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 Ln, Vanderbilt University, Nashville TN 37240

Vanderbilt












Marcelo Mendes Disconzi
MATH 8110 - Graduate partial differential equations

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: No textbook will be required. See the course syllabus for suggested references.

Classes meet on TR, 11:10-12:25pm at Stevenson Center 1210.

We will be following the COVID-19-related guidelines stipulated by Vanderbilt.

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, 1-3pm, Thursdays, 10-11am, or by appointment.
Instructor's office phone: (615) 322-7147.

Schedule
Below is an ongoing schedule for the course (for the academic calendar, click here). Click here for the class notes, and here for the class notes in handwritten form. The class notes will be updated and typeset as the course progress. Since typesetting them might take some time, typically the most up-to-date version of the notes will be in the handwritten form. Non-math majors taking the course can consult these notes on preliminary notions for some background on mathematical concepts, conventions, and notation that will be used in the course.

 Date  Material covered  Remarks
 Aug 27  Introduction. Examples of PDEs.  HW1 posted on Brightspace.
 Aug 31  Fundamental solution to the Laplacian. Solutions to Poisson's equation. Properties of harmonic functions.  HW2 posted on Brightspace.
 Sept 2  Maximum principle. Green's function.  
 Sept 7  The initial-value problem for the heat equation in R^n.  HW3 posted on Brightspace.
 Sept 9  The Cauchy problem for the 1d wave equation; D'Alembert's formula. Finite propagation speed for the wave equation in n dimensions. Domains of dependence and influence.  HW4 posted on Brightspace.
 Sept 14  Solutions to the wave equation in two and three dimensions. The inhomogeneous wave equation.  
 Sept 16  Weak derivatives.   HW5 posted on Brightspace.


Anonymous feedback
Students are encouraged to bring suggestions and 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 anonymous feedback.