Can someone explain where the following mathy things are used?
I'm interested in where it is used mainly, and also how it's used.

>Fourier Series
I know it's used to solve heat conduction equation and that's why the autist Fourier came up with all this but I'm sure there's more uses to this
>Partial Differential Equations
>Analytic Functions
>Complex Interpretations
>Vector Calculus

>Fourier Series
Spectral analysis
>Analytic Functions
>Complex Interpretations
>Vector Calculus
Almost everywhere. It's a basis of applied maths.
>Partial Differential Equations
Same. They are more obscure though, like string/membrane oscillations or gas flow.

>Fourier Series
Aren't the used all the time in signal processing? Anything to do with a superposition of waves really. Visible light, radio, sound, etc. Heard there are some more niche uses as well.
>PDE
I think these are used to death in finance. Don't ask me why. Something something modelling unknown functions.
>Analytic Functions
Aren't they related to doing approximations? If so, comp sci is a large field of use.
>Complex Interpretations
AFAIK they are used for getting really weird integrals, quantum mechanics, and solving polynomial equations. Also fractals.
>Vector Calculus
Fields. Gravity, electromagnetism, different flows. Makes sense since in these fields you are working with 3d spaces, movement, intensities, etc.

P89351
P89353
I'm actually looking for where they're used in Physics, also Physics that does not involve Electricity, Magnetism, Optics and all those electron or light related topics but things like force, heat, etc.

>Gravity
>different flows
>string/membrane oscillations or gas flow
Good, this is fine. I'll read more into this.

P89453
Those topics are ubiquitous. F(vector)=m d2/dt2 x(vector), well, the whole theoretical mechanics is a bunch of vectors and their integrals. Heat dissipation may be modelled by PDE. What else? I don't know.