Partial Differential Equations

 Mathematics V3028, Spring 2006

Time and Place : TR  1:10pm-2:25pm, 203 Mathematics Building

Instructor : Professor P. Daskalopoulos

Office : 526 Mathematics
Office hours: TR 2.30pm-3.30pm
Email :  pdaskalo@math.columbia.edu
Class Homepage :   http://www.math.columbia.edu/~pdaskalo/V3028.html


Course Description. This course is an introduction to partial differential equations, emphasizing on the three classical linear equations: the wave equation, the heat (diffusion) equation and the Laplace equation. We will present the properties of these equations together with the basic techniques that have proved useful in analyzing them. Many important ideas can be understood in terms of them. The methods that we will use include fundamental solutions and transform methods for problems on the line, and separation of variables, using orthogonal series, for problems in regions with boundary.

Prerequisites. Calculus 3A, Calculus 4A, and ordinary differential equations. Some mathematical sophistication. Other topics will be introduced as needed.

Text. Partial Differential Equations: An Introduction. By Walter A. Strauss.

Homework. There will be weekly problem sets. Homework will be collected (on the Tuesday the next week) and graded. The first problem set is due Tuesday, January 24.

Midterm Examination.There will be one seventy-five minute midterm examination which is tentatively scheduled on Thursday, March 9. There are no makeups for missed exams, regardless of the reason for absence.

Final Examination. There will be a three-hour final examination given at the end of the term, in the usual classroom. You must take the final examination at the time scheduled by the university; no final exams will be given earlier. In particular, examinations will not be rescheduled because of travel arrangements. It is your responsibility to schedule travel appropriately.

Grading. The course grades will be computed as follows: 20% Homework, 30% Midterm exam, 50% Final exam.

TA. Maria-Cristina Caputo caputo@math.columbia.edu. Office hours: Wednesday 10am-2pm at the Math Help Room.

Schedule of Lectures