Integration Over Converging Arcs in the Plane
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Novotny, Timothy Joseph
Most standard theorems on convergence of integrals consider the integrals of a family of functions over a fixed domain of integration; however, situations occur in which one needs to approximate a curve over which a function is to be integrated by means of a sequence of piecewise smooth curves. This thesis deals with situations of this nature and investigates conditions under which the limit of integrals over the approximating curves is equal to the integral over the curve to which they converge. Since curves can converge in more than one manner, it is necessary to consider the effects of different types of convergence.
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