I will be teaching a one-semester course on numerical methods at a liberal arts college. The students will be primarily math, physics, and engineering majors. Note that there is no computer science department at this institution.
This is my first time teaching such a course and I rarely use numerical methods in my research. What are some of the most essential topics that should appear in the course?
I would like to treat the course as a baby introduction to programming using Python. There is no assumption that the students will have had previous programming experience. The only prerequisite is Calculus II.
I should probably include the following topics, as they are mentioned in the course catalog:
- round-off errors
- computer arithmetic with algorithm and convergence
- solutions of equations in one variable with polynomial approximation
- numerical differential equations
- linear systems of equations
I’ve chosen Hamming’s Numerical Methods for Scientists and Engineers as the text, as it is quite inexpensive and has excellent reviews. It’s very thick though, and includes far more than I could cover in a single semester!