**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:** http://math.berkeley.edu/~wilken/204.F09

**Grading:** 100% Homework

**Homework:** 8-10 assignments

**Comments:**