Upon successful completion of this course, the student will be able to:

- understand mathematics-numeric interaction, and how to match numerical method to mathematical properties;
- make a good choice of methods for a particular ODE problem;
- construct appropriate finite-difference approximations to PDEs;
- analyze consistency, stability, and accuracy of a finite difference method;
- write programs to solve ODEs/PDEs by finite difference methods;
- solve challenging problems that are either purely mathematical or practical from various disciplines.