Numerical methods for steady-state differential equations. Two-point boundary value problems and elliptic equations. Finite difference, spectral and finite element methods. Numerical interpolation, integration, application of discrete Fourier transform.
Computational Science 6910 (Matrix Computations and Applications) or equivalent. In particular, basic knowledge of numerical linear algebra and ordinary differential equations is assumed, along with fluency in MATLAB (or willingness to learn it quickly).
R. J. LeVeque, Finite Difference Methods for Ordinary and Partial Differential Equations, SIAM 2007.
L. N. Trefethen and D. Bau, Numerical Linear Algebra, SIAM, 1997.
A. Iserles, Numerical Analysis of Differential Equations. Cambridge University Press, 1996.
K. W. Morton and D. F. Mayers, Numerical Solution of Partial Differential Equations, Cambridge University Press, 1994.