MATH 673, PARTIAL DIFFERENTIAL EQUATIONS I
FALL 2017
Instructor:
Konstantina Trivisa:
 Office: 3307 Mathematics Bldg
 Phone: (301) 4056865
 Office Hours: (Fall 2017)
Tu, Th 9:15  10:30 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 24 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 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
Grading (approximate):
 Homework: 40%
 Midterm : 30%
 Final: 30%
MIDTERM
The midterm exam for the class will be given on Thursday November 2 (in class).
FINAL
The final exam for the class will be a takehome exam.
Assignments: Homeworks will be assigned and collected.