Please note that these videos are from a 700-level physics course at Cornell taught by Prof. Tomás Arias. The subject is Density Functional Theory, an approximation technique in physics used to calculate such quantities an bond lengths and bond energies in crystals. One of the goals of this mini-course is to show students how, by using the correct programming paradigms, powerful scientific programs may be created quickly and reliably. This is the reason I am providing links to the mini-course.
Undergraduates are not expected to understand everything here! I am including all the videos because some of the mentors might find this interesting.
The first video is mostly about the theoretical origins of DFT.
Here he further develops the theory. He begins discussing steps leading to a better implementation in software at around 24:00. The EXPRESSIVE SOFTWARE PHILOSOPHY is introduced around 41:00 and following.
For about the first 30 minutes, Prof. Arias discusses how to represent the Poisson equation using the expressive software paradigm. It basically becomes an expression in linear algebra involving a number of matrices, the precise values of which depend on the basis set. However, it is best to leave the matrix multiplications as functions, because that will allow for more efficient coding in cases where the matrices are sparse or have some other special structure. After setting up the Possion equation in general terms, he spends the remaining 30 minutes showing how the specific case of a plane wave expansion should be implemented.
I'll add more later as I watch the videos.