MTH 282 Lecture Notes - Lecture 4: Bucatini, Fez, Adze
7 May 2020
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Definitioninvariance let f beanalytic in a domain d letpoand ti beloops in d if po can be continuouslydeformed to ti chd thenspfez d2 4 fcz dz. Ei compute fp3 dz let fcztf. ee is analytic in d. Eo 13 o fpfczgatz fpfczsdz fcofcadz ffcfdz f yffzsdz fc. fi dz. Dz f fpfttsdz fcyez. mx is analytic on d e e h13 fczs z. Tcanbe deformed withindto a positivelyoriented circle c i centered at. Cauchy"s integraltheorem is analytic in a simple closed contour p thenjpfcz dz o p a curve that does not cross itself. But what about f feltdz where eo is inside p. Suppose fczkgot acz zo 1 aaczzo54 then zfftzod z. az t ai ffztfzodz fzaz dz ao ziti. Ziti f zo t adz zo t and fa. dz faze zo dz x. Candy"s integral formula let p be a simple closedpositivelyoriented contour in some simple inside p then fczor z fppztftzt. dz. If f is analytic tamng p and zo b any point.
