It transforms calculus into algebra. It is incredibly useful for math involving rotations and periodic functions – practically anything that has to do with radio, waves, electricity, etc. The math is much much much simpler.
In Electrical Engineering, we solved a simple circuit that had inductors and capacitors the long way – calculus every step of the way. It covered two whiteboards and took most of the class period. We then solved the same problem with the Laplace transform in the frequency domain. It took a couple minutes and most of that was writing the problem down – it turned the math into “add these numbers here, divide by this number here, …… and we’re done”
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