Most people who deal with electronics have heard of the Fourier transform. That mathematical process makes it possible for computers to analyze sound, video, and it also offers critical math insights for tasks ranging from pattern matching to frequency synthesis. The Laplace transform is less familiar, even though it is a generalization of the Fourier transform. [Steve Bruntun] has a good explanation of the math behind the Laplace transform in a recent video that you can see below.
There are many applications for the Laplace transform, including transforming types of differential equations. This comes up often in electronics where you have time-varying components like inductors and capacitors. Instead of having to solve a differential equation, you can perform a Laplace, solve using common algebra, and then do a reverse transform to get the right answer. This is similar to how logarithms can take a harder problem — multiplication — and change it into a simpler addition problem, but on a much larger scale.
We assume it was a choice, but [Steve] presents wearing all black on a black background, so we found ourselves imagining him as a floating head of math knowledge. Kidding aside, what a great explanation of the topic! You’ll probably need some calculus to get the most out of the video, but it is interesting to just watch him cut through the equations.
Once you tackle the transform, you’ll find it interesting to learn about the S-plane which is the graphical representation of the Laplace transform. If you need a brush up on calculus we have mentioned before that calculus isn’t really hard. We also like a very old book on the subject.