Numerical methods is a sophomore-level course that serves as an introduction to a broad range of topics. During Spring 2013 at Utah State University, we covered modeling and error, root finding and solving systems of nonlinear equations, numerical linear algebra, curve fitting, numerical integration and differentiation, ordinary differential equations, and partial differential equations. Before taking the course, students are required to have already completed courses in calculus, linear algebra, and differential equations.
Just over 200 videos were recorded for the course. The style was inspired by the videos from the Khan Academy, and while I won’t make outstanding claims about my own videos, those are great. The videos I recorded for the course are available on my youtube page: https://www.youtube.com/user/kvyi/videos. Cholesky decomposition and fixed-point iteration are the two most popular right now. Have a look.