MATH 673, PARTIAL DIFFERENTIAL EQUATIONS I
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: 3307 Mathematics Bldg
- Phone: (301) 405-6865
- Office Hours: (Fall 2017)
Tu, Th 9:15 - 10:30 or by appointment.
MATH 411 or equivalent.
Lawrence C. Evans,
Partial Differential Equations
The syllabus of Math 673/AMSC 673
consists of the core material in Chapters 2-4 and of selected topics from Chapters 5 and 6.
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 1311
- COURSE OUTLINE
- Analysis of boundary value problems for Laplace's equation
- Initial value problems for the heat and wave equations
- Fundamental solutions
- Maximum principles and energy methods
- First order nonlinear PDE, conservation laws
- Characteristics, shock formation, weak solutions
- Entropy conditions, viscosity solutions
- Homework: 40%
- Midterm : 30%
- Final: 30%
The midterm exam for the class will be given on Thursday November 2 (in class).
The final exam for the class will be a take-home exam.
Assignments: Homeworks will be assigned and collected.