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's policies.

Textbook: Partial Differential Equations: Second Edition, by Lawrence C. Evans.

Time and Location: MWF 9:10-10:00am, SC 1310.

Contact Information and Office hours.
Lecturer's office: Stevenson Center 1515.
Lecturer's email: marcelo.disconzi@vanderbilt.edu.
Lecture's office hours: MWF 10:10am–11:10am, or by appointment.
Lecturer's office phone: (615) 615-7147.
General Math Office: Stevenson Center 1326, phone: (615) 322-6672.

Resources and extra material.
Multivariable caulculus is an important pre-requisite for this course. If you need to brush up your Calculus skills, there is a nice set of lecture notes by Gregory Naber, containing several examples, at:

http://www.gregnaber.com/lectures/calculus/

If typically you can learn things only by seeing tons of examples, you should have a look at the textbook "Schaum's outline of Partial Differential Equations" (or one of their variants), which contains more than 1000 problems solved. It can be found in the library or bought at a reasonable price on Amazon.

Exams.

Test 1	Wed, Oct 9, in class
Final Exam	Take-home

Announcements.
No announcements.

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

Date	Material Covered	Suggested HW problems	Assignments	Remarks
Aug 21	Introduction.
Aug 23	Review of multivariable calculus, chapter 1, appendix C.	HW1
Aug 26	More review. Intro to PDEs. Basic definitions. General form of a PDE. Linear PDEs.			If possible, read pages 20 to 22 of the textbook prior to Wed class.
Aug 28	Existence theorem for Poisson's equaion.
Aug 30	Existence theorem for Poisson's equaion.
Sept 2	Mean value formulas and maximum principle.	Problems 2, 3, 4, 5, 6, 10 and 11 of section 2.5. Prove theorems 14 on p. 37, and 15 on p. 41.	Problems 2, 3, 4, and 6 of section 2.5. Due: Sept 11.
Sept 4	Mollifiers, regularization. Regularity of harmonic functions.		Prove theorem 7 on p. 29 and theorem 10 on p. 31. Due: Sept 18th.
Sept 6	Green's function for the Laplacian, analyticity of harmonic functions, Harnack inequality.
Sept 9	Fundamental solution for the heat equation. Initial value problem.
Sept 11	Student presentation: distributions.		Do these problems. Due: Sept 18th.
Sept 13	Wave equation in 1d; D'Alembert's formula.
Sept 16	Wave equation in even and odd dimensions.		Problems 13, 14, 15, 18, 19, 21, 24 of section 2.5. Do also these problems. Due Sept 25th.
Sept 18	Finite propagation speed for the wave equation; uniqueness. Review of measure theory.
Sept 20	Review of functional analysis.		Extra credit. Due: Sept 30th.
Sept 23	Weak derivatives.
Sept 25.	Sobolev spaces.		Problems 1, 3, 4, 9, 10, 11, 14, 15 of chapter 5. Also these problems. Due: Oct 4th. Extra credit: 2, 5, 6 of chapter 5. Due: Oct 4th.
Sept 27	Sobolev embedding.
Sept 30	Sobolev embedding.
Oct 2	Sobolev embedding and other properties of Sobolev functions.
Oct 4	Sobolev embedding and other properties of Sobolev functions.
Oct 7	Extension and difference quotients for Sobolev functions.
Oct 9	Test.
Oct 11	Fall Break.
Oct 14	Test corrections Classification of equations in elliptic, parabolic and hyperbolic.
Oct 16	Definition and generalities about weak solutions of second order linear elliptic equations.
Oct 18	Existence of weak solutions for second order linear elliptic equations.
Oct 21	Fredholm alternative. Statement and applications.		Problems 1, 2, and 3 of section 6.6. Due: Oct 28th.
Oct 23	Fredholm alternative.
Oct 25	Fredholm alternative.
Oct 28	Elliptic regularity.
Nov 1	Elliptic regularity. Weak maximum principle.		HW. Due Nov 11.
Nov 6	Boundary maximum principle
Nov 8	Strong maximum principle
Nov 11	Negative norm Sobolev spaces			Notes.
Nov 13	Applications of negative norm Sobolev spaces: necessary and sufficient condition for existence of linear PDEs.
Nov 15	Seminar			The PDE seminar (4:10pm, SC 1307) will replace the class.
Dec 2nd	Local solvability. Egorov's counter-example.			Notes.
Dec 4	Discussion of the take-home 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.