PARTIAL DIFFERENTIAL EQUATIONS
Math 758, Spring 2018
Instructor: Adrian Tudorascu
Office: Armstrong Hall 410F
· Lecture Schedule
The class will meet twice a week, on Tuesday and Thursday in CHI-D (Chitwood Hall) G17 from 1:00 p.m. to 2:15 p.m. We will not meet on official holidays and on dates I need to travel for scientific purposes. On those dates, someone else may substitute; you will be notified in advance.
· Course Description and Goals
Most of the material will be presented in a manner consistent with the presentations in the text. Students are expected to read and study the examples and related material in the text and to work on the assigned problems sets. Similar problems will be used as examples during lectures as preparation for the exams.
Prerequisite: Math 452, Math 757.
Time permitting, the topics we plan to cover include: First Order Nonlinear PDE’s (Hamilton-Jacobi, Scalar Conservation Laws), Distributions, Sobolev spaces, Weak solutions for Elliptic, Parabolic and Hyperbolic PDE’s etc.
Upon completion of this course, the student should be able to apply these notions and techniques to problem solving. For this, the student is expected to have thoroughly understood the theory linking the concepts.
The text to be used for most of the course is “Partial Differential Equations; Second Edition” by Lawrence C. Evans, AMS, Graduate Studies in Mathematics (current bookstore edition).
· Grading Policy and Evaluation
There will be periodically assigned homework, one mid-term examination and one final examination. Each of the exams will account for 30% of the course grade, while the homework will account for 40%. The cutoffs will be 90% for an A, 85% for a B+, 80% for a B, 75% for a C+, 70% for a C and 60% for a D.
The Mid-term (take home) will be administered during the first or second week of March at a time to be agreed upon.
The Final Exam is scheduled for Friday, May 04 from 11:00am to 1:00pm!
Will be assigned via email. You will be made aware (in class or by e-mail) when a new assignment is posted and when it will be due. Students are strongly encouraged to work on all the problems at the end of each section and collaborate (see Course Policy below). Be aware that the problems and exercises tested on tests may be similar or even identical to some homework assignments.
· Office Hours
When: Tuesday and Thursday between 2:30--3:30pm
Or by appointment.
Where: My Office.
· Course Policy
Class attendance is encouraged. The Office Hours are to be used only after you will have thoroughly read the material and tried to understand it.
Most likely, no calculators will be allowed on any test.
It is important that you not discard returned tests and graded homework assignments! Not only do they constitute good material for review but they are also the only acceptable proof in case of misrecorded grades.
You may discuss your assignments with each other; however, solutions should be written down individually. You should not read anyone else's completed work or show yours to anyone else.
Exams are to be worked on and written down strictly individually.
How to succeed in this class:
- Attendance will not be taken in this class, however, it is expected that you will attend class regularly. If you do miss a class it is your responsibility to find out what was covered and whether any important announcements were made.
- The single most important thing that you should do is work out at least the assigned homework. You should do the assigned problems, along with an assortment of unassigned problems, as a study aid.
- Collaboration on homework is a good thing. You are encouraged to discuss the homework and to work together on the problems.
- Like all mathematics, the material in the course cannot be learned passively. However reasonable, simple, or rational you may find what you read or hear, you do not understand it if you cannot apply it yourself. Thus it is imperative that you test yourself by doing problems. If you have difficulty with a problem, ask your instructor or your fellow students about it; do not assume that the difficulty will cure itself without treatment.
Have you questions or concern about the course, please see me during the office hours!