MATH 674, PARTIAL DIFFERENTIAL EQUATIONS II
An introduction to the classical theory of PDE. The focus will be on
developing basic techniques to treat second order linear PDE such as
the Laplace equation, the heat equation and the wave equation, as well
as first order nonlinear PDE. The second semester will treat modern
methods for PDEs (distributions, functional analysis, Sobolev spaces,
bounded and compact operators in Hilbert spaces).
- Office: 4103 Mathematics Bldg
- Phone: (301) 405-5067
- Office Hours: (Fall 2004)
Tu, Th 9:00 - 10:15 or by appointment.
MATH 411 or equivalent.
Lawrence C. Evans,
Partial Differential Equations
The syllabus of Math 674/AMSC 674
consists of the core material in Chapters 5 and 6 and of selected topics from Chapters 4 and 7-9.
Elliptic partial differential equations of second order by D. Gilbarg and
Partial Differential Equations by F. John
An Introduction to Partial Differential Equations by M. Renardy and C. Rogers
Partial Differential Equations by W. Strauss
Class Times: Tuesday and Thursday: 11:00am - 12:15pm.
Location: MTH 1308
- COURSE OUTLINE
- Boundary value problems for elliptic partial differential
equations via operator-theoretic methods
- Hilbert spaces of functions
- Duality, weak convergence
- Sobolev spaces
- Spectral theory of compact operators
- Homework: 40%
- Midterm : 30%
- Final: 30%
Assignments: Homeworks will be assigned and collected.