A Slinky is a loose helical coil spring and is a well-known educational toy. In this paper a model for a Slinky is presented. The Slinky is represented as a sequence of rigid half coils connected by torsional springs. A range of Slinky configurations in static equilibrium are calculated. Where possible the torsion spring model is compared with the…

The dynamics of a simple pendulum are often presented to undergraduate engineering students in introductory courses in dynamics. It is usually the first dynamic system considered by students that is modelled by a differential equation. This paper presents the standard material given to students. It is fair to say that students are accepting this…

The natural exponential and logarithm are typically introduced to undergraduate engineering students in a calculus course using the notion of limits. We here present an approach to introduce the natural exponential/logarithm through a novel interpretation of derivatives. This approach does not rely on limits, allowing an early and intuitive…

In this note, some variants of Cauchy's mean value theorem are proved. The main tools to prove these results are some elementary auxiliary functions.

In this paper a class of regular surfaces, generated by rotation and twist of a rigid line segment, is considered. Firstly a complete description of those surfaces by means of local charts is obtained and then its orientability is characterized in terms of the number of half-twists, taking into account their direction (clockwise or…

Use of three-force member concept for rigid bodies whenever possible, to circumvent the more taxing use of equilibrium equations has been long-established. However, most students fail to reap its benefits due to a number of reasons, including the fact that its importance is hardly emphasized to them; skills and details needed for the concept are…

Implementing inquiry-oriented instructional proposals at the university level collides with many constraints related to the current pedagogical paradigm based on the transmission of previously established works of knowledge. One such constraint comes from defining subjects' curricula by a set of topics to study, not questions to inquire. Our…

We bring out an experience of organizing mathematical competitions that can be used as a medium to motivate the student and teacher minds in new directions of thinking. This can contribute to fostering research, innovation and provide a hands-on experience of mathematical concepts with the real world. Mathematical competitions can be used to build…

It is well known that mechanical engineering students often find mechanics a difficult area to grasp. This article describes a system of equations describing the motion of a balanced and an unbalanced roller constrained by a pivot arm. A wide range of dynamics can be simulated with the model. The equations of motion are embedded in a graphical…

We present an approach to the impulsive response method for solving linear constant-coefficient ordinary differential equations of any order based on the factorization of the differential operator. The approach is elementary, we only assume a basic knowledge of calculus and linear algebra. In particular, we avoid the use of distribution theory, as…

Social media platforms such as WhatsApp are increasingly used in formal education settings. However, there is little research to guide educators on how to set up effective peer tutoring groups on social media platforms, particularly between tutors and tutees who rarely meet face-to-face. In the context of a WhatsApp mathematics tutoring project,…

Rarely do university departments of mathematics redesign their basic mathematics courses. Through developing an online version of our associate degree in engineering in collaboration with Open Universities Australia, we redesigned the first in a sequence of five engineering mathematics courses. The online cohort proved different to our…

Complex numbers are essential in many fields of engineering, but students often fail to have a natural insight of them. We present a learning object for the study of complex polynomials that graphically shows that any complex polynomials has a root and, furthermore, is useful to find the approximate roots of a complex polynomial. Moreover, we…

We present an approach to the impulsive response method for solving linear constant-coefficient ordinary differential equations based on the factorization of the differential operator. The approach is elementary, we only assume a basic knowledge of calculus and linear algebra. In particular, we avoid the use of distribution theory, as well as of…

In this article, the author reports results in their efforts to model sublimation of carbon dioxide and the associated kinetics order and parameter estimation issues in their model. They have offered the reader two sets of data and several approaches to determine the rate of sublimation of a piece of solid dry ice. They presented several models…