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Math Help - Residues

  1. #1
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    Oct 2008
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    Residues

    hi my lecture notes were very vague this semester and nine o'clock in the morning isnt the easiest for a student that works till 1am each night.

    i need some help with Residues, if anyone knows of a good website that has a good explanation and example of residue calculus it would help out.

    the question im working on now is

    us residue calculus and appropriate contours to evaluate real integrals

    integral from 0 to infinity of 1/(x^4 +1) dx

    thanks heaps in advance
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  2. #2
    Super Member
    Joined
    Aug 2008
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    Quote Originally Posted by Reece View Post
    hi my lecture notes were very vague this semester and nine o'clock in the morning isnt the easiest for a student that works till 1am each night.

    i need some help with Residues, if anyone knows of a good website that has a good explanation and example of residue calculus it would help out.

    the question im working on now is

    us residue calculus and appropriate contours to evaluate real integrals

    integral from 0 to infinity of 1/(x^4 +1) dx

    thanks heaps in advance
    I know four: Art of Problem Solving, Physic Forum, SOS, and here. You just need to search the sites for complex analysis problems and study the solutions.

    Anyway, use:

    \mathop\oint\limits_{H_u}\frac{dz}{z^4+1} where H_u is the upper half-disc contour. The big denominator assures you that the integral over the semi-circle component of the contour goes to zero and the integral over the real axis component is twice your integral. There are only two poles in the contour right: e^{\pi i/4} and e^{3\pi i/4}. Now calculate the residues for these poles and use Residue Theorem.
    Last edited by shawsend; November 6th 2008 at 03:35 AM. Reason: corrected to say "twice your integral"
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  3. #3
    Member
    Joined
    Nov 2007
    Posts
    108
    Quote Originally Posted by Reece View Post
    hi my lecture notes were very vague this semester and nine o'clock in the morning isnt the easiest for a student that works till 1am each night.

    i need some help with Residues, if anyone knows of a good website that has a good explanation and example of residue calculus it would help out.

    the question im working on now is

    us residue calculus and appropriate contours to evaluate real integrals

    integral from 0 to infinity of 1/(x^4 +1) dx

    thanks heaps in advance
    Take a look at this tutorial written by ThePerfectHacker. It will definitely help you a lot, and it did help me.
    http://www.mathhelpforum.com/math-he...tegration.html
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