Course Number:

Credit Hours:

4

Course Title:

Ordinary Differential Equations

Course Description:

Covers the basics of ordinary differential equations including analytical, qualitative, and geometric methods. Topics include geometric interpretation of ordinary differential equations, such as direction fields, vector fields, and phase space; flow defined by a vector field; integral curves and phase curves; integrals of motion and their use in investigating properties of the flows; conservative systems with one degree of freedom and their phase portraits; linear systems and their properties; Wronskian exponents of matrices and their calculation; classification of singular points of first-order linear systems with constant coefficients in the plane; existence and uniqueness of solutions for ordinary differential equations and systems; notion of stability; investigating stability by linearization; Lyapunov functions in determining stability; second-order linear equations including Sturm theory for zeros of solutions; and asymptotics of solutions of second-order linear equations.