dc.contributor.advisor | Mitrea, Dorina, 1965- | eng |
dc.contributor.author | Judd, Kristin N. | eng |
dc.date.issued | 2008 | eng |
dc.date.submitted | 2008 Spring | eng |
dc.description | The 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.description | Title from title screen of research.pdf file (viewed on September 5, 2008) | eng |
dc.description | Thesis (M.S.) University of Missouri-Columbia 2008. | eng |
dc.description.abstract | The 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.bibref | Includes bibliographical references. | eng |
dc.identifier.merlin | b6463940x | eng |
dc.identifier.oclc | 245537820 | eng |
dc.identifier.uri | https://doi.org/10.32469/10355/5638 | eng |
dc.identifier.uri | https://hdl.handle.net/10355/5638 | |
dc.language | English | eng |
dc.publisher | University of Missouri--Columbia | eng |
dc.relation.ispartofcommunity | University of Missouri-Columbia. Graduate School. Theses and Dissertations. Theses. 2008 Theses | eng |
dc.rights | OpenAccess. | eng |
dc.rights.license | This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 License. | |
dc.subject.lcsh | Potential theory (Mathematics) | eng |
dc.subject.lcsh | Cauchy integrals | eng |
dc.title | An extension of Green's theorem with application | eng |
dc.type | Thesis | eng |
thesis.degree.discipline | Mathematics (MU) | eng |
thesis.degree.grantor | University of Missouri--Columbia | eng |
thesis.degree.level | Masters | eng |
thesis.degree.name | M.S. | eng |