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!

How and when to use Cauchy's integral formula

  1. Jun 3, 2014 #1
    Hello.
    How do I know when to use Cauchy integral formula. Why do we use the formula in this question? As you can see in my attempt, I got stuck.
    Are my values for f(z), z, z​0 here correct?
     

    Attached Files:

    Last edited: Jun 3, 2014
  2. jcsd
  3. Jun 3, 2014 #2

    maajdl

    User Avatar
    Gold Member

    You got the right answer, since f(zo)=1.
    You use the Cauchy integral when you have to evaluate an integral that matches the pattern of a Cauchy integral!
    Sometimes, the contour needs to be closed to get a match and the integral on the closing path can be evaluated by some other means.
    The Cauchy integral is very useful in physics and in signal theory.
     
  4. Jun 3, 2014 #3
    No, I just solved it and f(z) is not 1, but 1/(z-1).
     
  5. Jun 4, 2014 #4

    maajdl

    User Avatar
    Gold Member

    You proved that your integral is 2 Pi I * the Cauchy integral of f(z)=1 around z=I .
    Therefore, your integral is 2 Pi I f(I) = 2 Pi I .
     
  6. Jun 4, 2014 #5

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    I never look at photo attachments of handwritten work; in fact, if you read the "PF Guidelines" post by vela, you will see that you are not supposed to use them except for very special circumstances---for several good reasons. You should take the trouble to type out your work if you want the helpers to take the trouble to offer free assistance.
     
  7. Jun 4, 2014 #6

    micromass

    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor
    2016 Award

    Exactly! Thread locked. Please create a thread where you write out your work.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: How and when to use Cauchy's integral formula
Loading...