We study a 1-parameter family of trigonometric definite integrals, showing how the joint usage of Information and Communication Technologies and paper-and-pencil work lead to different outputs, revealing different mathematical meanings and different concrete meanings. This family of integrals is useful for describing a phenomenon in soil…

We compute closed forms for some parametric integrals. The tools used are MacLaurin developments and other infinite series. Finally, Stirling numbers appear. (Contains 1 figure.)

We present a sequence of improper integrals, for which a closed formula can be computed using Wallis formula and a non-straightforward recurrence formula. This yields a new integral presentation for Catalan numbers.

We compute in three different ways the same definite parametric integral. By-products are the derivation of a combinatorial identity and two integral presentations of Catalan numbers. One of them leads to a presentation using the [gamma] function.

This is the third part of a study of plane transformations described in a complex setting. After the study of homotheties, translations, rotations and reflections, we proceed now to the study of plane similarities, either direct or inverse. Their group theoretical properties are described, and their action on classical geometrical objects is…

We describe and analyze a situation involving symbolic representation and graphical visualization of the solution of a system of two linear differential equations, using a computer algebra system. Symbolic solution and graphical representation complement each other. Graphical representation helps to understand the behavior of the symbolic…

Geometric constructions have previously been shown that can be interpreted as rays of light trapped either in polygons or in conics, by successive reflections. The same question, trapping light in closed Fermat curves, is addressed here. Numerical methods are used to study the behaviour of the reflection points of a triangle when the degree of the…

When a professional engineer solves a mathematical problem using technology, he/she generally uses a single one-step "high-level" command of a readily available computer package to obtain the solution immediately. This should not happen during his/her learning cursus. In an engineering mathematics course, the educator should decompose the solution…