Analytic functions without Cauchy integral theorem

dc.contributor.advisorWright, Martin
dc.contributor.committeeMemberIngram, William T.
dc.contributor.committeeMemberSinkhorn, Richard D.
dc.contributor.committeeMemberMcElrath, Eby N.
dc.creatorMocega, Esther E.
dc.date.accessioned2022-06-22T13:40:17Z
dc.date.available2022-06-22T13:40:17Z
dc.date.issued1968
dc.description.abstractCauchy's Theorem. Let R be a simply connected domain and f a function on R to E[squared] which is differentiable over R. Let C be any closed rectifiable curve in R. Then I [integral][lowerd C]f(z)dz = 0. Through the years Cauchy's Theorem was the only means of proving that if a complex valued function f(z) is differentiable over a domain R then f(z) has derivatives of all orders in R. A proof of the above statement without the use of an Integral was given for the first time in 1960 by H. E. Connell, The purpose of this thesis is to make a resume of all the theorems leading to Connell's proof.
dc.description.departmentMathematics, Department of
dc.format.digitalOriginreformatted digital
dc.format.mimetypeapplication/pdf
dc.identifier.other13655430
dc.identifier.urihttps://hdl.handle.net/10657/9717
dc.language.isoen
dc.rightsThis item is protected by copyright but is made available here under a claim of fair use (17 U.S.C. Section 107) for non-profit research and educational purposes. Users of this work assume the responsibility for determining copyright status prior to reusing, publishing, or reproducing this item for purposes other than what is allowed by fair use or other copyright exemptions. Any reuse of this item in excess of fair use or other copyright exemptions requires express permission of the copyright holder.
dc.titleAnalytic functions without Cauchy integral theorem
dc.type.dcmiText
dc.type.genreThesis
thesis.degree.collegeCollege of Arts and Sciences
thesis.degree.departmentMathematics, Department of
thesis.degree.disciplineMathematics
thesis.degree.grantorUniversity of Houston
thesis.degree.levelMasters
thesis.degree.nameMaster of Science
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