Browse Classroom Capsules and Notes

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The Chair, the Area Rug, and the Astroid

An innocuous-seeming minimization problem points to properties of line envelopes.

A Normal Density Project

Explores the Gaussian normal density through polynomial approximations

Hyperbolic Functions and Proper Time in Relativity

Links hyperbolic functions to distance measurement in space-time

How Not to Land at Lake Tahoe!

The article describes a model for aircraft landing using cubic polynomials.

In Praise of \( y = x^{\alpha}\sin(1/x)\)

The article discusses a class of counterexamples in analysis.

The Disk and Shell Method

The paper gives a verification that the disk and shell methods calculate the same volume for regions revolved around the y-axis. This argument may be used in class.

Counterexamples to L'Hôpital's Rule

From the introduction, "I am not, of course, claiming that L'Hôpital's rule is wrong, merely that unless it is stated and used very carefully it is capable of yielding...

Calculus with Analytic Geometry

In this review of a calculus book authored by George Simmons, Underwood Dudley draws seven general conclusions about the way such books are and the way they should be.

L'Hôpital's Rule Via Integration

The article gives a proof of L'Hôpital's Rule in the infinity-over-infinity case.

Teaching Integration by Substitution

The author discusses the technique of integration by substitution with particular emphasis on trigonometric substitution.