Articles on the factorization of polynomials using a rejection theorem; a general formula for the N-th of a sequence; and integration by undetermined coefficients. (MM)

The paper presents applications and methods of analysis for non-linear hyperbolic partial differential equations. The paper is concluded by an account of wave front analysis as applied to the piston problem of gas dynamics. (JG)

The approximate value of a given sum is obtained through the development of some results of inequalities. Inequalities are also used to show how the concepts of sum and integral are related. (MP)

Presents a dialog in question-and-answer form to explain the rationale behind using radians instead of degrees in calculus. (ASK)

Perhaps next time teachers head towards the fundamental theorem of calculus in their classroom, they may wish to consider Fermat's technique of finding expressions for areas under curves, beautifully outlined in Boyer's History of Mathematics. Pierre de Fermat (1601-1665) developed some important results in the journey toward the discovery of the…

The pre-equilibrium approximation is one of the several useful approximation methods that allows one to go from complex systems of differential equations to simple approximation methods. It is shown that the longtime behavior of systems subjected to pre-equilibrium can be obtained by a simple kinetic reasoning.

Two heuristic and three rigorous arguments are given for the fact that functions of the form Ce[kx], with C an arbitrary constant, are the only solutions of the equation dy/dx=ky where k is constant. Various of the proofs in this self-contained note could find classroom use in a first-year calculus course, an introductory course on differential…

A criterion (formula) for the termination of a continued fraction expansion leading to the solution of a standard differential eigenvalue problem from mathematical physics is presented. The criterion generates the eigenvalues in any specific case and is illustrated by elementary examples yielding well-known polynomial eigenfunctions. This…

This article describes some of the work of Jan Hudde who anticipated some results of calculus. Prior to a career as a Burgomaster of Amsterdam, Hudde engaged in mathematics. His method of finding maxima and minima is especially interesting.