yeah i realized after i wrote it that it is a little ambiguous to say it like that. but i felt like you would know what i meant.
so i think when you combine those two integrals (by addition) i come out with something like this...
\int e-rt*\frac{1}{r}*(2 - \frac{4}{r+1})dr
which is an...
thanks jackmell. that helps a heap.
i have done the analysis of all the other contours and unless i have made a mathematical mistake I am pretty confident they are all 0. but your suggestion is a great way to check it.
the only thing I am confused about is how you arrived at your expression...
Homework Statement
Find the Inverse Laplace Transform of
\frac{1}{s}*\frac{\sqrt{s}-1}{\sqrt{s}+1}
The Attempt at a Solution
for this question i found the singularities to be at 0 and when s = 1. (as the sqrt of 1 is ± 1) there is also a branch point that runs from 0→-∞. so if you...
Let f: ℂ→ ℂ be an entire function. If there is some nonnegative integer m and positive constants M,R such that
|f(z)| ≤ M|z|m, for all z such that |z|≥ R,
show that f is a polynomial of degree less that or equal to m.
im really lost on this question. i feel like because...
oh yeah... that makes sense...
your right we can't get i and -i in on a path integral across the real axis
maybe i need to build a circle or something? i guess i have less of an idea now?
thanks for your help?
any idea where i should go from here?
The question asks to show using the residue theorem that
\intcos(x) / (x2 +1)2 dx = \pi / e
(the terminals of the integral are -∞ to ∞ but i didnt know the code to write that)
I found the singularities at -i and +i
so i think we change the function inside the integral to cos(z) / (z2...
The question asks to show using the residue theorem that
\int cos(x)/(x2+1)2 dx = \pi/e
(the terminals of the integral are -\infty to \infty but i didnt know the code to write that)
I found the singularities at -i and +i
so i think we can then say
\intcos (z) / (z+i)2(z-i)2 dz...
im now more confused...
are you saying i don't need the ML inequality?
I don't understand where the R in the first line comes from? and where do you go from the last line to get closer to the solution?
im sorry i havnt understood
Having trouble with this question:
The question is: establish the inequality
|\inteizzdz| \leq \pi(1-e-R2)/4R
on C {z(t) = Reit, t \in [0,\pi/4, R>0
When i saw the modulus of an integral i thought ML inequality.
I think the length will be R\pi/4 but I am struggling with...
Once i expanded them i realized they looked exactly like the triangle inequality where the modulus of the summation of terms was less than or equal to the modulus of each term summed.
i didnt try to conclude |e^z| = e^|z|
from what i was reading i think they are equal when z is real and...