Calculus: Organizing techniques of integration

introduction & overview

The purpose of this notebook is to organize the useful techniques of integration which are taught in freshman calculus and then presumed known (ha!) at the beginnings of a course in ordinary differential equations.

Heads up: I’m going to mention hyperbolic trig functions, but until you meet them, they are not relevant and you should ignore them. I’m just trying to be thorough, but I fear that I might be confusing. So I’m going to mention them in the details, but omit them from the summary.

First off, there are three categories of integrals:

1. known
2. special techniques
3. general techniques

Here it is in a nutshell: If an integral is on the “known” list, you’re wasting time trying to use special or general techniques. if an integral can be done using special techniques, you’re wasting time using general techniques.

Calculus: where did e come from?

I assembled the following in response to a question from a calculus student. What he asked was literally, “Who first found e?” What he was really asking, I suspect, was more along the lines of: “Where the heck did e come from, and how on earth did anyone find it?”