Vipul: 2 revisions

2008-05-18T19:12:54Z

2 revisions

← Older revision	Revision as of 19:12, 18 May 2008
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Vipul at 18:57, 26 April 2008

2008-04-26T18:57:48Z

← Older revision		Revision as of 18:57, 26 April 2008
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			{{basic fact}}
	==Statement==		==Statement==

Vipul: New page: ==Statement== Suppose $f$ is a holomorphic function on a domain $U \subset \mathbb{C}$ , and $g := f'$ is its complex differential. Suppose $\...$

2008-04-14T00:25:39Z

New page: ==Statement== Suppose <math>f</math> is a holomorphic function on a domain <math>U \subset \mathbb{C}</math>, and <math>g := f'</math> is its complex differential. Suppose <math>\...

New page

==Statement==

Suppose <math>f</math> is a [[holomorphic function]] on a [[domain]] <math>U \subset \mathbb{C}</math>, and <math>g := f'</math> is its complex differential. Suppose <math>\gamma</math> is a piecewise smooth curve in <math>U</math>, starting at <math>z_0</math> and ending at <math>z_1</math>.

Then, we have:

<math>\int_\gamma g(z) \, dz = f(z_1) - f(z_0)</math>

This is the complex analog of the fundamental theorem of calculus.

Fundamental theorem of complex calculus - Revision history

Vipul: 2 revisions

Vipul at 18:57, 26 April 2008

Vipul: New page: ==Statement== Suppose f is a holomorphic function on a domain U \subset \mathbb{C}, and g := f' is its complex differential. Suppose \...

Vipul: New page: ==Statement== Suppose $f$ is a holomorphic function on a domain $U \subset \mathbb{C}$ , and $g := f'$ is its complex differential. Suppose $\...$