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Browse Classroom Capsules and Notes

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

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

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

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

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....

A new and elementary proof for a theorem in differential equations

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.

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

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