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...Topic notes jeremy orlo conformal transformations introduction in this we will look at the geometric notion of maps it turn out that analytic functions are automatically once have understood general a specic family called fractional linear trans formations and particular their properties as an application use to solve dirichlet problem for harmonic on unit disk with specied values circle end return some questions uid ow denition mappings westart somewhat hand wavy informal conformalmapsarefunctionsoncthatpreservetheanglesbetween curves more precisely suppose f z is dierentiable t smooth curve through be concrete let s function point w under map tangent vector mapped these notations following if there angle scale such any rotates by scales found rotating scaling dened region say each note factor rotation depends but not example thegurebelowshowsaconformalmapf mappingtwocurvesthrough two vectors original both rotated scaled same amount conformaltransformations y v x u aconformal all ammo...