/sci/ - Science & Math

Baby fourier analysis is really kicking my ass, it was all fun and games when it was just fourier series, but after we moved onto fourier transforms the difficulty ramped up. >muh tempered distributions and Schwarz functions and weak derivation and fundamental solutions of differentiative operators and shit.
>mfw someone actually came up with all this shit and I can't even comprehend it when handed to me on a silver platter like this
>mfw I will never make it

>>9698954
>Also will shit like integration by parts be proven in a later course?
Anon... It's supposed to be obvious. I get it, it can run over your head at first and seem like something complicated, but if you actually put any thought into it and still didn't get it, I'm not sure if university is the right place for you.

I take it that you know the product rule for differentiation and other basic results from calc 1 and calc 2. This is what it boils down to, just taking an integral over both sides and shuffling the terms around. I hope this helps.
[math]D_x(f(x)g(x)) = f(x)g'(x) + f'(x)g(x)[/math]
[math]\int_{a}^{b}D_x(f(x)g(x)) = \int_{a}^{b}f(x)g'(x) + \int_{a}^{b}f'(x)g(x)[/math]
[math]\int_{a}^{b}D_x(f(x)g(x)) - \int_{a}^{b}f(x)g'(x) = \int_{a}^{b}f'(x)g(x)[/math]
[math][f(x)g(x)]_a^{b} - \int_{a}^{b}f(x)g'(x) = \int_{a}^{b}f'(x)g(x)[/math]
[math]\int_{a}^{b}f'(x)g(x) = [f(x)g(x)]_a^{b} - \int_{a}^{b}f(x)g'(x)[/math]