Functions and Analysis


The Total Differential Integral of Calculus

Authors: Gerardo Alvarado

I deduce a series which satisfies the fundamental theorem of calculus without dependence on an explicit function. I prove Taylor's theorem and show that it is closely related. I deduce a series for the logarithm function and from this series deduce the power series representation of the logarithm function along with the interval of convergence. I also solve an ordinary differential equation.

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Submission history

[v1] 10 Mar 2007

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