Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Complex Integration

  1. Jan 18, 2009 #1
    1. The problem statement, all variables and given/known data

    Evaluate the following intergral:


    2. Relevant equations

    Intergral from gamma of (y)dz, where gamma is the union of the line segments joining 0 to i and then i to i+2

    3. The attempt at a solution

    I have no idea how to do this!
     
  2. jcsd
  3. Jan 18, 2009 #2

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    Hi kmeado07! :smile:

    (have a gamma: Γ :wink:)

    Γ is an L-shaped path …

    just integrate along each bit of it separately.

    (but what is y? :confused:)
     
  4. Jan 18, 2009 #3

    HallsofIvy

    User Avatar
    Science Advisor

    Presumably, if you are expected to do a problem like this, you know something about path integrals. The line from 0 to i, in the complex plane, can be written as z= (1+i)t where t ranges from 0 to 1. The line from i to i+ 2 can be written as z= (1+ t)+ i where, again, t ranges from 0 to 1. Do those two integrals separately with z replace by those and dz by (1+i)dt in the first integral and by dt in the second.

    Unfortunately, you see to have forgotten to say what the integrand, y(z), is!
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook