MATH 673, PARTIAL DIFFERENTIAL EQUATIONS I
FALL 2004
Instructor:
Konstantina Trivisa:
- Office: 4103 Mathematics Bldg
- Phone: (301) 405-5067
- Office Hours: (Fall 2004)
Tu, Th 9:00 - 10:15 or by appointment.
- Email:
trivisa@math.umd.edu
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).
Prerequisites:
MATH 411 or equivalent.
Main Text:
-
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.
Further reading
Elliptic partial differential equations of second order by D. Gilbarg and
N. Trudinger
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 0101
- 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
Grading (approximate):
- Homework: 40%
- Midterm : 30%
- Final: 30%
Assignments: Homeworks will be assigned and collected.
MIDTERM
midterm.pdf,
FINAL
final.pdf,