Policies

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

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. Four Lectures will be given to review the basics of some first and second order equations.

Text and References:

1. [Boyce] William E. Boyce, Richard C. DiPrima and Douglas B. Meade, “Elementary Differential Equations and Boundary Value Problems,” 11th edition, Willey, 2017.

2. [Coddington] E. A. Coddington and N. Levinson,Theory of Ordinary differential Equations, McGraw Hill Education, 2017.

3. [Simmons] George F. Simmons and Steven G. Krantz, Differential Equations: Theory, Technique, and Practice, McGraw Hill Education, 2006.

4. [Perko] L. Perko, Differential Equations and Dynamical Systems, 3rd Edition, Springer, 2008.

Course Learning Outcomes (CLO):

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

• • apply power series method to solve certain types of differential equations and able to understand Legendre polynomials and Bessel functions.

  • give examples of differential equations for which either existence or uniqueness of solution fails.

  • solve boundary value problems and Sturm-Liouville problems.

  • state correctly and apply basic facts of systems: fundamental matrices, eigen-values, non-homogeneous systems.

  • sketch the phase portraits and apply standard methods to check the stability of critical points for autonomous system.