Calculus of Higher Order Noncommutative Functions

Leonard Charles Stevenson
This thesis extends some standard results familiar from undergraduate calculus to the setting of higher order noncommutative functions. These extensions are accomplished using a difference-differential operator in a completely algebraic, topological free, manner. The results include a version of the mean value theorem, the Taylor formula and an antiderivative. The Taylor formula is applied to obtain results about power series on nilpotent matrices and higher order polynomials.
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