If you went to engineering school, you probably remember going to a lot of calculus classes. You may or may not remember a lot of calculus. If you didn’t go to engineering school, you will find that there’s an upper limit to how much electronics theory you can learn before you have to learn calculus. Now imagine Khan Academy, run by an auctioneer and done without computers. Well, you don’t have to imagine it. Thinkwell has two videos that purport to teach you calculus in twenty minutes (YouTube, embedded below).
We are going to be honest. If you need a refresher, these videos might be useful. If you have no idea how to do calculus, maybe these are going to whiz by a little fast. However, either way, the videos have some humor value both from the FedEx commercial-style delivery to the non-computerized graphics (not to mention the glass-breaking sound effects). Of course, the video is about ten years old, but that’s part of its charm.
Although calculus has a reputation of being tough, the concept is quite simple. If you have a function that represents something, the derivative of that function describes the rate of change at any point. The integral describes the area under the curve of the function. At first glance, those things don’t appear related, but in fact, they are inverses of each other. That is if you take a derivative and then integrate the result, you’ll wind up with the original function (well, at least, that’s one of the answers you’ll get). Conversely, if you integrate a function then take the derivative you will wind up back where you started.
This is useful in electronics when dealing with AC circuits. The behavior of capacitors and inductors depend on rates of change and while you can memorize certain common formulas, they are just answers to calculus problems that someone else worked for you.
One thing we did notice is that the video covers the theory behind taking a derivative but doesn’t cover much about the rote rules most people remember for common cases. Once you notice that the derivative of 2x is 2 and the derivative of 4x squared is 8x, for example, you can probably deduce the generic rule that would tell you that the derivative of 3x to the fifth power is 15x to the fourth power.
Hackaday has covered this topic, too. If you want something more leisurely than these videos, we might suggest Khan Academy. If you prefer a fast read, the book Quick Calculus is short, inexpensive, and a good refresher. A hundred-year-old classic book is available free if you are too cheap to drop a few dollars. We love that book’s subtitle: “Being a very-simplest introduction to those beautiful methods of reckoning which are generally called by the terrifying names of the differential calculus and the integral calculus.” If you are starting from scratch and want the college experience, try MIT.