This is a supplementary video to the Real Analysis series. It connects the topic of absolutely continuous function to the general version of the fundamental theorem of calculus..
Part 1 - Expansion of the Theorem
The fundamental theorem of calculus is, as the name suggests, the main result for the analysis of differentiable functions. It connects the notions of a derivative with the one of an integral. However, it turns out that the statement does not only hold for continuously differentiable functions. One can extend it to so-called absolutely continuous functions. Here, we will explain how such generalizations can be reached.
We will apply this theorem in the Complex Analysis series and also in a technical part of the Fourier Transform series, where we will show the convergence of so-called Fourier series.