If you have any questions, please ask. I love yapping.
yap
Let's say we have some periodic function f. The goal is to represent it as a bunch of sine waves. This is called a Fourier series (FS).
The FS coefficients are given by
⌠2⋅π
1 ⎮ -i⋅k⋅x
f̂(k) = ─── ⎮ f(x)⋅e dx
2⋅π ⌡0
for whole numbers k. We can then approximate the original function with
n
___
╲ -i⋅k⋅x
╱ f̂(k)⋅e
‾‾‾
k = -n
and make the approximation better by making n larger.
For non-periodic functions, we can still get an approximation! The Fourier Transform (FT) uses a continuous range of frequencies instead of whole numbers, and the sum is replaced by an integral (the inverse FT).
FT's are used everywhere, for example in signal processing and spectroscopy. If a recording contains an annoying high-pitched noise, we can apply the FT and filter the unwanted frequencies. Spectroscopy separates light into its different wavelengths. By comparing the resulting spectral lines with known measurements, we can determine which elements and molecules are present in stars and planets, for example.
idk what more to add ._.
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needles
Local tomboy is getting better at giving themselves E injections
still a little scary though 
Funnily we were terrified of needles forever and still need to look away when we get vaccines or bloodwork, but giving ourself injections is way less scary than letting a nurse or doc do it
Needles scare me, but I still often find myself thinking about doing more shots anyways.