Recent content by ibensous

I was wondering if anyone knows of an example where f and g are two functions that do not have limits at the real number c but f+g and fg have limits at c. I know that if f and g are functions and L= limx->c f(x) and D = limx->c g(x) then the limx->c (f+g) = L + D and limx->c (fg) = LD but...

I know the a_{-1} term is inside the Laurent Series. So your saying because plugging in n=1 gives me the a_{-1} term I just use that to compute the residue? So, I'd have a_{-1} = -1/2 and \int_{C} (z)cos{\frac{1}{z} = 2\pi iRes(f(z), 0)=-\pi i?

I see how the a_{-1} term is the only important term. Like, in this case how would I compute the a_{-1}? I had the impression that if the order of a pole is infinite then there is no way to remove the singularity unless the function has a limit that can be defined. I'm not sure if this is...

Yes, I know that when I compute the residue I'm looking at a_{-n} in the expansion but there are a couple problems. First, I can't figure out the order of the pole. I''m suppose to take the derivative of the function and if i plug in z_{0} and get a singularity then I do it again...until I...

Ok, so I'm suppose to be able to remove the singularity to find the residue of the function (z)cos{\frac{1}{z} I tried to see how "bad" the singularity was by taking the limit, but I can't figure out if \lim_{ z \to 0 } (z)cos{\frac{1}{z} goes to 0 or if it is...

Awesome. Thanks for all the help.

Principles of Mathematical Analysis. The Rudin book is used to compare the levels. I've looked over Rudins book and if Sarasons is easier then that then I know I won't have too hard a time in the course. Well I've had 4 semesters of calculus. I still remember how to prove Greens Theorem and...

=/ that doesn't help at all. I've tried getting in contact with the professor but he's never around. I wrote the name of the book because I was told that the difficulty of the class is usually based on the book used. So, the book is by Sarason. Does anyone know how hard of a book it is compared...

I was just wondering if I was ready to take a 4th year undergrad course in Complex Analysis. The book we will be using is called Complex Function Theory and its buy Sarason. I've taken a course in multivariable calculus, number theory, discrete mathematics, differential equations and modern...