Teaching / Course archive

Math 580: Fall 2012

PDE 1

Course Record

Institution: McGill
Term: Fall 2012
Level: graduate
Topics: PDE

Overview

PDE I course covering distributions, first order equations, conservation laws, harmonic functions, Dirichlet problems, Sobolev spaces, spectral theory, heat and wave equations, and student projects.

Schedule and Topics

Date	Topic
Th 9/6	Idea of distributions and seminorms.
Mo 9/24	First order semilinear equations and method of characteristics.
Th 9/27	First order quasilinear equations, conservation laws, and wave breaking.
Th 10/11	Analyticity, maximum principles, and Green's function approach.
Th 11/1	Dirichlet energy, Sobolev spaces, weak and strong derivatives.
Fr 11/9	Spectral theory for compact self-adjoint positive operators.
Mo 11/26	Heat equation: semigroup property, smoothing, decay, and well-posedness.
We 12/5	Wave energy and basic classifications of PDEs.

Topic List

Test functions, distributions, and operations on distributions
Semilinear and quasilinear first order equations
Conservation laws, weak solutions, shock waves, and entropy conditions
Harmonic functions, Green's functions, Poisson formula, and Dirichlet problems
Sobolev spaces, weak derivatives, Hilbert space methods, and spectral theory
Heat equation, wave equation, and energy estimates

Books and Related Pages

Books

Lawrence C. Evans, Partial differential equations. AMS, 1998.
Fritz John, Partial differential equations. Springer, 1982.
Jurgen Jost, Partial differential equations. Springer, 2007.
Qing Han, A basic course in partial differential equations. AMS, 2011.

Assignments and Projects

Assignments and Exams

Assignments 1-6.
Student project reports and presentations.

Local Materials

Notes