## COURSE DESCRIPTION

Initial value problems: finite difference methods, accuracy and stability, heat equation, wave equations, conservation laws and shocks, level sets, Navier-Stokes.

Solving large systems: elimination with reordering, iterative methods, preconditioning, multigrid, Krylov subspaces, conjugate gradients.

Optimization and minimum principles: weighted least squares, constraints, inverse problems, calculus of variations, saddle point problems, linear programming, duality, adjoint methods.

**Prerequisites:** 18.03 and 18.034

**Text Book:** Gilbert Strang,
*Computational Science and
Engineering*,
Wellesley-Cambridge Press, 2007

**Reference Books:**

- Time Dependent Problems and Difference Methods
- Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations
- Applied Numerical Linear Algebra
- Numerical Methods for Conservation Laws by R. J. LeVeque
- Iterative Methods for Sparse Linear Systems
- Spectral Methods in MATLAB
- Convex Optimization

## RECENT UPDATE

### Pset 4 is posted. Due on April 29th.

Read 6.9 in Applied Numerical Linear Algebra for multigrid method.

### Pset 3 is posted. Due on April 8th.

Read LeVeque's book or lecture notes in 16.920 for nonlinear conservation laws.

### Pset 2 is posted. Due on Mar. 13th.

### Pset 1 is posted. Due on Feb. 27th.

Read lecture notes of 18.330 regarding Fourier Transform.