## Spring 2019 - Scientific Computing II

Syllabus Updated 02/04/2019. New classroom MTH B0423 Main references__Finite Difference Methods for Ordinary and Partial Differential Equations__LeVeque, here.__Iterative methods for sparse linear systems__Saad, here.__Remarks around 50 lines of Matlab: short finite element implementation__Alberty, Carstensen, Funken, here.__Ten lectures on wavelets__Daubechies, here.__Numerical optimization__, Nocedal, Wright here.

__Numerical analysis__by T. Sauer,

- 01/29
__Numerical methods for elliptic PDEs__Maria Cameron's notes here,
Linear elliptic PDEs: definitions, boundary conditions and boundary value problems, models, strong maximum principle.
- 01/31
__Numerical methods for elliptic PDEs__Maria Cameron's notes.
Finite difference approach: discretization, error analysis,
TnT.
- updated version - HW1, code.
- 02/05
__Numerical methods for elliptic PDEs__
Finite differences: error analysis, Neumann BCs.
TnT.
- 02/07
__Numerical methods for elliptic PDEs__
Finite differences: periodic BCs, non-constant coefficients.
TnT.
- UPDATED HW2.
- 02/12
__Numerical methods for elliptic PDEs__
FD example, code. Finite Elements: General idea, Integral formulation.
- 02/14
__Numerical methods for elliptic PDEs__
Weak derivatives and Sobolev spaces. Domain discretization.
TnT.
- HW3.
- 02/19
__Numerical methods for elliptic PDEs__
Quadrature, see Notes from Shaozhong Deng.
- 02/19
__Numerical methods for elliptic PDEs__
Error analysis.
- HW4, code.
- 02/26
__Numerical methods for elliptic PDEs__
Numerical linear algebra for sparse matrices: Jacobi, Gauss-Seidel.
- 02/28
__Numerical linear algebra for sparse matrices__
SOR, Slow convergence of Jacobi.
This code has a bug... can you find it?
TnT.
- HW5, code.
- 03/05
__Numerical linear algebra for sparse matrices__
Multigrid.
- 03/07
__Numerical linear algebra for sparse matrices__
Multigrid: V cycle, W cycle. Steepest descent, 2D illustrations.
TnT.
- HW6, Test Matrix A code and Vcycle code.
- 03/12
__Numerical linear algebra for sparse matrices__
Conjgate gradient.
- 03/14
__Numerical linear algebra for sparse matrices__TnT.
Conjgate gradient.
- HW7, Test Matrix A code and Vcycle code.
- 04/02
__Numerical methods for time-dependent PDEs__
Parabolic problems:
the heat equation, local truncation error.
- 04/04
__Numerical methods for time-dependent PDEs__
Parabolic problems:
method of lines, stability theory, stiffness.
- HW8.
- 04/09
__Numerical methods for time-dependent PDEs__F.E. code.
Parabolic problems: Convergence, Finite element approach.
- 04/11
__Numerical methods for time-dependent PDEs__
Advection equation: Problem, method of lines.
- UPDATED VERSION - ALL IN LATEX NOW - HW9.
- 04/16
__Numerical methods for time-dependent PDEs__
Lax-Friedrichs, Lax-Wendroff, Characteristic tracing and interpolation.
- 04/18
__Numerical methods for time-dependent PDEs__
The CFL condition, hyperbolic systems.
- updated - HW10.

## Teaching at UMD

- 2018 Fall Scientific Computing I (Grad).
- 2018 Spring Introduction to Numerical Analysis (Undergrad). Material posted on ELMS-Canvas Here, some details here.

## Teaching at NYU

- Analysis Section 003 (Spring 2016).
- Calculus 3 Section 004 (Fall 2015).
- Math for Econ 1 Section 001 (Spring 2015).
- Calculus 1 Section 046 (Fall 2014).

## Teaching activities at UPMC - Paris 6