Updated 1/28/22   This is a tentative course outline and is subject to revision during the term.

Week Monday Wednesday Friday
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
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
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
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
Jan 31
Wellposedness of weak formulation, Lax Milgram Theorem, Coercivity, Quasi-optimal approximation property
Feb 2
Homework 4 due
Feb 4
Feb 7
Elliptic equations
Feb 9
Parabolic equations
Feb 11
Parabolic equations
Feb 14
Parabolic equations
Feb 16
Parabolic equations
Homework 5 due
Feb 18
Parabolic equations
Feb 21
Presidents' Day Holiday
Feb 23
Parabolic equations
Homework 6 due
Feb 25
Hyperbolic equations
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