Note: If this course is being taught this semester, more information can be found at the course home page.
Ordinary differential equations (as taught in either 163, 165, 173, or 263), measure theory and integration (as taught in 266 or 471), and functional analysis (472).
This course is a prerequisite or co-requisite for
Much of the current understanding of natural processes (e.g., heat diffusion, vibration of strings) is due to partial differential equations. This course offers an introduction to the basic properties of these equatons and to the methods used in analyzing them. Topics to be discussed include: representations formulas for solutions of the Laplace, heat, and wave equation; complete integrals and the method of characteristics; the Cauchy-Kovalevskaya theorem; Sobolev spaces.