Course Syllabus

Notes on ODE Theory

Lecture 1

Lectures 2-3

Lecture 4: Harmonic Regularity and Liouville's Theorem and Green's Functions and Distributions

Poisson Kernel of the unit ball and Energy Methods also a supplement on the Poisson Formula for the half space.

Lecture 6

Lecture 7: Heat equation in bounded domains, maximum principle.

Lecture 8: Heat equation uniqueness in unbounded domain.

Lecture 9: Wave equation, D'Alembert's formula, finite speed of propagation, Dirichlet boundary conditions.

Lecture 10: Wave equation in 2 and 3 dimensions, Huygen's Principle.

Lecture 11 and Lecture 12: Method of characteristics.

Lecture 13: Scalar conservation laws.

Lecture 14: Travelling wave solutions of PDE.

Lecture 15: Intro to Hamilton-Jacobi Equations.

Lecture 15-17: Intro to Hamilton-Jacobi Equations (all lectures).

Homework 1

Homework 2

Homework 3

Homework 4

Homework 5

Homework 6

Homework 7

Homework 8