Catalog Description and Textbooks
This course sequence constitutes an introduction to differential equations. Topics covered are as follows (Math-611 covers topics 1,2, and the first part of 3, Math-612 covers the rest):
- basic theory of ODEs and vector fields
- the Laplace equation and the wave equation
- Fourier analysis, distributions, and constant coefficient linear PDEs
- Sobolev spaces
- linear elliptic equations
This is a midlevel graduate course. The prerequisites are a solid background in real and functional analysis, and very basic complex analysis.