Browse Classroom Capsules and Notes

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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.

Chaos and Love Affairs

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

Periodic Equilibria under Periodic Harvesting

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

The Hiding Path

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

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....

An Elementary Proof of an Oscillation Theorem for Differential Equations

A new and elementary proof for a theorem in differential equations

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.

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.

Application of the Lambert W Function to the SIR Epidemic Model

The author uses the Lambert W function to express the equilibrium solutions of the SIR epidemic model.

Euler-Cauchy Using Undetermined Coefficients

It is shown that Euler-Cauchy equations with certain types of nonhomogeneous terms can be solved by the method of undetermined coefficients.