1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Complex Analysis - Contour Intergral

  1. Oct 15, 2008 #1
    1. The problem statement, all variables and given/known data

    The problem is to integrate:

    [tex]\oint_{C}\frac{dz}{z^{2}-1}[/tex]

    C is a C.C.W circle |z| = 2.

    2. Relevant equations



    3. The attempt at a solution

    I used the Cauchy integral formula:

    [tex]\oint_{C}\frac{f(z)}{(z-z_{0})^{n+1}}dz = \frac{2 \pi i}{n!}f^{n}(z_{0})[/tex]

    Which gives an answer of [tex]2 \pi i[/tex] since there is a singularity inside of the contour C...

    Does this look right?
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Oct 15, 2008 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    That's not right at all. z^2-1 is not the same as (z-1)^2. And even if the problem were dz/(z-1)^2 the integral of that around |z|=2 would be zero (since f(z) in your formula is 1). Use z^2-1=(z-1)(z+1) and then look up the residue theorem. Or write 1/((z-1)(z+1))=A/(z-1)+B/(z+1) (figure out A and B) and then you can use the Cauchy integral formula on each part.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Complex Analysis - Contour Intergral
  1. Complex Analysis (Replies: 0)

  2. Complex Analysis (Replies: 4)

  3. Complex Analysis (Replies: 4)

  4. Complex analysis (Replies: 10)

Loading...