18.086 - Computational Science and Engineering II (Spring 2014)


Instructor: Xiangxiong Zhang

Office: E17-301P (outside of Room E17-317)

Email: zhangxx [at] math . mit .edu

Lectures: TR 9:30 - 11:00 am E17-136

Office Hours: TR 2:00-3:30 pm

Grader: Mr. Rik Sengupta [rsengupt at math dot mit dot edu], avaialbe for answering questions regarding HW grading, at desk in E17-401L, Monday 2pm-3pm.


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:


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.