I wanted to read about how Laplace Transforms work with circuits. In the first Wikibooks article I came across about Laplace Transforms, it mentioned Oliver Heaviside as a “famous electrical engineer”. Naturally, I was curious, and I searched about him. Oliver Heaviside is an exceedingly interesting character. He was an English electrical engineer who was born in 1850. Inspired by Maxwell’s equations, he strove to apply them to the field of electrical engineering; more specifically, to the field of telegraphy. He invented Operator Calculus, a method similar to Laplace Transforms, which can be used to solve ordinary differential equations. In fact, I saw a lesson on solving ODE’s using operator calculus in Ordinary Differential Equations. Turns out Heaviside came under a lot of fire from the Royal Society because he did not justify Operator Calculus “rigorously” enough. Heaviside’s reply? “Screw you” (although much more nineteenth century and expressed much more eloquently). Ah, here it is.
“I think I have given sufficient information to enable any competent person to follow up the matter in more detail if it is thought to be desirable. It is obvious that the methods of the professedly rigorous mathematicians are sadly lacking in demonstrativeness as well as in comprehensiveness.”
Among Operator Calculus, Heaviside also invented an intuitive method for decomposing partial fractions, called the Cover Up method. I can confirm that this is still a popular method for solving the nasty buggers; a friend of mine, who is very talented at math (and believe me, I don’t say that lightly), uses it. Finally, in what is probably his most important but most unknown contribution to physicists everywhere, he simplified Maxwell’s equations from 20 equations and 20 variables using the recently developed notation of vector calculus (solidified in Vector Analysis, 1901, by some other English mathematicians), to the 4 equations we all know and love.
Backtracking a little bit, I was curious about Operator Calculus, which led me to click on a link to a website called “Dead Reckonings: Lost Art in the Mathematical Sciences”. This gem has a bunch of fascinating articles that explore the relationship between mathematics and art. Its article on Oliver Heaviside is awesome, much more inspiring than his Wikipedia article (it’s also where I got the quote from). Nevertheless, I began exploring the website, and came across Nomography. A nomogram is a visual aid, like a slide rule or chart, that was used quite often. The basic function of a nomogram is to express the mathematical relations between n different variables such that if you know n-1 variables, you can find an estimate of the unknown variable using the nomograph. For example, you could design a nomogram for the relationship F = ma. Besides being extremely useful, nomograms are beautiful. They’re fallen prey, like everything else requiring ingenuity, to the computer, but someone has coded open source software called PyNomo that lets you create vectorized nomograms. The thing is, you need Python to do it. Another excuse for learning a programming language, I guess.
That’s about it for today. By trying to learn about Laplace Transforms, I came across basically everything I’m interested in right now. Heaviside, being an electrical engineer, designed his methods to be amenable to topics in electrical engineering…such as differential equations. That led me to nomograms, art, and Python, something I’m definitely going to try out soon. I just had to document my mathematical journey. Here are some of the links: