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    An extension of Green's theorem with application

    Judd, Kristin N.
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    Date
    2008
    Format
    Thesis
    Metadata
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    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.
    URI
    https://doi.org/10.32469/10355/5638
    https://hdl.handle.net/10355/5638
    Degree
    M.S.
    Thesis Department
    Mathematics (MU)
    Rights
    OpenAccess.
    This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 License.
    Collections
    • Mathematics electronic theses and dissertations (MU)
    • 2008 MU theses - Freely available online

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