Complex Analysis: Conformal Mappings

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Discussion Overview

The discussion focuses on finding conformal transformations that map a disk of radius R to various geometric regions, specifically an equilateral triangular region, a rectangular region, and an elliptic disk. The scope includes theoretical aspects of complex analysis and applications of conformal mappings.

Discussion Character

  • Exploratory, Technical explanation

Main Points Raised

  • One participant seeks conformal transformations for mapping a disk of radius R to an equilateral triangular region with side A.
  • The same participant also requests transformations for mapping the disk to a rectangular region with length L and width W.
  • Additionally, the participant is interested in mapping the disk to an elliptic disk with semi-major axis a and semi-minor axis b.
  • Another participant suggests consulting Ahlfors' text for relevant information on conformal mappings.
  • A different participant recommends Churchill's book as another resource for exploring conformal transformations.

Areas of Agreement / Disagreement

No consensus has been reached regarding specific methods or transformations, and multiple resources have been suggested without a definitive agreement on the best approach.

Contextual Notes

The discussion does not provide detailed assumptions or specific mathematical steps related to the transformations, leaving some aspects unresolved.

Who May Find This Useful

Readers interested in complex analysis, particularly those exploring conformal mappings and their applications in various geometric contexts.

JulieK
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I am looking for conformal transformations to map:

1. Disk of radius R to equilateral triangular region with side A.

2. Disk of radius R to rectangular region with length L and width W.

3. Disk of radius R to elliptic disk with semi-major axis a and semi-minor axis b.

Thanks!
 
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Many thanks!
 

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