Math 210 A,B,C,D, Syllabus


Numerical Methods in Computational Science and Engineering

A

Matrix Analysis and Computation

1.

Graduate level-matrix theory with introduction to matrix computations

2.

Advanced matrix analysis technqiues, like SVD's, pseudoinverses, variational characterisation of eigenvalues, perturbation theory

3.

Matrix computations for linear systems and eigenvalue decompositions, including direct and iterative methods

B

Numerical Simulation for Ordinary Differential Equations

1.

Linear multistep methods and Runge-Kutta methods for ordinary differential equations: stability, order and convergence

2.

Stiffness

3.

Differential algebraic equations

4.

Numerical solution of boundary value problems

C

Numerical Solution of Partial Differential Equations-Finite Difference Methods

1.

Finite difference methods for hyperbolic, parabolic and elliptic PDE's with application to problems in science and engineering

2.

Convergence, consistency, order of accuracy and stability of finite difference methods

3.

Von Neumann stability analysis. Dissipation and dispersion, finite volume methods

4.

Software design and adaptivity

D

Numerical Solution of Partial Differential Equations-Finite Element Methods

1.

Weighted residual and Finite element methods for hyperbolic, parabolic and elliptic PDE's, with application to problems in science and engineering

2.

Error estimates

3.

Standard and discontinous Galerkin methods