The historic total global human population dataset is available on Wikipedia and provides an opportunity for modelling with simple models such as the exponential and logistic differential equations for population. Using the per-capita population growth rate (PPGR) predicted by these two models and estimated PPGR from the data, we are able to…

An alternative method for obtaining analytical solutions of the time-independent Schrödinger equation (TISE) is developed and applied to 1-dimensional model quantum systems of interest in atomic and molecular physics. The method is based on proposing a wave function that is a product of two functions, one of them an integrating factor. The…

The logistic differential equation is ubiquitous in calculus and differential equations textbooks. If the model is developed from first principles in these courses, it is usually done in an abstract mathematical way, rather than in one based in ecology. In this short note, we look at examples of how the model is derived in mathematical texts and…

Calculus is perhaps the most widely taught and researched upper-secondary/post-secondary mathematics subject the world over. The research literature is amassing greater clarity around students' understandings of calculus, yet calculus instruction tends to be at odds with this literature, maintaining a focus on procedural aspects of the subject.…

Spring-mass systems are presented as an application of second-order, constant coefficient differential equations in many differential equations textbooks. The phenomenon of resonance can then be analysed after nonhomogeneous differential equations are introduced. With some simplifying assumptions, the movement of the roof of a one-story building…

The objective of this research is to study if the use of the calculator decreases students' anxiety in the subject of differential and integral calculus. Specifically, the research is carried out with 30 engineering students. Auzmendi anxiety factor questions are used to measure anxiety. The study is carried out in two moments; in the first the…

The present paper explores the relationship between attitudes towards mathematics (ATM) and achievement in college calculus in active learning (AL) and lecture-based (LB) classrooms. Previous work on this relationship has mainly been limited to LB instruction, neglecting the impact of innovative approaches such as AL. Less attention has been paid…

We view the (real) Laplace transform through the lens of linear algebra as a continuous analogue of the power series by a negative exponential transformation that switches the basis of power functions to the basis of exponential functions. This approach immediately points to how the complex Laplace transform is a generalisation of the Fourier…

Background: The demand for professionals with expertise in Science, Technology, Engineering, and Mathematics (STEM) continues to grow. To meet this demand, universities are actively seeking strategies to engage more students in STEM disciplines and improve their learning outcomes. One promising approach is gamification, specifically using…

The purpose of this study is to conduct a bibliometric analysis of the research published in the field of mathematics misconception from 1947 to 2023, to determine the general knowledge structure and participation in research publication. An analytical approach was used based on Scopus database data. This study used mixed methods; quantitative…

Research into didactics of calculus has maintained a long-standing interest in students' grasp of the relations between definite integrals and areas. This study comes to contribute to this line of research by unpacking how students use the concept of area to find definite integrals. Specifically, we focus on mathematical situations where the…

Recent research on integration has shown the importance of quantities-based meanings for integrals. However, this research body is still in need of detailed empirical accounts of "how" students develop such understandings across an entire unit on integration. This paper contributes by providing one such account, based on a…

In introductory math courses such as precalculus, students often have difficulty with assignments that require explanations or synthesizing knowledge. When students receive low scores on such assignments, instructors often wish to help students understand the material they struggled with. A common strategy is to allow the students to revise and…

Mathematics provides us with tools to capture and explain phenomena in everyday biology, even at the nanoscale. The most regularly applied technique to biology is differential equations. In this article, we seek to present how differential equation models of biological phenomena, particularly the flow through ion channels, can be used to motivate…

Using the sawtooth map as the basis of a coupled map lattice enables simple analytic results to be obtained for the global Lyapunov spectra of a number of standard lattice networks. The results presented can be used to enrich a course on chaos or dynamical systems by providing tractable examples of higher dimensional maps and links to a number of…