Browse Classroom Capsules and Notes

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A Bug Problem

This capsule discusses rates of change related to a vessel obtained as a surface of revolution. The question is about the rate a bug must move on the surface as liquid is being poured into the...

Do Dogs Know Calculus of Variation

This article generalizes a problem of dogs fetching a ball in the water and presents it as a problem of calculus of variation.

Period Three Begins

By exploiting the geometry of the cobweb plot, the author provides a simple and elementary derivation of the parameter for the period-three cycle of the logistic map.

The Fresnel Integrals Revisited

Without using double integrals, a new method is presented to evaluate the two Fresnel integrals about sine and cosine that has a wider applications than previous methods.

An Elementary Proof of an Oscillation Theorem for Differential Equations

A new and elementary proof for a theorem in differential equations

Wronskian Harmony

A closed form of the Wronskian for \( sin(kx) \) and for \( e^{kx}, k=1,2,\ldots,n \) is obtained. The derivation depends on trigonometric identities and properties of the determinant....

The Hiding Path

Interesting example of fox-chasing-rabbit differential equation questions.

Periodic Equilibria under Periodic Harvesting

The authors investigate the maximum number of periodic solutions for a population growth differential equation with two examples.

Chaos and Love Affairs

Love affairs are modeled, amusingly, using chaotic dynamical systems.

Power Series Expansions for Trigonometric Functions via Solutions to Initial Value Problems

Using initial value problem with repeated differentiations, the author obtains the complicated coefficients of the power series for powers of the secant function.