Welcome to the MATH 835 website for this semester
This is what the guide says we will do...
Methods of solution for evolutionary partial differential equations and systems primarily from a classical perspective. Linear and nonlinear equations and systems; characteristics; shocks and discontinuous solutions; similarity solutions; modern applications and dynamical systems approaches. PREREQ: MATH617 or equivalent.
This is where and when...
MWF
9:05AM  9:55AM at Ewing Hall 209
The book
Sandro Salsa. Partial Differential Equations in Action. From Modelling to Theory. Chapters 2, 4 and 5.
Newsbox
A document with some
notes has been added in the Everything else page.
Tell me about any typos you find in there. I have posted more exams for your records. Go to the Everything else page. Use the original (with space to write) for the repeat of the inclass exam. 
The table with the detailed schedule
The expression (See class) in the problem list means that one or more problems will be proposed in the class time. Take home exams will be composed of (slight variations of) proposed problems and variants thereof.
Week 
Lecture 
Section 
Description 
Problems 

1 
08/29 
W 
2.1.2 
DIFFUSION. Meet the heat equation 

08/31 
F 
2.1.3 & 2.1.5 
The parabolic boundary 

2 
09/05 
W 
2.1.4 
Separation of variables 
2.1, 2.2, 2.3 
09/07 
F 
2.1.4 
The Weierstrass Mtest and Fourier series 
See class 

3 
09/10 
M 
2.2.1 
Weak initial conditions
and uniqueness 
See class 
09/12 
W 
2.2.2 
The maximum principle 
2.4, 2.5, 2.7, 2.16 

09/14 
F 
2.3 
The heat kernel 

4 
09/17 
M 
2.3.3 
The Dirac delta 
See class 
09/19 
W 
2.8 
The Cauchy problem for the heat equation 
2.13, 2.14, 2.15 

09/21 
F 
INCLASS
QUIZ #1 

5 
09/24 
M 
2.4 
MODELS INVOLVING DIFFUSION. From random walks to the heat equation 
Read
sections 2.4 and 2.5. 
09/26 
W 
2.5 
Introducing drift 

09/28 
F 
Diffusion, convection,
reaction 

6 
10/01 
M 
4.2.1, 4.2.2 
SCALAR
CONSERVATION LAWS. The linear transport equation 
4.1, 4.2 
10/03 
W 
4.2.3, 4.2.4 
Inflow and outflow 

10/05 
F 
TAKE HOME
EXAM #1 DUE 

7 
10/08 
M 
4.3.1, 4.3.2 
Characteristics in a
traffic flow model 

10/10 
W 
4.3.3 
Rarefaction waves 
4.4, 4.7, 4.9 

10/12 
F 
4.3.4, 4.4.1 
Shock waves 
4.3, 4.5, 4.6, 4.10 

8 
10/15 
M 
4.4.2, 4.4.3 
Weak solutions 

10/17 
W 
4.4.3 
Weak solutions (cnt'd) 

10/19 
F 
INCLASS
QUIZ #2 

9 
10/22 
M 
4.4.4., 4.4.5  The entropy condition and the Riemann problem  4.11 
10/24 
W 
4.4.7 
Burger's equation  
10/26 
F 
Applications (Euler and
shallow waters) 

10 
10/29 
M 
[Sandy] 

10/31 
W 
[Sandy] 

11/02 
F 
5.1 
THE WAVE
EQUATION. Some solutions to the wave equation 

11 
11/05 
M 
5.1 
More solutions and some
arguments 

11/07 
W 
5.2, 5.3 
The vibrating string 
5.2, 5.3 

11/09 
F 
5.4.1, 5.6 
TAKE HOME EXAM #2 DUE D'Alembert's solution 
5.4, 5.5, 5.6 

12 
11/12 
M 
5.4.3 
The fundamental solution 
5.10, 5.11 
11/14 
W 
5.7.2  Energy arguments  
11/16 
F 
5.9.1,5.9.2 
The Huygens Principle 
5.16, 5.17 

13 
11/19 
M 
5.9.2, 5.9.4 
Kirchhoff's formula 

Thanksgiving
weekend 

14 
11/26 
M 
TAKE HOME
EXAM #3 DUE Weak solutions 

11/28 
W 
Integral equations 

11/30 
F 
INCLASS QUIZ #3 

15 
12/03 
M 
Project presentations
(Gold team) 

12/05 
W 
Project presentations
(Blue team) 

12/06 
R 
Project presentations
(Maroon team) 

And
we are done 