This document is intended to help beginning and intermediate programmers develop sound programming habits. Writing robust code is a challenge because it requires the programmer to manage simultaneously many distinct but interrelated tasks. Such complexity can be managed by a divide-and-conquer strategy: deconstruct a programming task, build the pieces, test the pieces, connect them into a functioning program, and then test the entire code.
Derivatives occur in all manner of technical work, for we routinely need to know how quantities respond when other quantities change. In this document we discuss simple derivatives, differentials, and partial derivatives. In addition, considerable attention is given to the subtleties surrounding partial derivatives, including physical interpretations and transformations among independent variables.
In this document we show that a quantum mechanical description of the hydrogen atom is sufficient to deduce the electronic structure of all the elements; hence, it allows us to build the periodic table. The quantal description is confirmed by observations of absorption spectra for hydrogen.