Calendar
Updated 1/28/22 This is a tentative course outline and is subject to revision during the term.
| Week | Monday | Wednesday | Friday |
|---|---|---|---|
| 1 |
Jan 3
Three pillars of this course, Review of vector calculus |
Jan 5
Derivations of some PDEs |
Jan 7
Boundary conditions for PDEs, Elementary Fourier analysis for PDEs |
| 2 |
Jan 10
Dispersion relation, elliptic equations, finite difference method (FDM) |
Jan 12
Lax equivalence theorem, Consistency, Stability, Convergence, Maximum principle
Homework 1 due |
Jan 14
Maximum principle, Stability, Discrete maximum principle, Discrete L^\infty stability |
| 3 |
Jan 17
Martin Luther King, Jr. Holiday |
Jan 19
Review of 1d Poisson equation, Discrete L^\infty stability(proof), General 1d elliptic equations
Homework 2 due |
Jan 21
General 1d elliptic equations, 2d Poisson equation
|
| 4 |
Jan 24
FDM for 2d Poisson equation, Preparations for finite element method (FEM) |
Jan 26
Weak formulation, Sobolev space H^1 and H^1_0, Galerkin approximation
Homework 3 due |
Jan 28
Stiffness matrix, Wellposedness of weak formulation |
| 5 |
Jan 31
Wellposedness of weak formulation, Lax Milgram Theorem, Coercivity, Quasi-optimal approximation property |
Feb 2
Homework 4 due |
Feb 4
Midterm |
| 6 |
Feb 7
Elliptic equations |
Feb 9
Parabolic equations |
Feb 11
Parabolic equations |
| 7 |
Feb 14
Parabolic equations |
Feb 16
Parabolic equations
Homework 5 due |
Feb 18
Parabolic equations |
| 8 |
Feb 21
Presidents' Day Holiday |
Feb 23
Parabolic equations
Homework 6 due |
Feb 25
Hyperbolic equations |
| 9 |
Feb 28
Hyperbolic equations |
Mar 2
Hyperbolic equations
Homework 7 due |
Mar 4
Hyperbolic equations |
| 10 | Mar 7
Hyperbolic equations |
Mar 9
Hyperbolic equations |
Mar 11
Final Project Presentation |
| Exam Week | Mar 14 | Mar 16
Final Exam |
Mar 18 |