Mathematics: Adv Ordinary Diff Equations

Linear and nonlinear systems, approximate solutions, existence, uniqueness, dependence on initial conditions, stability, asymptotic behavior, singularities, self-adjoint problems. Prerequisite: Graduate student or Instructor permission; knowledge of differential equations required.

Prereqs: MATH 3230; Open to Degree and PACE students

This course provides a modern analytical treatment of nonlinear ordinary differential equations. Phase plane analysis and the bifurcation theory will be introduced. Fixed points, limit cycles and chaos will be studied. Quantitative techniques such as the multiscale perturbation method for the treatment of limit cycles and bifurcations will be presented. While the course focuses on the analytical treatment of ordinary differential equations, numerical computations of these equations in Matlab will also be described. A term project will be assigned, where students can use the learned theories to do certain hands-on projects of current interest. Textbook: Nonlinear Dynamics and Chaos (2nd edition), by Steven Strogatz

The students are expected to master the analytical techniques and theories presented in class and apply them to homework problems. They are also expected to learn how to compute ordinary differential equations in Matlab and use it to do some of the homework problems. In addition, they are encouraged to apply this newly learned knowledge to some research projects of current interest. Students should have had knowledge of elementary ordinary differential equations (the equivalent of Math 3230) before taking this class.

A total of approximately 7 homeworks will be given on irregular basis. Computers will need to be used on some of the problems. There will also be a midterm exam and a term project. No final exam. Grading: homework: 50%; midterm exam: 25%; term project: 25%.