Recent content by juan.

I'm trying to solve Laplace equation using Fourier COSINE Transform (I have to use that), but I don't know if I'm doing everything OK (if I'm doing everything OK, the exercise is wrong and I don't think so). NOTE: U(..) is the Fourier Transform of u(..) This are the equations (Laplace...

Perfect! But I have 2 problems: - I never used a contour like this: D. It was always with the line in the x axis - Then, I don't understand where \int_{C_1}{ } F(s).e^{s.t}ds came from. If you look at the Inverse Transform of Laplace, you can see a \frac{1}{2j\pi} and the limits of the integral...

I need to know what's the Residue Theorem for a Laplace Transform. Does anyone know the name or something, so I can search it? I couldn't find anything. For example, if I have this two equations: X(s).(s-1) = -Y(s)+5 Y(s).(s-4) = 2.X(s)+7 I know how to solve them using Simple Fractions, but...

Hello everyone! I'm having some troubles when I try to solve improper integrals exercises that have singularities on the real axis. I have made a lot of exercises where singularities are inside a semicircle in the upper half side, but I don't know how to solve them when the singularities are on...

Oh, that's true! ThanksssssssssssssssssssssSorry, Euler, I forgot about you haha

Thanks for your answers! I can see now that e^{t.(i-s)}, with t->\infty is equal to 0, but why? I can separate that exponential in 2 parts: real and immaginary. In the real part, of course I have e^{-t.s}=0 but in the immaginary part I have: e^{i.t} and that's not 0. So, I have 0.\infty, with...

Hello everyone, I have a question about integrating in Laplace Transform. For example, if I have: f(t)=e^{i.t} I have to solve this equation: \int_{0}^{\infty}e^{i.t}.e^{-s.t}dt If I do like this, it's very simple...

Hello everyone. I'm having some troubles with Jordan's Lemma and I can't find how to fix it, because everyone in internet and in the books I read do not prove this. Now, I'm following Wunsch (Complex Variables with Applications) but it only does this part for a easy problem. For example, if I...

Hello everyone. I found this forum looking for some help about Jordan's Lemma and it's very interesting. I have already done 4 courses of Physics in an Engineering University, so I hope I can help other people with their questions. Thanks for reading!