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, 8:10am–9:35am, at Stevenson Center 1431 (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: Thursdays, 09:30am–12:30pm, or by appointment.
Instructor's office phone: (615) 322-7147.

Exams

Description Date
Location and Time
Remarks
Test 1 Thu, Feb 9 In class
Test 2 Thu, Mar 23
In class Change: the exam has been changed from the previously scheduled date of Mar 21. Study guide for the second test.
Final Exam Thu, May 4 9am, at SC 1431
Study guide for the final.

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.

Date Material covered Homework Remarks
Tue, Jan 10
Introduction. Examples of PDEs.


Thu, Jan 12
More examples. Formal definition of PDEs. Homogeneous and linear PDEs. Some notation.
HW 1.
HW 1 due on Tue, Jan 24.
Solutions to HW 1.
Tue, Jan 17 More on linear equations. Solving first order PDEs by examples.


Thu, Jan 19 The method of characteristics. HW 2. HW 2 is due on Tue, Jan 31.
Solutions to HW 2.
Tue, Jan 24 Limitations of the method of characteristics. Shock waves.

Thu, Jan 26 Theorem on existence and uniqueness of first order PDEs.

Tue, Jan 31 The 1d wave equation: forward and backward waves and speed of propagation. Class notes as of Jan 31. HW 3. HW 3 is due on Tue, Feb 7.
Solutions to HW 3.
Thu, Feb 2 D'Alembet's formula. Class notes.

Tue, Feb 6 More on the 1d wave equation. The initial-boundary value problem and separation of variables. Class notes.

Thu, Feb 9 Test 1. Test solutions.

The, Feb 14 More on separation of variables for the 1d wave equation. Fourier series. Class notes. HW 4.
Practice problems.
HW 4 is due on Tue, Feb 28.
Solutions to HW4.
Thu, Feb 16 More on Fourier series.

Tue, Feb 21 Convergence of Fourier series. Convergence of formal solutions to the wave equation. Class notes. Summary of theorems.

Thu, Feb 23 The Schrodinger equation. Separation of variables.

Tue, Feb 28 The Schrodinger equation. Spherical harmonics. Class notes.
Notes on the Schrodinger equation.
Practice problems.
Thu, Mar 2 The Schrodinger equation. The radial part. Class notes.

Tue, Mar 14 Fourier transform. Class notes. HW 5.
Practice problems.
HW 5 is due on Tue, April 11.
Solutions to HW5.

Thu, Mar 16 Laplace transform. Class notes.

Thu, Mar 23 Test 2. Test solutions.

Tue, April 4 Tools from calculus in R^n. Class notes.

Thu, April 6 Laplace's and Poisson's equation in R^n. Fundamental solution to Laplace's equation. Class notes. Practice problems.
Tue, April 11 Theorem on existence of solutions to Poisson's equation in R^n. Class notes.

Tue, April 11
Make-up class
Student presentation: Further properties of the Laplace transform; the Navier-Stokes equations.

Thu, April 13 Theorem on existence of solutions to Poisson's equation in R^n. Class notes. HW 6. HW 6 is due on Monday, April 17.
Tue, April 18 Green's function. Class notes.

Tue, April 18
Make-up class
Solutions to the wave equation in R^n. Class notes.

Thu, April 20 Conservation of energy and finite propagation speed for the wave equation in R^n. Duhamel's principle. Class notes. Practice problems.


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.