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Breaking functions down to their constituent parts is nice and all, but this is a step too far.
(fedia.io)
this post was submitted on 29 Nov 2025
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Explanation: Top left is a Taylor series, which expresses an infinitely differentiable function as an infinite polynomial. Center left is a Fourier transform, which extracts from periodic function into the frequencies of the sines and cosines composing it. Bottom left is the Laplace transform, which does the same but for all exponentials (sines and cosines are actually exponentials, long story). It seems simpler than the Fourier transform, until you realize that the s is a complex number. In all of these the idea is to break down a function into its component parts, whether as powers of x, sines and cosines or complex exponentials.
Edit: I'll try to explain if something is unclear, but... uh... better not get your hopes up.
Oh, look at that hornet's nest. I wonder what happens if I poke it
As someone who worked with system modelling, analysis and control for years... I do think the Laplace transform is easier to work with ๐๐โโ๏ธ
What kind of work do you do?
I'm in the process of wrapping up my degree and I work a lot with signals and controls. I agree that Laplace is much less of a headache than Fourier.
I was at the intersection between mechanical and electrical engineering as well as computer science. And worked in/with (electric) mobility, agriculture, medical/rehabilitation tech., solar energy, energy grid, construction and building tech. As well as some very limited stuff with economics. And I intentionally chose my study courses to be able to work in multiple areas and inter-disciplinary. My latest work is more on the business and management side of things and less technical, though.
What are you studying and what direction are you hoping to head in?