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Browse Classroom Capsules and Notes

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Displaying 161 - 170 of 225

Calculus in the Operating Room

Two realistic modeling problems related to blood loss and transfusions during surgery.

Rethinking Rigor in Calculus: The Role of the Mean Value Theorem

The author proposes the Increasing Function Theorem as an alternative to the Mean Value Theorem in introductory calculus.

The Geometric Series in Calculus

The author argues that many topics in differential and integral calculus could be better approached by an appropriate use of geometric series.

An Application of Geography to Mathematics

The authors review the history of the evaluation of the integral of the secant as it arose as an explanation of the construction of Mercator projections.

Nice Cubic Polynomials for Curve Sketching

Using Pythagorean triplets to construct cubic polynomials such that the polynomial and its first and second derivatives have integer roots.

The Changing Concept of Change: The Derivative from Fermat to Weierstrass

The author reviews the history of the derivative from use, through discovery, exploration, and development, to formal definition.

A Diophantine Equation from Calculus
This article revisits the famous calculus optimization problem of removing four corner squares from a sheet and folding up the edges to form a box of maximal volume. The authors analyze the...
Indeterminate Forms Revisited
The author gives a proof of l'Hospital's Rule and obtains extensions. This is the text of an invited address to a joint session of the American Mathematical Society and the Mathematical...
The Importance of Being Continuous

The author discusses issues connected with determining a continuous antiderivative for an integrand continuous over a given interval. The solutions obtained by computer algebra systems often...

A Comparison of Two Elementary Approximation Methods

The methods of the title are a differential approximation of a differentiable function over a given interval and a linear interpolation over the same interval.

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