Syllabus

*This is a tentative schedule.

Week 1
Mon 7 Jan Introduction: What is a PDE?
Evans: Chapter 1
Weds 9 Jan Laplace: Fundamental solution
Evans: Section 2.2
Fri 11 Jan Laplace/Poisson: Properties of Harmonic functions and uniqueness
Evans: Section 2.2
Week 2
Mon 14 Jan
Laplace/Poisson: Maximum principles and uniqueness
Weds 16 Jan
Laplace/Poisson: Energy methods
Fri 18 Jan
Laplace/Poisson: Analytic solution techniques
Notes
Week 3
Mon 21 Jan
Martin Luther King Jr Day -- Go to X-hour
Elliptic PDEs: Definition and weak solutions
Weds 23 Jan
Elliptic PDEs: Existence of weak solutions
Fri 25 Jan
Elliptic PDEs: Maximum Principle
Week 4
Mon 28 Jan
 Finite difference methods
Weds 30 Jan
 Convergence of second order finite difference methods
Fri 1 Feb
 Finite difference methods for Elliptic PDEs
Week 5
Mon 4Feb
 Heat equation: Fundamental Solution
Weds 4 Feb
 Heat Equation: Solutions of the free space initial value problems
Fri 8 Feb
Carnival --- Go to X-hour
 Heat Equation: Maximum Principle and uniqueness
Week 6
Mon 11 Feb
 Heat Equation: Energy methods
 Parabolic Equations: Definition
Weds 13 Feb
 Parabolic Equations:  Maximum Principles
Fri 15 Feb
 Wave Equation: d'Alembert's formula
Week 7
Mon 18 Feb
 Discretization techniques for intial value problem ODE's
Weds 20 Feb
 Stiff ODE's
Fri 22 Feb
 Discretization of diffusion equations
Week 8
Mon 25 Feb
TBD
Weds 27 Feb
TBD
Fri 1 Mar
TBD
Week 9
Mon 4 Mar
Presentations
Weds 6 Mar
Presentations
Fri 8 Mar Presentations
Week 10
Tues 12 Mar Happy Spring Break!