**MATH 723**

**Meeting times**: MWF 1:25 - 2:15 PM at **LeConte (****LC****) 405**.

**Instructor**: Dr**. Peter G. Binev**

http://www.math.sc.edu/~binev/

e-mail: binev@math.sc.edu

phones: 576-6269 (at LC 425) *or* 576-6304 (at SUM 206H)

**Office hours**: MWF 11:00 - 12:00 AM at LeConte 425 or by appointment.

**Credits: **3

** **

**Prerequisites**: MATH 703/704 or permission of instructor

**Learning Outcomes**: Upon the successful completion of this course students will be able to:

· recall methods for finding representation formulas for solutions of basic linear and nonlinear PDEs;

· apply the basic properties of transport, Laplace's, heat, wave, and nonlinear first-order equations to analyze their solution;

· utilize the theory of Sobolev spaces to derive facts about solutions of elliptic equation.

**Cell Phones and Calculators**: All electronic devices, especially cell phones, ** must be disabled** during the class. No calculators are allowed.

**Homework and Presentations**: A few homework problems will be assigned each class. The homework will not be collected or graded. The problems will be discussed in class and some of them presented by a student. The students will have to present a proof will be several five-minute quizzes at the end of some classes on problems similar to ones from the homework. Each quiz will be graded 0 or 1 (no partial scores). The quiz grade will be the number of successfully solved quizzes but will not exceed 10. It will account for 10% of the final grade.

**Project / Final Exam**: In place of the final exam each student has to prepare a project considering a theoretical subject from the textbook which was not discussed in class. A 25-minutes talk should be prepared and presented at the end of the semester or during the time slot for the final exam on Wednesday, December 12 at 12:30 PM.

**Grading**: The final grade will be determined from the homework presentations and participation in the discussions (50%) and the project talk (50%). The letter grades will be assigned as follows: **A** for at least 90%; **B+** for at least 86%; **B** for at least 80%; **C+** for at least 76%; **C** for at least 70%; **D+** for at least 66%; **D** for at least 60%; **F** for less than 60%.

**Academic Dishonesty: **Cheating and plagiarism will not be allowed. The University of South Carolina has clearly articulated its policy governing academic integrity and students are encouraged to carefully review it: http://www.housing.sc.edu/academicintegrity/policy.html.

**ADA**: If you have special needs as addressed by the Americans with Disabilities Act and need any assistance, please notify the instructor immediately.

**Important Dates**:

August 29 – Last day to drop without **W**

September 3 – Labor Day - no classes

October 10 – Last day to drop without **WF**

October 18-19 – Fall Break

November 21-23 – Thanksgiving - no classes

December 7 – Last Class

December 12 – Final day to present the project talk, starting at 12:30 PM