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Math Help - what is the cauchy-coursat theorem state specificly in word?

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    what is the cauchy-coursat theorem state specificly in word?

    what is the cauchy-coursat theorem state specificly in word?
    Is it calculate the area or the legth,which area and what legth?
    please give a example!
    And what is deformation of contour?
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    MHF Contributor Drexel28's Avatar
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    Re: what is the cauchy-coursat theorem state specificly in word?

    Quote Originally Posted by victorlui View Post
    what is the cauchy-coursat theorem state specificly in word?
    Is it calculate the area or the legth,which area and what legth?
    please give a example!
    And what is deformation of contour?
    It's Cauchy-Goursat by the way. Anyways, it says that if you integrate a function on a rectifiable curve which is contained within some simply connected region for which your function is holomorphic then the integral is zero. By deformation what is really meant is a 'homotopy' (google it). You can use CG to prove that if \Gamma and \Gamma' are curves for which there exists a homotopy which doesn't pass through a singularity (intuitively) then \displaystyle \int_\Gamma f\;dz=\int_{\Gamma'}f\;dz.
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    MHF Contributor FernandoRevilla's Avatar
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    Re: what is the cauchy-coursat theorem state specificly in word?

    Hope this helps:

    Cauchy's integral theorem - Wikipedia, the free encyclopedia


    Edited: Sorry, I didn't see Drexel28's post.
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    Re: what is the cauchy-coursat theorem state specificly in word?

    This may be too hard for me to understand,is there any ways too explain this for me(which never learn complex analysis)to understand?
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    MHF Contributor FernandoRevilla's Avatar
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    Re: what is the cauchy-coursat theorem state specificly in word?

    Quote Originally Posted by victorlui View Post
    This may be too hard for me to understand,is there any ways too explain this for me(which never learn complex analysis)to understand?
    There is no royal road to Geometry (Euclid said to king Ptolemy). Idem to Complex Analysis.
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    Re: what is the cauchy-coursat theorem state specificly in word?

    Quote Originally Posted by FernandoRevilla View Post
    There is no royal road to Geometry (Euclid said to king Ptolemy). Idem to Complex Variable.
    So,there are no basic definition of the those integration?
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    MHF Contributor Drexel28's Avatar
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    Re: what is the cauchy-coursat theorem state specificly in word?

    Quote Originally Posted by victorlui View Post
    So,there are no basic definition of the those integration?
    Do you know line integrals from....wherever they teach line integrals (multivariable or vector calc).
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    Re: what is the cauchy-coursat theorem state specificly in word?

    Quote Originally Posted by Drexel28 View Post
    Do you know line integrals from....wherever they teach line integrals (multivariable or vector calc).
    i know the basic integral , but never learned the contour integral...
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    MHF Contributor Drexel28's Avatar
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    Re: what is the cauchy-coursat theorem state specificly in word?

    Quote Originally Posted by victorlui View Post
    i know the basic integral , but never learned the contour integral...
    So you don't know this?
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    Re: what is the cauchy-coursat theorem state specificly in word?

    Quote Originally Posted by victorlui View Post
    what is the cauchy-coursat theorem state specificly in word?
    Is it calculate the area or the legth,which area and what legth?
    please give a example!
    And what is deformation of contour?
    I have said in another thread of yours. Get a textbook. Work through it from the start. At the moment you are trying understand things that depend on many other things that you also do not understand (and those things in turn depend on things you do not know).
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