ENGINEER 1P03 Lecture Notes - Lecture 6: Internal And External Angles, Conformal Map, Concentric Objects

• School: McMaster University
• Department: Engineering (General)
• Course: ENGINEER 1P03
• Professor: Robert Fleisig

Document Summary

Angle is preserved (cid:1875) =(cid:2011)(cid:1878) (cid:1878)0 (cid:1878) (cid:1878)1 (cid:1878)0 gets mapped to origin, and (cid:1878)1 to infinity. Choose (cid:2011) in order to map to a region within right half plane (cid:1875) = (cid:1878) +(cid:1878) Maps upper half plane minus circle of radius about the origin to upper half plane (cid:1878) = get mapped to (cid:1875) = 2 (cid:1875) = sin (cid:2024) (cid:1878) 2. Maps upper half strip from 0 to to upper half plane (cid:1878) = 0, get mapped to (cid:1875) = 1. =(cid:1827)(cid:1873) +(cid:1828) or =(cid:1827)(cid:1874) +(cid:1828) (cid:1827)(cid:1828) =2 (cid:2009) (cid:2010) =2 (cid:2010) = 2(cid:2009) (cid:1875) =(cid:1878) (cid:1878) + ,(cid:1834)2 2 =2. Maps circles of radii centred at (cid:1834) and imaginary axis to concentric circles. Re (cid:1878) = 0 (cid:1875) = 1 (cid:1878) (cid:1834) = (cid:1875) =(cid:1834) =(cid:1834) (cid:1834)2 2 (cid:1878) +(cid:1834) = (cid:1875) =(cid:1834)+ =(cid:1834)+ (cid:1834)2 2. Sides of polygons can meet at infinity, at an angle of (cid:2024)