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picture1_Bilinear Transformation Example 180323 | Exerciseset04


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File: Bilinear Transformation Example 180323 | Exerciseset04
EXERCISE SET #4 Bilinear Transformation: is defined by , . This wf(z)(azb) (czd) adbc 0 transformation can be considered as a combination of the tranformation of translation, rotation (and stretching), inversion. It ...

icon picture PDF Filetype PDF | Posted on 30 Jan 2023 | 2 years ago

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...Exercise set bilinear transformation is defined by this wf z azb czd adbc can be considered as a combination of the tranformation translation rotation and stretching inversion it has property that circles are mapped into in w plane where infinite radius straight lines included maps any three distinct points one which may at infinity if then invariance cross ratio i e determines map f ii following mappings conformal not why what effect each mapping on angles b zez c iz d sin g h zz write down laplace equation under change variables xx yy xucosv yusinv polar coordinates uiv xy itany x show composition two transformations also fixed point itself most wz unless simply identity verify complex number with za az onto being sent to origin given circle form u v find pre image xa yb express terms ans known sends pz p nonzero q bc ad for written cz sequence tranformations above thus conclude uniquely determined conditions uv zi wizi wi respectively upper half we interior unit hint such way while ...
								

							

						
	
												
				
					
					
					
			
					
				
				
		
	

	
		





	

	
				

						

						
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Posted on: 30 Jan 2023 | 2 years ago
										
										
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