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.
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| 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 in-class 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 M-test 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 |
IN-CLASS
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 |
IN-CLASS
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 |
IN-CLASS 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 |
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