A few times in the past, I’ve tried to start a blog, and I’ve never followed through with the discipline to post frequently and consistently.
This time, I hope, I shall remain active.
WordPress makes the inclusion of mathematical content easy, and so this blog will serve for any content that I might wish to write.
As an initial test, I offer the trivial derivation of the formula for integration by parts:
We begin by considering two functions and . Each function maps from from the reals to the reals. Consider a real number , and consider the product . The differential of the product is
Solving for one of the terms on the right, we find
Integrating both sides leads directly to the desired result