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dc.contributor.advisorMitrea, Dorina, 1965-eng
dc.contributor.authorJudd, Kristin N.eng
dc.date.issued2008eng
dc.date.submitted2008 Springeng
dc.descriptionThe entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file.eng
dc.descriptionTitle from title screen of research.pdf file (viewed on September 5, 2008)eng
dc.descriptionThesis (M.S.) University of Missouri-Columbia 2008.eng
dc.description.abstractThe main result of this thesis is a generalization of Green's Theorem. Green' s Theorem states: If Omega is an open subset of R[logical and]2 containing a compact subset K with smooth boundary. Let P and Q be two real valued functions on Omega which are differentiable with continuous partial derivatives. Then the integral over the boundary of K of Pdx [plus] Qdy is equal to the double integral over K of a package of partial derivatives (namely the partial derivative of Q with respect to x minus the partial derivative of P with respect to y). In this thesis we prove that the conditions on P and Q can be weakened. In fact, we prove that the conclusion of Green's Theorem holds if P and Q are only differentiable on a neighborhood of K and the package of partial derivatives is continuous on K. After proving the main result we can conclude two further results, a generalization of the Divergence Theorem in R[logical and]2 and a generalization of Cauchy's Integral Formula.eng
dc.description.bibrefIncludes bibliographical references.eng
dc.identifier.merlinb6463940xeng
dc.identifier.oclc245537820eng
dc.identifier.urihttps://doi.org/10.32469/10355/5638eng
dc.identifier.urihttps://hdl.handle.net/10355/5638
dc.languageEnglisheng
dc.publisherUniversity of Missouri--Columbiaeng
dc.relation.ispartofcommunityUniversity of Missouri-Columbia. Graduate School. Theses and Dissertations. Theses. 2008 Theseseng
dc.rightsOpenAccess.eng
dc.rights.licenseThis work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 License.
dc.subject.lcshPotential theory (Mathematics)eng
dc.subject.lcshCauchy integralseng
dc.titleAn extension of Green's theorem with applicationeng
dc.typeThesiseng
thesis.degree.disciplineMathematics (MU)eng
thesis.degree.grantorUniversity of Missouri--Columbiaeng
thesis.degree.levelMasterseng
thesis.degree.nameM.S.eng


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