Policies

Purpose/Expectations: Graduate courses in partial differential equations are extremely necessary. The main objective is to provide mathematics majors with an introduction to the theory of partial differential equations (PDEs) through applications and methods of solution. Students will become knowledgeable about PDEs and how they can serve as models for physical processes. The course will also develop an understanding of the elements of analysis of PDEs.

Students are expected to attend every lecture and tutorial. In order to fully benefit from the course, the students should start doing homework and assignments. The entire syllabus will be covered approximately in 39 lectures as per schedule given below.

Text and References:

1. [Strauss] Walter A. Strauss, Partial Differential Equations: An Introduction, Willey, 2nd Edition, 2007.

2. [Evans] L. C. Evans, Partial Differential Equations, American Mathematical Society, 2nd Edition, 2010.

3. [Sneddon] I. N. Sneddon, Elements of Partial Differential Equations, Dover Publications, 2006.

4. [John] F. John, Partial Differential Equations, 4^th edition, Springer, 1991.

5. [Renardy] M. Renardy and R. C. Rogers, An Introduction to Partial Differential Equations, Springer, 2^nd edition, 2004.

Course Learning Outcomes (CLO):

On successful completion of this course, students will be able to:

• • state correctly and apply to examples the basic facts about the first order PDEs and method of characteristics.

  • classify second-order partial differential equations and transform them into canonical form.

  • state correctly and apply to examples the basic facts about the Wave equation: energy method, Huygens principle and Duhamel’s principle.

  • state correctly and apply to examples the basic facts about the Laplace equation: maximum principle and energy methods.

  • solve heat equation and can apply mean-value formula and energy methods.