Here’s a wrap up of three recent posts.
The first post is about an equation that may look mysterious but is very easy to prove. It relates two things the reader may not be familiar with: the Mellin transform and the Riemann zeta function.
The post reminds me of the talk Simple Made Easy that, among other things, distinguishes between familiarity and simplicity. In that talk, Rich Hickey explains that some things we think of as simple are actually complex but familiar. The post mentioned above is the opposite, simple but unfamiliar.
The post on inverting Laplace transforms is half commentary and half technical. The commentary explains why the Laplace transform, as presented in introductory classes, is basically useless. Substantial applications of the Laplace transform require facing the inversion problem, which requires more advanced math.
This leads to the technical half of the post, two theorems for inverting the Laplace transform.
The final post is a very brief introduction to delay differential equations, also known as difference-differential equations or retarded equations. This post connects to the previous post in that Laplace transforms are one way to solve these equations.
If you found this newsletter via Twitter, you might wonder about the significance of the associated image. I like to include an image from one of the blog posts, but none of the posts discussed in this edition contain interesting images. So I grabbed a photo of Robert Hjalmar Mellin, inventor of the Mellin transform.