Instructor: Jon Wilkening

Lectures: TuTh 11-12:30, Room 7 Evans

Course Control Number: 54761

Office: 1091 Evans

Office Hours: Tues 10-11, 3-4

Prerequisites: Undergraduate Analysis and Linear Algebra

Required Text:
Coddington and Levinson, Theory of Ordinary Differential Equations

Recommended Reading:
Hurewicz, Lectures on Ordinary Differential Equations
Courant and Hilbert, Methods of Mathematical Physics, vol 1

Syllabus: Rigorous theory of ordinary differential equations. The first third of the course deals with fundamental existence, uniqueness and continuity theorems for initial value problems. We'll also discuss variational equations, linearization, periodic coefficients and Floquet Theory. Then we move on to boundary value problems, studying Green's functions, Sturm-Liouville theory, and eigenvalue problems (linear and nonlinear). If time permits, I'll also talk about ODE in abstract spaces, semigroup theory and the Hille-Yosida theorem. We end with phase plane analysis, the Poincare-Bendixson Theorem, bifurcation theory, the Liapunov-Schmidt reduction, Hamiltonian systems, generalized coordinates, and Hamilton-Jacobi equations.

Course Webpage: /~wilken/204.F09

Grading: 100% Homework

Homework: 8-10 assignments

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