Spring 2013 Course Syllabus - Mathematics 8142.001

Course: Mathematics 8142.001.
Course Title: Partial Differential Equations.
Time: 2:00pm-3:20pm.
Place: Wachman 617.
Instructor: Mendoza, Gerardo A.
Instructor Office: Wachman 618.
Instructor Email: gerardo.mendoza@temple.edu
Instructor Phone: 1-5053.
Course Web Page: http://math.temple.edu/~gmendoza/
Office Hours: by appointment.
Prerequisites: Participants are assumed to have a solid background in undergraduate analysis (i.e. advanced calculus) and linear algebra, as well as the skills to provide complete proofs, or understand that they do not have a correct, complete proof. This is the second semester of a year-long sequence, so students are also required to have some advanced exposure to PDEs.
Textbook: (1) Partial Differential Equations: Second Edition, by Lawrence C. Evans, and (2) Basic Linear Partial Differential Equations, by Francois Treves.
Course Goals: The course gives students the opportunity to acquire a solid background in partial differential equations and ancillary topics such as function spaces, their generalizations, and the abstract analysis tools used in the study of Partial Differential Equations. Students who successfully complete the two semester sequence should be well prepared to take the PDE section of the Ph.D. Comprehensive Examination.
Topics Covered: Elliptic (formally selfadjoint) second order operators: Dirichlet and Neumann problems, maximum principles, mean value theorems. Parabolic equations: Cauchy problem, maximum principle. Hyperbolic equations: Cauchy problem, Huygens principle, energy methods. Analytic equations: Cauchy-Kovalevska theorem, Holmgren's uniqueness theorem.
Course Grading: The primary assessment tool will be extended weekly or bi-weekly homework problems. Exams, if I deem it necessary to get a better sense of where the students are with respect to the material being covered. There will be t least one 3-hour long exam in the style of the PDE section of the written comprehensive examination.
Exam Dates: Mid-term exams will be scheduled with enough advance notice. We will have at least one 3-hour long exam in the style of the PDE section of the written comprehensive examination to be scheduled by consensus.
Attendance Policy: Attendance is required. This is not a trivial topic, the dynamics of in-class interaction has no replacement.

Any student who has a need for accommodation based on the impact of a disability should contact me privately to discuss the specific situation as soon as possible. Contact Disability Resources and Services at (215) 204-1280, 100 Ritter Annex, to coordinate reasonable accommodations for students with documented disabilities.

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Students will be charged for a course unless a withdrawal form is processed by a registration office of the University by the Drop/Add deadline date given below. For this semester, the crucial dates are as follows:

• The first day of classes is Tuesday, January 22.
• The last day to drop/add (tuition refund available) is Monday, February 4.
• Spring recess is the week of Sunday, March 10 - Sunday, March 17.
• The last day to withdraw (no refund) is Tuesday, March 26.
• The last day of classes is Monday, May 6.

During the first two weeks of the fall or spring semester or summer sessions, students may withdraw from a course with no record of the class appearing on the transcript. In weeks three through nine of the fall or spring semester, or during weeks three and four of summer sessions, the student may withdraw with the advisor's permission. The course will be recorded on the transcript with the instructor's notation of "W," indicating that the student withdrew. After week nine of the fall or spring semester, or week four of summer sessions, students may not withdraw from courses. No student may withdraw from more than five courses during the duration of his/her studies to earn a bachelor's degree. A student may not withdraw from the same course more than once. Students who miss the final exam and do not make alternative arrangements before the grades are turned in will be graded F.

The grade I (an "incomplete") is reserved for extreme circumstances. It is necessary to have completed almost all of the course with a passing average and to file an incomplete contract specifying what is left for you to do. To be eligible for an I grade you need a good reason and you should have missed not more than 25% of the first nine weeks of classes. If approved by the Mathematics Department chair and the CST Dean's office, the incomplete contract must include a default grade that will be used in case the I grade is not resolved within 12 months.