MATH 723

# Differential Equations I

## Fall 2012

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.

### Description: Basic theory for partial differential equations including representations of solution for transport, Laplace's, heat, wave, and nonlinear first-order equations; fundamental solutions, maximum principles, Green’s function, energy method and Dirichlet principle; Sobolev spaces: weak derivatives, extension and trace theorems.

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