Marcelo Mendes Disconzi
Department of Mathematics, Vanderbilt University

email: marcelo.disconzi at vanderbilt.edu
office: Stevenson Center 1515
phone: (615) 322 7147   fax: (615) 343 0215
mail to: 1326 Stevenson Center, Vanderbilt University, Nashville TN 37240

Vanderbilt












Marcelo Mendes Disconzi
MATH 234 - Spring 13

General Information.
For a description of the course, including the grading policy, consult the course syllabus. Students are responsible for reading the syllabus and being aware of all the course and university's policies.

Textbook: An introduction to partial differential equations, by Yehuda Pinchover and Jacob Rubinstein.

Time and Location: Tuesday and Thursday, 2:35pm–3:50pm, Stevenson Center 1120.

Contact Information and Office hours.
Lecturer's office: Stevenson Center 1222.
Lecturer's email: marcelo.disconzi@vanderbilt.edu.
Lecture's office hours: Tuesday and Thursday 11:00am–12:00pm, Tuesday 1:00pm–2:00pm, or by appointment,  at the lecturer's office.
Lecturer's office phone: 322-1998.
General Math Office: Stevenson Center 1326, phone: 322-6672.

Resources and extra material.
If you need to brush up your Calculus skills, there is a nice set of lecture notes by Gregory Naber, containing several examples, at:

http://www.pages.drexel.edu/~gln22/Lecture%20Notes%20on%20Calculus.htm

If typically you can learn things only by seeing tons of examples, you should have a look at the textbooks "Schaum's outline of Partial Differential Equations" (or one of their variants), which contains more than 1000 problems solved. It can be found in the library or bought by a reasonable price on Amazon.

Exams.

Test 1
Thu, Feb 28, in class
Test 2
Tue, Apr 30, 9:00am (location TBA)


Announcemtns.


Click here for a practice exam! And here for solutions.


Schdeule.
Below is a schedule for the course. Unless stated otherwise, all problems and sections are from the textbook.

Date
Material Covered
Suggested HW problems
Assignments Remarks
Tue Jan 8
Introduction and examples of important PDEs.
1.2 of chapter 1.


Thu Jan 10
Basic concepts (sec. 1.1, 1.2, 1.4, 1.5).
Solutions of the heat equation by separation of variables (sec. 5.1, 5.2).
1.7 of chapter 1.
These problems.
Due: Jan 18.

Tue Jan15
More on the heat equation (sec. 5.2).
Solutions of 1-d wave equation by separation of variables (sec. 5.3)
5.1 to 5.6 of chapter 5.
Problems 5.1, 5.3, 5.4, and 5.5 of chpter 5.
Due: Jan 28.

Thu Jan 17
Solutions of the wave equation by separation of variables (sec. 5.3 and a little of 5.4). 5.14 of chaper 5.

Tue Jan 22
More on separation of variables.
The energy method for the wave equation (sec 5.5).
Discussion on non-uniqueness of solutions.
5.17, 5.18 and 5.19 of chapter 5.
These problems.
Due: Feb 7.
It is useful here to review the results about existence and uniqueness of solutions for ODEs.
Thu Jan 24
Function spaces and linear operatos.
Discussion on differentiability of functions.
Do the extra credit assignment 1. Extra credit assignment.
Due: Feb 7.

Tue Jan 29
Dirichlet and Neuman problem for the Laplacian (sec. 7.1 and 7.2).
Maximum principle (sec. 7.3).
7.1, 7.2, 7.5, 7.7, 7.9, 7.13 of chapter 7.
7.1, 7.2, 7.5, 7.7(a) of chapter 7.
Due: Feb 14th.
For the problems in polar coordinates, you can check your multivariable calculus book or some other PDE textbook.
Thu Jan 31
Maximum principle (sec. 7.3).


Tue Feb 5
Review of multi-variable calculus.
Green's identities (sec. 7.4).


Integration by parts in more than one dimension, Green's identities and the chain rule for functions of several variables are very important here. Review these topics thoroughly if necessary.
Thu Feb 7
Green's function for the Dirichlet problem (sec. 8.2).
8.4, 8.8, 8.9, 8.10, 8.11 of chapter 8.
8.4(a), 8.8, 8.11 of chapter 8.
Due: Feb 28th.

Tue Feb 12
Green's function for the Dirichlet problem (sec. 8.2).


Thu Feb 14
Final remarks on the Green's function.



Tue Feb 19
Optimization problems and calculus of variation: the minimal surface equation (sec. 10.1).


We are going to do many calculations similar to the ones done in class. Make sure you understand them. Also, read section 10.1 of the textbook.
Thu Feb 21
More on calculus of variations.
Problems from chapter 10


Tue Feb 26
No class: extended office hours during the time of the class in light of the midterm.



Thu Feb 28
Test 1



Tue Mar 5
Spring Break



Thu Mar 7
Spring Break



Tue Mar 12
Finite propagation speed for the wave equation (sec. 4.4).
General comments on elliptic, parabolic and hyperbolic equations.

Problmes 10.1, 10.2, 10.3 and 10.5 of chpater 10.
Due: March 28th.

Extra credit: problems 4.2, 4.3 and 4.5 of chapter 4.
Due: March 28th.
Some of the terminology in these problems is different than what we used in class (although the concepts are the same). Make sure to check the textbook for the meaning of those.
Thu Mar 14
Generalities on the heat equation.


Derivation of the heat equation
(Nithin's presentation).
Tue Mar 19
Numerical methods:
finite difference (sec. 11.1 and 11.2).



Thu Mar 21
More on finite difference (sec. 11.3).



Tue Mar 26
Stability and consistency of a numerical scheme (sec. 11.3).


Numerical solutions with Mathematica - Mathematica code - right click to download file (Clayton's presentation).
More details.
Thu Mar 28
Convergence of a numerical scheme.



Tue Apr 2
Finite difference for Laplace's equation.
Maximum principle.



Thu Apr 4
Finite diference for the wave equation.
Problems 11.1, 11.2, 11.6 , 11.10, 11.11 of chapter 11.
Note: for 11.6, see the definition on page 317; the parts of the problems where you are asked to use a computer are optional.


Tue Apr 9
Rudiments of the finite element method.



Thu Apr 11




Tue Apr 16
Student's presentations.


Curvature and PDE (Parker's presentation).
Thu Apr 18




Tue Apr 30
Test 2, 9:00am (location TBA)






Anonymous feedback.
Students are encouraged to bring suggestions and to discuss with the course instructor any concerns they may have, including something they think is not being properly handled in the course. But if you do not feel comfortable about doing that, here you have the opportunity to send some anonymous feedback.