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

1. ## 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?
And what is deformation of contour?

2. ## Re: what is the cauchy-coursat theorem state specificly in word?

Originally Posted by victorlui
what is the cauchy-coursat theorem state specificly in word?
Is it calculate the area or the legth,which area and what legth?
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 $\displaystyle \Gamma$ and $\displaystyle \Gamma'$ are curves for which there exists a homotopy which doesn't pass through a singularity (intuitively) then $\displaystyle \displaystyle \int_\Gamma f\;dz=\int_{\Gamma'}f\;dz$.

3. ## 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.

4. ## 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?

5. ## Re: what is the cauchy-coursat theorem state specificly in word?

Originally Posted by victorlui
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.

6. ## Re: what is the cauchy-coursat theorem state specificly in word?

Originally Posted by FernandoRevilla
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?

7. ## Re: what is the cauchy-coursat theorem state specificly in word?

Originally Posted by victorlui
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).

8. ## Re: what is the cauchy-coursat theorem state specificly in word?

Originally Posted by Drexel28
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...

9. ## Re: what is the cauchy-coursat theorem state specificly in word?

Originally Posted by victorlui
i know the basic integral , but never learned the contour integral...
So you don't know this?

10. ## Re: what is the cauchy-coursat theorem state specificly in word?

Originally Posted by victorlui
what is the cauchy-coursat theorem state specificly in word?
Is it calculate the area or the legth,which area and what legth?