What Is the Fourier Transform?

When I think of Laplace Transforms I always think of control theory - poles, zeros etc.

Probably that's why we are learning about it in the "Control Theory" classes at university. :-)

Jokes aside, I graduated as "Computer Engineer" (BSc) and then also did a "Master in Computer Science"; I was (young and) angry at the universe why soooo many classical engineering classes and then theory I had to sit through (Control theory, Electrical engineering, Physics), and we never learned about the cool design patterns etc etc.

Today I see that those formative years helped me a lot with how I develop intuition when looking at large (software) systems, and I also understand that those ever changing best design patterns I can (could have) just look up, learn, and practice in my free time.

I wish a today-me would have told my yesterday-me all this.

I learned about it after I graduated with a CS degree - I mean in true university degree fashion we'd been taught about Laplace and Z transforms (and related things) but with no practical applications.

After graduating I joined an academic research team based mainly in a EE department who were mainly Control Engineers - we were mainly doing stuff around qualitative reasoning and using it for fault diagnosis, training etc.

My control theory professor (who was also my physics advisor -- it was a small college) explained it like this: Physicists like Fourier transforms because they go from minus to plus infinity, like the universe. Control engineers like Laplace transforms because they start at zero, and a control system also has a starting point.

To be fair (and because I've just remembered - it was ~40 years ago) we did get some practical stuff covered in the maths part of my CS degree in the application of group theory (groups, rings & fields) to coding theory.

The two-sided Laplace transform would probably have made his head explode.