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 3120 - Introduction to PDEs

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. Students taking this course for graduate credit should consult the MATH 5120 syllabus.

Textbook: No textbook will be adopted. Support references are given in the syllabus.

Classes meet on TR, 1:102:25pm at Stevenson Center 1432 (4th floor of the Mathematics Building).

Contact Information and Office Hours
Instructor's office: Stevenson Center 1515 (5th floor of the Mathematics Building).
Instructor's email: marcelo.disconzi@vanderbilt.edu.
Instructor's office hours: Tuesdays 35pm, Thursdays 34pm, or by appointment.
Instructor's office phone: (615) 322-7147.

Exams and assignments

Description % of the final grade Date
Location and Time
Remarks
Midterm 30% Thu, Feb 27 In class Review questions.
Final 35% Wed, Apr 29
3pm, location TBA
HW assignments 35% on a regular basis (see below) posted on webpage


Schedule
Below is an ongoing schedule for the course (for the academic calendar, click here). This will be updated regularly and, therefore, students should check this webpage frequently. The due date for each assignment will be posted as the course progresses. Click here for the class notes (these will be updated on a regular basis).

Date Material covered Homework Remarks
Jan 7 Introduction. Examples of PDEs.
HW 1.
HW 1 Solutions.
HW 1 due on 1/16 at 5pm.
Jan 9 The Schrodinger equation and separation of variables.

Notes on the Schrodinger equation.
Jan 14 More on Schrodinger's equation. Separation of variables for the 1d wave equation.
HW 2.
HW 2 Solutions.
HW 2 is due on 1/23 at 5pm.
Jan 16 Fourier series.

Summary of theorems.
Jan 21 The 1d wave equation on the real line. D'Alembert's formula.


Jan 23 More on 1d waves: generalized solutions and propagation of singularities.
Some general tools for the study of PDEs.
HW 3.
HW 3 Solutions.
HW 3 is due on Jan 30 at 5pm.
Jan 28 Formal aspects of PDEs: general definitions and notation. Laplace's and Poisson's equation in R^n. Fundamental solution to Laplace's equation.


Jan 30 Existence of solutions to Poisson's equation. Harmonic functions and their properties.
HW 4.
HW 4 Solutions.
HW 4 is due on 2/13 at 5pm.
Feb 4 Project: heat equation.
Project.
Project Solutions.
Project due on 2/13 at 5pm.
Feb 6 Project: heat equation.


Feb 11 More on harmonic functions: maximum principle and selected results. The wave equation in R^n: finite propagation speed.


Feb 13 Solutions to the wave equation in R^2 and R^3.
HW 5.
HW 5 Solutions.
HW 5 is due on 2/20 at 5pm.
Feb 18 Duhamel's principle. The Minkowski metric, Lorentz fields, and commutator properties.
HW 6.
HW 6 Solutions.
HW 6 is due on 2/27 at 5pm.
Feb 20 Decay of solutions for the wave equation in R^n.


Feb 25 Review for the test.


Feb 27 Midterm

Feb 29 - Mar 8 Spring break

Mar 10


Mar 12


Mar 17


Mar 19


Mar 24


Mar 26


Mar 31


Apr 2


Apr 7


Apr 9


Apr 14


Apr 16



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 doing that, here you have the opportunity to send some anonymous feedback.