Results 1 to 5 of 5

Math Help - Contour Integrals

  1. #1
    Newbie
    Joined
    May 2010
    Posts
    2

    Contour Integrals

    I'm working on a problem that has contour integrals and checked the answers my professor provided with a solution sheet, however there's a part in the solution sheet I don't understand.

    This is the question given:


    This is the solution:




    And this is the part I don't understand from this solution:



    Thanks in advance for any help.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    16,201
    Thanks
    1789
    Quote Originally Posted by granma View Post
    I'm working on a problem that has contour integrals and checked the answers my professor provided with a solution sheet, however there's a part in the solution sheet I don't understand.

    This is the question given:


    This is the solution:




    And this is the part I don't understand from this solution:



    Thanks in advance for any help.
    Do you think possibly it was the "i" that was already in the integral: (cos^2 \theta)(\underline{i} e^{i\theta})?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    May 2010
    Posts
    2
    Quote Originally Posted by HallsofIvy View Post
    Do you think possibly it was the "i" that was already in the integral: (cos^2 \theta)(\underline{i} e^{i\theta})?
    Yes, that's what I think it is, and if that's the case there shouldn't be i^2 later on etc... I'm assuming it's probably just a typo? I think it's best if I directly contact my professor about this.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Senior Member AllanCuz's Avatar
    Joined
    Apr 2010
    From
    Canada
    Posts
    384
    Thanks
    4
    Quote Originally Posted by HallsofIvy View Post
    Do you think possibly it was the "i" that was already in the integral: (cos^2 \theta)(\underline{i} e^{i\theta})?
    I don't think this is the case (though it appears likely),

     \int ( cos^2 \theta ) ( i e^{ i \theta } ) d \theta

    We need to get to the above from

     i \int ( \frac{1}{2} [ e^{i \theta } + e^{-i \theta} ]^2 )( i e^{ i \theta} ) d\theta

    Let's look at

     \frac{1}{2} [ e^{i \theta } + e^{-i \theta} ]^2

     ( \frac{1}{2} [ e^{i \theta } + e^{-i \theta} ] )^2 = ( \frac{1}{2} [ (cos \theta + i sin \theta ) + (cos \theta - i sin \theta) ] )^2

    ( \frac{1}{2} ( 2 cos \theta ) )^2 = cos^2 \theta

    Which transforms

     i \int ( \frac{1}{2} [ e^{i \theta } + e^{-i \theta} ]^2 )( i e^{ i \theta} ) d\theta = i \int cos^2 \theta (i e^{i \theta} ) d \theta

    We have an extra i here....I don't know where it came from but I'm relatively sure it didn't come from what was already in the integral.
    Last edited by AllanCuz; May 21st 2010 at 05:52 AM.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor

    Joined
    Apr 2005
    Posts
    16,201
    Thanks
    1789
    Quote Originally Posted by granma View Post
    Yes, that's what I think it is, and if that's the case there shouldn't be i^2 later on etc... I'm assuming it's probably just a typo? I think it's best if I directly contact my professor about this.
    Oh, I see your point- the i also remained inside the integral! Yes, it most likely a typo- they intended to take the i outside the integral but accidently also left it inside.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Contour Integrals (to Evaluate Real Integrals)
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: January 17th 2011, 10:23 PM
  2. Contour Integrals
    Posted in the Differential Geometry Forum
    Replies: 0
    Last Post: September 29th 2010, 11:59 AM
  3. Contour Integrals
    Posted in the Advanced Math Topics Forum
    Replies: 5
    Last Post: May 23rd 2010, 06:34 AM
  4. contour integrals
    Posted in the Calculus Forum
    Replies: 5
    Last Post: March 1st 2010, 03:19 PM
  5. Contour Integrals
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: December 6th 2009, 03:45 AM

Search Tags


/mathhelpforum @mathhelpforum