Partial Differential Equations I: Basic Theory

by Michael E. Taylor

The first of three volumes on partial differential equations, this one introduces basic examples arising in continuum mechanics, electromagnetism, complex analysis and other areas, and develops a number of tools for their solution, in particular Fourier analysis, distribution theory, and Sobolev spaces. These tools are then applied to the treatment of basic problems in linear PDE, including the Laplace equation, heat equation, and wave equation, as well as more general elliptic, parabolic, and hyperbolic equations. The book is targeted at graduate students in mathematics and at professional mathematicians with an interest in partial differential equations, mathematical physics, differential geometry, harmonic analysis, and complex analysis. In this second edition, there are seven new sections including Sobolev spaces on rough domains, boundary layer phenomena for the heat equation, the space of pseudodifferential operators of harmonic oscillator type, and an index formula for elliptic systems of such operators. In addition, several other sections have been substantially rewritten, and numerous others polished to reflect insights obtained through the use of these books over time.

Genres: Mathematics

676 pages, Hardcover

First published June 25, 1996

Reviews

[HikBook]

Chapter 1, Section 4. The function phi(x)=1/z is holomorphic on the complex plane except at origin.
It is integrable near 0 and bounded outside a neighboorhood of 0, and hence it defines a tempered distribution. Aditionally, partial_{z barra}phi(z) a a tempered distbution with support at 0.

Proposition 4.8. partial_{z barra} (1/z)=pi delta