Results 1 to 4 of 4

Math Help - complex integration

  1. #1
    Newbie
    Joined
    Oct 2009
    Posts
    21

    complex integration

    Integrate the funtion around 4 different contours
    g(z)=z^2+1/z^2-1
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Banned
    Joined
    Oct 2009
    Posts
    4,261
    Thanks
    2
    Quote Originally Posted by bookie88 View Post
    Integrate the funtion around 4 different contours
    g(z)=z^2+1/z^2-1

    Just like that?? Well, then integrate about 4 contours none of which contains in its interior or on its boundary neither the point z = 1 or z = -1 and then your function if analytic and thus the integrals all equal zero...simple!

    Tonio
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Sep 2009
    Posts
    32
    Quote Originally Posted by bookie88 View Post
    Integrate the funtion around 4 different contours
    g(z)=z^2+1/z^2-1
    the significance of different contours lies in whether or not your contour encircles (if its a closed contour) the singular points of g(z)

    singular points are just where g(z) is undefined, so here, where the denomenator equals 0
    where z=1 or -1

    so a contour that doesnt encircle these points, would be
    \gamma = 3+e^{i\theta}

    integrating g(z) around this contour gives 0

    this is by the residue theorem, closed contour integration theorem... something along those lines

    for a contour that encircles the singularities
    e.g.
    \gamma = 2e^{i\theta}
    you have to calculate the residues of g(z) at the points of singularities
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by walleye View Post
    the significance of different contours lies in whether or not your contour encircles (if its a closed contour) the singular points of g(z)

    singular points are just where g(z) is undefined, so here, where the denomenator equals 0
    where z=1 or -1

    so a contour that doesnt encircle these points, would be
    \gamma = 3+e^{i\theta}

    integrating g(z) around this contour gives 0

    this is by the residue theorem, closed contour integration theorem... something along those lines

    for a contour that encircles the singularities
    e.g.
    \gamma = 2e^{i\theta}
    you have to calculate the residues of g(z) at the points of singularities
    We all understand what you're saying. However, the question does not specify which four contours to use so the question is answered by choosing any four contours at all, including the four suggested in post #2 .... (A flaw in either the original question or in how the question has been posted ....)
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Complex integration
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 24th 2010, 01:30 AM
  2. Complex integration
    Posted in the Differential Geometry Forum
    Replies: 0
    Last Post: October 19th 2010, 01:14 PM
  3. Complex integration
    Posted in the Calculus Forum
    Replies: 3
    Last Post: August 8th 2010, 08:50 AM
  4. Complex Integration
    Posted in the Calculus Forum
    Replies: 8
    Last Post: May 5th 2010, 05:15 PM
  5. Complex Integration
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: October 2nd 2009, 12:21 AM

Search Tags


/mathhelpforum @mathhelpforum