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…

We present an intriguing topic in a mathematical modelling course where Lanchester models are taught to our students. Lanchester models are some of the earliest and most important models used for combat modelling. We describe modelling activities and the use of technology that can be implemented in teaching this topic in this paper.

The SIR model is a differential equations based model of the spread of an infectious disease that compartmentalises individuals in a population into one of three states: those who are susceptible to a disease (S), those who are infected and can transmit the disease to others (I), and those who have recovered from the disease and are now immune…

The process of turning a doctoral student into an independent researcher is usually guided by a professor. In this work, the supervisor-supervisee relationship is represented by a scheme inspired by Michaelis-Menten kinetics, which has been used to determine the rate of enzyme-catalysed reactions. Here, the time evolution of the number of…

A discrete model of invasion by subversive alien bodysnatchers is constructed and analysed numerically as a proposed undergraduate project. Several extensions of the model are demonstrated, including a spatial system of ten planets arranged on a one-dimensional lattice, and we discuss some of the practical considerations that arise when…

Epidemiological models have enhanced relevance because of the COVID-19 pandemic. In this note, we emphasize visual tools that can be part of a learning module geared to teaching the SIR epidemiological model, suitable for advanced undergraduates or beginning graduate students in disciplines where the level of prior mathematical knowledge of…

This article offers modelling opportunities in which the phenomena of the spread of disease, perception of changing mass, growth of technology, and dissemination of information can be described by one differential equation--the logistic differential equation. It presents two simulation activities for students to generate real data, as well as…

"Use of mathematical representations to model and interpret physical phenomena and solve problems is one of the major teaching objectives in high school math curriculum" [National Council of Teachers of Mathematics (NCTM), "Principles and Standards for School Mathematics", NCTM, Reston, VA, 2000]. Commonly used pre-calculus textbooks provide a…

This paper reports on studies of the deterministic and stochastic behaviours of a predator-prey system with prey-dependent response function. The first part of the paper deals with the deterministic analysis of uniform boundedness, permanence, stability and bifurcation. In the second part the reproductive and mortality factors of the prey and…

A British project in engineering science is described. Computer assisted instruction packages are being developed to provide students with experience with models or systems of models related to lecture material on electrical, electronic, nuclear, and mechanical engineering. (SD)

This paper describes an interactive modelling, simulation, animation, and real-time control (MoSART) environment for a class of 'cart-pendulum' electromechanical systems that may be used to enhance learning within differential equations and linear algebra classes. The environment is useful for conveying fundamental mathematical/systems concepts…

In this paper, a didactical proposal is presented to introduce the variational methods for solving boundary value problems to engineering students. Starting from a couple of simple models arising in linear elasticity and heat diffusion, the concept of weak solution for these models is motivated and the existence, uniqueness and continuous…

The role of computer science in relation to education is discussed from two points of view: (1) the use of computer models for studying the learning process, and (2) the use of the computer as a teaching device. (SD)

Achievements, limitations, and difficulties of social science simulation efforts are discussed with particular reference to three examples. The pedagogical use of complementary developmental, philosophical, mathematical, and scientific approaches is advocated to minimize potential abuses of social simulation research. (LS)