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).

Due to the coronavirus outbreak, starting on March 16, we are moving to online classes for the remainder of the semester, and classes are canceled for the week of March 9-13. Online classes will meet at the regular class time through Zoom embedded in Brightspace (make sure you have Zoom installed in your computer). To attend the online meetings, log into your Brighspace account, select our course, and click on Zoom (on the horizontal menu on top). You will see the class online meetings schedule (with the meeting IDs if the Zoom app requests it). If you have difficulty connecting to a meeting or experience some technical issue (e.g., your audio is not working), let me know right away by email; I will keep my inbox open during classes for this purpose. During our faculty training session for online classes, it was pointed out that some people have difficulty with Brightspace's functions while using Safari, thus you are recommended to use a different browser.

HW will continue to be assigned regularly and must be delivered on the due date and time by email in scanned, pictured, or typeset format. Please email your HW directly to the grader at zhongtian.hu@vanderbilt.edu.

Office hours will be held by appointment. Send me an email to schedule an appointment, and a Zoom meeting will be set up accordingly.

For more information on online classes and Brightspace support, see the Brightspace resources for students. For more information about Zoom, see the Zoom quick guide. For more on the coronavirus outbreak and how it affects Vanderbilt, see the VU CODVID-19 webpage.

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 In view of the coronavirus outbreak, students have the option to use their grade from the midterm as their grade for the final exam, as discussed in class. If you still want to take the final exam, please contact the instructor to discuss details.
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 Canceled due to the coronavirus outbreak


Mar 12 Canceled due to the coronavirus outbreak

The classes below will meet virtually through Zoom embedded in Brightspace due to the coronavirus outbreak. See above for more information about moving to online classes.
Date Material covered Homework Remarks
Mar 17 The canonical form of second order linear PDEs: elliptic, parabolic, and hyperbolic equations. General strategy for the study of PDEs. Well-posedness. The method of characteristics.
HW 7.
HW 7 Solutions.
HW 7 is due on 3/26 at 5pm.
Mar 19 Local existence and uniqueness for first-order quasilinear equations via the method of characteristics.


Mar 24 Burgers' equation and shock-waves.


Mar 26 Scalar conservation laws. Weak solutions.
HW 8.
HW 8 Solutions.
HW 8 is due on 4/9 at 5pm.
Mar 31 No class (make-up class on Apr 7).


Apr 2 No class (make-up class on Apr 9).


Apr 7 The Rankine-Hugoniot conditions.


Apr 7
(make-up
class)
Systems of conservation laws. Simple waves.

Apr 9 Rarefaction waves.


Apr 9
(make-up
class)
The Riemann problem. Riemann invariants.
HW 9.
HW9 Solutions.
HW 9 is due on 4/29 at 5pm.
Apr 14 Blow-up of solutions for 2x2 systems of conservation laws.


Apr 16 Non-uniqueness of weak solutions. Entropy solutions.




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.