MTH (0144) 544 - Ordinary Differential Equations

Credits: 3.00

Ordinary differential equations are used in every field of science and engineering to describe dynamical systems. Students will be exposed to sophisticated solution techniques and analysis for the study of smooth dynamic systems. Students apply these methods to classical mechanics and electrical circuits.

Free Note: Open only to students in the M.S. in Mathematics.

Students will be able to:
- solve first and second order differential equations — assessed by Quizzes 1-3
- apply criteria for existence and uniqueness of solutions – assessed by the mid-term examination
- deduce qualitative properties of dynamical systems and identify asymptotic behavior – assessed by Quizzes 4 & 5, and the mid-term examination
- classify equilibria by their stability, invariant manifolds, and topological type – assessed by Quiz #6
- illustrate solutions with phase plane analysis – assessed by the final examination
- define and identify chaotic behavior in dynamical systems – assessed by Quizzes 7, 8, 9
- identify and describe bifurcations of parameterized dynamical systems – assessed by Quizzes 9 & 10
- apply differential equations to models of real-world systems – assessed by Final Exam