Midwit question - Whats the point of the Laplace transform?
Ive used it a little to solve linear ODEs or systems of ODEs analytically by using tables.
Its a bit more convenient once you get a hang of it as opposed to a convenctional method like separation of variables.
But its limited. E.g. non-linear problems (which most real life applications are) cannot be solved.
Ive heard that it has value in control theory and electronics, but I postulate that the reason it is so popular there is the same reason chinese people stick to chop sticks (and not a knife and fork, which would be a numerical solver, e.g. Euler).
Numerical solvers can solve all equations the Laplace transform can, and many more. The Laplace transform seem like autistic wankery. Can anyone redpill me on the usefullness of this thing?

Look into probability theory, particularly into moment generating functions. These are the origins of the transform

turns differential equations into algebraic equations
that's pretty much it, and a massive simplification

>>16732788 (OP)
>white people be like
and still haven’t invent the rice spoon

>>16732788 (OP)
It is a shittier version of the Fourier transform, since it doesn't have a well-defined inverse. I am still yet to see a single differential equation which can be solved by the Laplace transform, but which cannot be solved via more elegant means.
That said, it is nice when considering RLC circuits, as you can apply the Laplace transform to the entire circuit, and then view inductance and capacitance as imaginary resistance, so that all three notions become unified via this complexified resistance.

>>16732788 (OP)
https://youtu.be/n2y7n6jw5d0?t=1m

>>16732794
>the rice spoon
that bitch feels so odd in the mouth

>>16732794
I'm white and I hate this shit. So utterly unnecessary and redundant. A specific type of plate and utensil for every single type food is utter fucking insanity. Next you'll be telling me that there's a formal way on how to wipe your ass.

>>16732788 (OP)
IIRC it's useful for numerical approximations. As to exactly how that works I do not know as I only have knowledge on introductory diffeqs.

>>16733201
>plate and utensil for every single type
it's like having a million different variants of the word 'herd'

>>16733201
Likely that shit was contrived by nobles so that it's easy to see who came from the provinces or is merely a rich merchant and who is the nobleman from the capital. Peasant would never think about that.