Partial Differential Equations I / Edition 1 available in Hardcover
- Pub. Date:
- Springer-Verlag New York, LLC
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.
Table of Contents
Contents: Contents of Volumes II and III.- Introduction.- Basic Theory of ODE and Vector Fields.- The Laplace Equation and Wave Equation.- Fourier Analysis, Distributions, and Constant-Coefficient Linear PDE.- Sobolev Spaces.- Linear Elliptic Equations.- Linear Evolution Equations.- Appendix A: Outline of Functional Analysis.- Appendix B: Manifolds, Vector Bundles, and Lie Groups.- Index.