The general aim is to promote the use of individual-based models (biological agent-based models) in teaching and learning contexts in life sciences and to make their progressive incorporation into academic curricula easier, complementing other existing modelling strategies more frequently used in the classroom. Modelling activities for the study…

Mathematical methods are described for the determination of steady-state concentrations of all species in multiequilibria systems consisting of several acids and their conjugated bases in aqueous solutions. The main example consists of a mixture of a diprotic acid H[subscript 2]A, a monoprotic acid HB, and their conjugate bases. The reaction…

Course instructors need to assess the efficacy of their teaching methods, but experiments in education are seldom politically, administratively, or ethically feasible. Quasi-experimental tools, on the other hand, are often problematic, as they are typically too complicated to be of widespread use to educators and may suffer from selection bias…

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…

A typical introductory course in ordinary differential equations (ODEs) exposes students to exact solution methods. However, many differential equations must be approximated with numerical methods. Textbooks commonly include explicit methods such as Euler's and Improved Euler's. Implicit methods are typically introduced in more advanced courses…

US high school (HS) students are lagging behind their foreign peers in math performance. It is thus necessary to design teaching modules that motivate US HS students to learn more math and to improve their math skills. Our study set out to test two different software programs designed for the development of such skills. MATLAB Simulink provides a…

This paper illustrates both a problem in mathematical physics, whereby the method of separation of variables, while applicable, leads to three ordinary differential equations that remain fully coupled via two separation constants and a five-term recurrence relation for series solutions, and an exactly solvable problem in electrostatics, as a…

Linear functional relationships are intended to be symmetric and therefore cannot generally be accurately estimated using ordinary least squares regression equations. Orthogonal regression (OR) models allow for errors in both "Y" and "X" and therefore can provide symmetric estimates of these relationships. The most…

This dissertation will look at large scale collaboration through the lens of online communities to answer questions about what makes a collaboration persist. Results address how collaborations attract contributions, behaviors that could give rise to patterns seen in the data, and the properties of collaborations that drive those behaviors. It is…

In recent years, I started covering difference equations and z transform methods in my introductory differential equations course. This allowed my students to extend the "classical" methods for (ordinary differential equation) ODE's to discrete time problems arising in many applications.

This article describes a computational project designed for undergraduate students as an introduction to mathematical modeling. Students use an ordinary differential equation to describe fish weight and assume the instantaneous growth rate depends on the concentration of dissolved oxygen. Published laboratory experiments suggest that continuous…

When elementary ordinary differential equations (ODEs) of first and second order are included in the calculus curriculum, second-order linear constant coefficient ODEs are typically solved by a method more appropriate to differential equations courses. This method involves the characteristic equation and its roots, complex-valued solutions, and…

In this article we provide two detailed examples of how we incorporate biological examples into two mathematics courses: Linear Algebra and Ordinary Differential Equations. We use Leslie matrix models to demonstrate the biological properties of eigenvalues and eigenvectors. For Ordinary Differential Equations, we show how using a logistic growth…

Ordinary differential equations (ODEs) are one of the important topics in engineering mathematics that lead to the understanding of technical concepts among students. This study was conducted to explore the students' understanding of ODEs when they solve ODE questions using a traditional method as well as a computer algebraic system, particularly…

Easter Island is a fascinating example of resource depletion and population collapse, and its relatively short period of human habitation combined with its isolation lends itself well to investigation by students in a first-semester ordinary differential equations course. This article describes curricular materials for a semester-long case study…