis" puede pertenecer a otra edición de este libro.

Reseña del editor

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.

Reseña del editor

Originally published: 3rd ed. Prospect Heights, Ill.: Waveland Press, 2003.

"Sobre este título" puede pertenecer a otra edición de este libro.

Editorial
American Mathematical Society
Año de publicación
2011
Idioma
Inglés
ISBN 10 
0821868896
ISBN 13 
9780821868898
Encuadernación
Tapa dura
Número de edición
3
Número de páginas
526
Contacto del fabricante
no disponible
Persona responsable
no disponible