Calculating insolation as a function of date and latitude.

In preparation for some work I will be doing I've been working on calculation of insolation as a function of time and latitude. In this post I will explain the method and compare results to a readily obtainable plot of insolation at various latitudes.

Note, all of the following calculations and the comparison with another source are for top of atmosphere and do not take into account absorption/scattering by the atmosphere, or reflection from clouds.