Synopses & Reviews
"The popularity of this text is based on the fact that the author explains and develops important parts of the theory of partial differential equations in a very easily accessible and yet thorough way. Special emphasis is on those parts of the theory which are important in physical applications like the heat equation, the Cauchy problem and the Laplace (or potential) equation. For the third edition (1980), this text was thoroughly rewritten and augmented, particularly in the areas of Fourier transform techniques, Hilbert space, and finite difference methods. More information was incorporated on equations of higher dimensions, and the collections of problems was greatly expanded. Now, for the fourth edition, the book has again been updated with an additional chapter on Lewy's example of linear equations without solution."
This book is a very well-accepted introduction to the subject. In it, the author identifies the significant aspects of the theory and explores them with a limited amount of machinery from mathematical analysis. Now, in this fourth edition, the book has again been updated with an additional chapter on Lewy's example of a linear equation without solutions.
Table of Contents
The Single First-Order Equation
x Second-Order Equations: Hyperbolic Equations for Functions of Two Independent Variables
x Characteristic Manifolds and the Cauchy Problem
x The Laplace Equation
x Hyperbolic Equations in Higher Dimensions
x Higher-Order Elliptic Equations with Constant
x Parabolic Equations
x H. Lewy's Example of a Linear Equation without Solutions