Conformal mapping - Revision history

Vipul: 2 revisions

2008-05-18T19:11:50Z

2 revisions

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Vipul: /* Definition */

2008-04-20T20:52:09Z

Definition

← Older revision		Revision as of 20:52, 20 April 2008
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	* <math>f</math> is a [[holomorphic function]] and <math>\|f'(z)\| \ne 0</math> for all <math>z \in U</math>		* <math>f</math> is a [[holomorphic function]] and <math>\|f'(z)\| \ne 0</math> for all <math>z \in U</math>
	* <math>f</math> maps smooth curves to smooth curves, and preserves both the magnitude and orientation of angle between curves ~~and~~ their intersection.		* <math>f</math> maps smooth curves to smooth curves, and preserves both the magnitude and orientation of angle between curves at their intersection.

	==Relation with other properties==		==Relation with other properties==

Vipul: New page: ==Definition== Suppose $U$ is an open subset of $\mathbb{C}$ . A map $f: U \to \mathbb{C}$ (or to a subset of $\mathbb{C}$ is termed a '''confor...

2008-04-16T21:25:44Z

New page: ==Definition== Suppose <math>U</math> is an open subset of <math>\mathbb{C}</math>. A map <math>f: U \to \mathbb{C}</math> (or to a subset of <math>\mathbb{C}</math> is termed a '''confor...

New page

==Definition==

Suppose <math>U</math> is an open subset of <math>\mathbb{C}</math>. A map <math>f: U \to \mathbb{C}</math> (or to a subset of <math>\mathbb{C}</math> is termed a '''conformal mapping''' if it satisfies the following equivalent conditions:

* <math>f</math> is a [[holomorphic function]] and <math>|f'(z)| \ne 0</math> for all <math>z \in U</math>
* <math>f</math> maps smooth curves to smooth curves, and preserves both the magnitude and orientation of angle between curves and their intersection.

==Relation with other properties==

===Weaker properties===

* [[Isogonal mapping]]: This is a smooth mapping that preserves the magnitude of angles, but not necessarily the orientation. An isogonal mapping could be conformal or [[anticonformal mapping|anticonformal]]

Conformal mapping - Revision history

Vipul: 2 revisions

Vipul: /* Definition */

Vipul: New page: ==Definition== Suppose U is an open subset of \mathbb{C}. A map f: U \to \mathbb{C} (or to a subset of \mathbb{C} is termed a '''confor...

Vipul: New page: ==Definition== Suppose $U$ is an open subset of $\mathbb{C}$ . A map $f: U \to \mathbb{C}$ (or to a subset of $\mathbb{C}$ is termed a '''confor...