I am confused to the differences between fourier and laplace. Searching on the web reveals that they are due to convergence. I am basically confused as to what that means. Additionally, I am confused between transforms and series. So, if your answer could relate that as well, it would be much appreciated.
2026-04-12 07:10:35.1775977835
What does it mean when fourier/laplace series/transform converges?
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The difference between a Fourier/Laplace Series and a Transform, is that a the series only works for periodic function ($T: 0 \rightarrow 2\pi$) while a transform is extended to non-periodic functions (so $T$ tends to infinity).
I am a little unsure about the convergence part, but usually one or the other is chosen based on what kind of problem you're doing; if you're working with an IVP with an initial condition of $t=0$, then a Laplace transform would be better. If you're working with PDEs, Fourier Transforms are best.