AMS 528, Numerical Analysis III 
An introduction to scientific computation, this course considers the basic numerical techniques designed to solve problems of physical and engineering interest. Finite difference methods are covered for the three major classes of partial differential equations: parabolic, elliptic, and hyperbolic. Practical implementation will be discussed. The student is also introduced to the important packages of scientific software algorithms. AMS 528 may be taken whether or not the student has completed AMS 526 or AMS 527 
3 credits, ABCF grading 

Required Texts:

Numerical Partial Differential Equations: Finite Difference Methods (TAM 22), by J.W. Thomas, Springer (1995), Volume I; ISBN 0-387-97999-1

Numerical Methods for Conservation Laws, by Randall J. LeVeque, 2nd edition, Birkhauser Verlag, 1992, ISBN 978-376-4-32723-1

AMS 528 Instructor Page

Learning Outcomes:

1) Demonstrate mastery of: 
      * Finite difference methods for PDE;
      * Consistency, convergence and stability, Lax theorem;
      * Parabolic equations, implicit schemes, convection diffusion equations;
      * Two dimensional problems, alternate directional implicit (ADI);
      * Hyperbolic equations, numerical schemes, stability analysis and CFL condition;
      * Numerical dispersion and numerical dissipation, tracking and capturing;
      * Conservation Law, Glimm scheme and Godunov scheme, high order schemes, limiters;
      * Elliptic equations, iterative methods;
      * Introduction to the finite element method;
      * Meshless and particle methods for PDE's.