Recent content by lucad93

I don't know if it is the right section to post in. I have a problem with a "simple" Fourier transform. This is the function to transform: $$f(t)=\frac{\sin\left({2\pi t}\right)}{t}$$. My first idea was to write that as $$\sin\left({2\pi t}\right)\cdot\frac{1}{t}$$ but then my fantasy crashed...

Hello everybody! I have to decompose to simple fractions the following function: $$V(z)=\frac{z^2-4z+4}{(z-3)(z-1)^2}$$. I know I can see the function as: $$V(z)=\frac{A}{z-3}+\frac{B}{(z-1)^2}+\frac{C}{z-1}$$, and that the terms A, B, C can be calculated respectively as the residues in 3...

Hello! I have a problem with the following exercise, in which i must calculate the ray of a power serie. This is the power serie: $$\sum_{K=0}^{+\infty}(k+1)z^{k+1}$$. I decide to use the ratio test, and so i calculate $$\lim_{k\rightarrow +\infty}\frac{a_{n+1}}{a_{n}}$$ for n going to infinity...

Hello everybody! I'm sorry if it's not the right section to post in. I'm trying to solve this exercise: $$\frac{1}{2i\pi}*\int_{8-i\infty}^{8+i\infty}\frac{e^{s(t-5)}}{(s+4)^2}ds$$ The request is to find the result in function of $$t$$ I know i must use the Riemann inversion formula, and so the...