You don’t need to go deeply into differential calculus or any heavy math to apply one of the Enrico Fermi’s most known techniques. Fermi gave us the first nuclear reactor and studied cosmic radiation and spiral galaxies.
But the one thing that Fermi gave us that we can use every day is what is called a “Fermi Calculation”. Probably not “invented” by him, but certainly was named after him.
A Fermi Calculation or a Fermi estimate, is an estimation relying on dimensional analysis and the approximation of extreme scientific calculations. We also call it a “back-of-the-envelope” calculation. Fermi was known to be particularly good to make quite accurate approximate calculations with little or no actual data. One famous anecdote is about Fermi estimating the power of the Trinity atomic bomb explosion from the behavior of pieces of paper that he dropped at that instant.
The secret of doing a good estimate is picking the right assumptions. This entails: 1.- picking the right order of magnitude of the variables involved, and 2.- picking the right relationship among them, are they additive? is it a geometric relationship? Exponential?
So for example, if we are trying to estimate how many people can a stadium hold, and we know that a person needs around 5 sqft to be somewhat comfortable (that’s two people for every 10sqft), we can say that a stadium that has a facade of about 500ft can hold about 50,000 people. (5002/5).
The “Drake Equation”, an estimation of the number of active, communicative extraterrestrial civilizations in our own galaxy, and the “Fermi Paradox” are the result of these types of estimates.