One of the unique advantages of electrochemistry is that the relationship between thermodynamics and kinetics is quantitative, which is the basis of voltammetry. Mathematical models of electrochemical systems take advantage of this relationship to predict the effect of changing a system property (e.g., concentration, scan rate, or rate constant)…

Science learning for undergraduate students requires grasping a great number of theoretical concepts in a rather short time. In our experience, this is especially difficult when students are required to simultaneously use abstract concepts, mathematical reasoning, and graphical analysis, such as occurs when learning about RC circuits. We present a…

To span the great distance from the solar system to the farthest clusters of galaxies in the universe, astronomers break down the distance indicators into steps. The nearest ones are measured geometrically, with what is known as parallax. Among the objects whose distances are thus directly measured are a rare type of star known as a Cepheid…

The mathematical models that describe enzyme kinetics are invaluable predictive tools in numerous scientific fields. However, the daunting mathematical language used to describe kinetic behavior can be confusing for life science students; they often struggle to conceptualize and relate the mathematical representations to the molecular phenomena…

A general tank-draining problem was used as an experimental project in two undergraduate-level chemical engineering courses. The project aimed to illustrate the critical nature of experimentation in addition to use of mass and energy conservation principles in developing mathematical models that correctly describes a system. The students designed…

In undergraduate physical chemistry, Schrödinger's equation is solved for a variety of cases. In doing so, the energies and wave functions of the system can be interpreted to provide connections with the physical system being studied. Solving this equation by hand for a one-dimensional system is a manageable task, but it becomes time-consuming…

Our paper describes a solution we found to a still existing need to develop mathematical modeling courses for undergraduate biology majors. Some challenges of such courses are: (i) relatively limited exposure of biology students to higher-level mathematical and computational concepts; (ii) availability of texts that can give a flavor of how…

The science of biology has been transforming dramatically and so the need for a stronger mathematical background for biology students has increased. Biological students reaching the senior or post-graduate level often come to realize that their mathematical background is insufficient. Similarly, students in a mathematics programme, interested in…

A solid understanding of the structure and function of cells can help establish the foundation for learning advanced concepts in the biological sciences. The concept of the cell is introduced in middle school life science courses and is continued at the undergraduate level in college (NRC 2012; Reece et al. 2014). Cells are introduced to students…

The lithium ion battery will be a reliable electrical resource for many years to come. A simple model of the lithium ions motion due to changes in concentration and voltage is presented. The battery chosen has LiCoO[subscript 2] as the cathode, LiPF[subscript 6] as the electrolyte, and LiC[subscript 6] as the anode. The concentration gradient and…

The initial interaction among student, instructor, and content on the first day of class is critical in setting the stage for the remainder of the semester. While many students would like to ease into the semester, experienced faculty realize that the first day of class provides a one-time opportunity to shape the students' first impression…

Helping students develop an understanding of how to interpret experimental data trends is an important part of the introductory physics laboratory. Unfortunately, many of my colleagues have lamented that too many of their students do this poorly. This is a common refrain, and past research has already revealed student difficulties with…

Mathematical models and mathematical modeling play different roles in the different areas and problems in which they are used. The function and status of mathematical modeling and models in the different areas depend on the scientific practice as well as the underlying philosophical and theoretical position held by the modeler(s) and the…

Systems Biology, one of the current approaches to the understanding of living things, aims to understand the behaviour of living systems through the creation of mathematical models that integrate the available knowledge of the system's component parts and the relations among them. Accordingly, model building should play a central part in any…

Normally, a mechanics laboratory at the undergraduate level includes an experiment to verify compliance with Hooke's law in materials, such as a steel spring and an elastic rubber band. Stress-strain curves are found for these elements. Compression in elastic bands is practically impossible to achieve due to flaccidity. A typical experiment for…