Calculus I and II Page

This is the humble beginning of my papers on calculus, starting with techniques of integration, proofs of the Intermediate Value Theorem, Rolle's Theorem, and with indefinite integrals.

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Proof of Rolle's Theorem using a flow chart: Let f be a continuous function defined on the closed interval [a,b], and differentiable on the open interval (a,b). Let f(a)= f(b). Then there exists a c in (a,b) such that f'(c) = 0.

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Proof of the Intermediate Value Theorem using a flow chart.

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Techniques of integration, paper 1

Techniques of integration, paper 2

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Techniques of integration, paper 3

Techniques of integration, paper 4

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Techniques of integration, paper 5 This paper introduces the Weierstrass substitution technique for integration.

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Using the unipodal algebra to integrate:

An Instructive Unipodal Integral A unipodal integration of the integrals

$\int \; (a\; cosh\; x\; -\; sinh\; x)cosh\; bx\; dx.$

and

$\int \; cos\; x\; cosh\; x\; dx.$

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Techniques of integration of the Jacobi Elliptic Functions.

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