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, Quasioptimal 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 