On the integration of elementary functions: Computing the logarithmic part

Date

2012-05

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Abstract

We first provide an algorithm to compute the logarithmic part of an integral of an algebraic function. The algorithm finds closed-form solutions that have been difficult to compute by other means.

We then provide an algorithm to compute the logarithmic part of a function lying in a transcendental elementary extension. We are able to fully justify the algorithms using techniques of Gr"obner bases, differential algebra, and algebraic geometry.


This dissertation won 2nd Place in the Texas Tech University Outstanding Thesis and Dissertation Award, Mathematics, Physical Sciences & Engineering, 2012.

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Keywords

Differential calculus, Logic, symbolic and mathematical, Differential algebra, Geometry, algebraic

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