Marcelo Mendes Disconzi
Department of Mathematics, Vanderbilt University

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


Marcelo Mendes Disconzi
MATH 234 - Spring 14

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 policies.

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

Time and Location: Tuesday and Thursday, 1:102:25pm, Stevenson Center 1120.

Contact Information and office hours.
Lecturer's office: Stevenson Center 1515.
Lecturer's email:
Lecture's office hours: Tuesday and Thursday 2:304:00pm, or by appointment.
Lecturer's office phone: 322-7147.
General Math Office: Stevenson Center 1326, phone: 322-6672.

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

If learn things best 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 solved problems. It can be found in the library or bought at a reasonable price on Amazon.


Thu, Feb 27, in class
Final Exam
May 1, 3-5pm, location SC 1120


Click here for a practice final. Here the solution. Here the source.
Here a list of formulas.

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

Material Covered
HW problems
Jan 7
Introduction. Derivation of the wave equation for an oscillating string.

Some background material. You can also get the Latex source file.
Jan 9
Initial and boundary conditions for the wave equation.
The heat equation.

Jan 14
More on the heat equation.
5.1, 5.5, 5.6, 5.7, 5.10, and 5.14.
Due: Jan 23.

Jan 16
Separation of variables for the wave equation.
Dirichlet and Neumann boundary conditions.
5.2, 5.3, 5.4, 5.11
Due: Jan 31.

Jan 20

Last day to drop the class with no grade
Jan 21
Separation of variables for the wave equation.
Brief discussion on convergence; formal, strong/classical, and weak solutions.

Jan 23
One-dimensional wave equation. Uniqueness, finite propagation speed, D'Alembert's formula.
4.2, 4.3, 4.4, 4.5, 4.6, 4.7, 4.8, 4.9.
Due: Feb 7.
For these problems, read carefully corollary 4.11. Doing problem 4.1 before starting the assigned HW problems may be helpful.
Jan 28
Review of multivariable calculus.

Jan 30
More review of multivariable calculus.
These problems. Due: Feb 17.
Also, these problems. Due: Feb 21.
And these problems. Due: Feb 21.

Feb 4
Laplacian in spherical coordinates.

Feb 6
The three-dimensional Schrodinger equation.

Feb 11
Schrodinger equation: the angular equation; spherical harmonics.

Class notes. You can also get the Latex source file.
Feb 13
Properties of Legendre polynomials; orthogonal polynomials.

Feb 18
Schrodinger equation for the Coulomb potential: the radial equation.

Feb 20
Schrodinger equation for the Coulomb potential: the radial equation. These problems. Due: March 14.
Feb 25
Review for the midterm.

Feb 27

Mar 4
Spring break

Mar 6
Spring break

Mar 11
Test correction

Mar 13
Fundamental solution for the Laplacian in n dimension

Mar 14

Last day to drop with a W in the course
Mar 18
Volumes and areas in n dimenions.
Polar coordinates in n dimensions.

Mar 20
Applications: Green's function for half-space and a ball.

Mar 25
More on the fundamental solutions. Some rigorous derivations.
HW problems from the class notes. Due: April 4.
You can also get the Latex source file.
Here the solutions, with the source file.

Mar 27
Solution of Dirichlet problem via Green's function.

Apr 1
Mean value formulas and the maximum principle. Applications.

Apr 3
More on mean value formulas and the maximum principle.

Apr 8
Elementary theory of distributions.
HW problems from the class notes.
Due: April 18.
You can also get the Latex source file.
Here the solutions, and the source file.

Apr 10
Distribtuions and weak solutions.

Apr 15

Apr 17

May 1
Final Exam

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.