Calendar
Updated 3/13/23 This is a tentative course outline and is subject to revision during the term.
| Week | Monday | Wednesday | Friday |
|---|---|---|---|
| 1 |
Jan 9
Three pillars of this course, Review of vector calculus |
Jan 11
Derivations of some PDEs |
Jan 13
Boundary conditions for PDEs, Elementary Fourier analysis for PDEs |
| 2 |
Jan 16
Martin Luther King, Jr. Holiday |
Jan 18
Dispersion relation, elliptic equations, finite difference method (FDM) |
Jan 20
Lax equivalence theorem, Consistency, Stability, Convergence, Maximum principle
Homework 1 due |
| 3 |
Jan 23
Maximum principle, Stability, Discrete maximum principle, Discrete L^\infty stability |
Jan 25
Review of 1d Poisson equation, Discrete L^\infty stability(proof), General 1d elliptic equations |
Jan 27
General 1d elliptic equations, 2d Poisson equation
Homework 2 due |
| 4 |
Jan 30
FDM for 2d Poisson equation, Preparations for finite element method (FEM) |
Feb 1
Weak formulation, Sobolev space H^1 and H^1_0, Galerkin approximation |
Feb 3
Stiffness matrix, Wellposedness of weak formulation
Homework 3 due |
| 5 |
Feb 6
Wellposedness of weak formulation, Lax Milgram Theorem, Coercivity, Quasi-optimal approximation property |
Feb 8
Elliptic equations |
Feb 10
Review
Homework 4 due |
| 6 |
Feb 13
Midterm |
Feb 15
Parabolic equations |
Feb 17
Parabolic equations |
| 7 |
Feb 20
Presidents' Day Holiday |
Feb 22
Parabolic equations |
Feb 24
Parabolic equations
Homework 5 due |
| 8 |
Feb 27
Parabolic equations |
Mar 1
Parabolic equations
|
Mar 3
Hyperbolic equations
Homework 6 due |
| 9 |
Mar 6
Hyperbolic equations |
Mar 8
Hyperbolic equations
|
Mar 10
Hyperbolic equations
Homework 7 due |
| 10 | Mar 13
Hyperbolic equations |
Mar 15
Final Project Presentation |
Mar 17
No class |
| Exam Week | Mar 20 | Mar 22
Final Exam |
Mar 24 |