This paper introduces a course design for a post-Calculus undergraduate course on mathematical modeling for the life sciences. The course includes differential equations, discrete, and cellular automata approaches (among others) to modeling questions in the life sciences, as well as a variety of biological topics. The course focuses on model…

This article describes the use of a spreadsheet to reinforce basic calculus that is expected of all university-level chemistry majors. The example provided shows a calculation using Excel to estimate, using a Riemann summation, the radiant exitance of a hot object using Planck's Law of Blackbody Radiation. The approach reinforces the elementary…

The voltage waveform that minimizes the energy loss in the resistance when charging the capacitor in a resistor-capacitor circuit is investigated using the calculus of variation. A linear voltage ramp gives the best efficiency, which means a constant current source should be used for charging. Comparison between constant current source and…

The real power of calculus is revealed when it is applied to actual physical problems. In this paper, we present a calculus inspired physics experiment suitable for high school and undergraduate programs. A model for the theory of the terminal velocity of a falling body subject to a resistive force is developed and its validity tested in an…

In the past decade, traditional classroom teaching models have been transformed in order to better promote active learning and learner engagement. "Implementation and Critical Assessment of the Flipped Classroom Experience" seeks to capture the momentum of non-traditional teaching methods and provide a necessary resource for individuals…

Although nowadays there are mythbusting teams ready to empirically confirm or deny advertising claims that may seem too good to be true, it is often economically prohibitive to perform the kinds of experiments that are called for. It is therefore sometimes more sensible and efficacious to perform a thought experiment instead, especially if the…

Most thermodynamic properties are either extensive (e.g., volume, energy, entropy, amount, etc.) or intensive (e.g., temperature, pressure, chemical potential, mole fraction, etc.). By the same token most of the mathematical relationships in thermodynamics can be written in extensive or intensive form. The basic laws of thermodynamics are usually…

Modelling elastic filament dynamics is a topic of high interest due to the wide range of applications. However, it has reached a high level of complexity in the literature, making it unaccessible to a beginner. In this paper we explain the main steps involved in the computational modelling of the dynamics of an elastic filament. We first derive…

An anharmonic solution to the differential equation describing the oscillations of a simple pendulum at large angles is discussed. The solution is expressed in terms of functions not involving the Jacobi elliptic functions. In the derivation, a sinusoidal expression, including a linear and a Fourier sine series in the argument, has been applied.…

Thermodynamic quantities such as the average energy, heat capacity, and entropy are calculated using a Monte Carlo method based on the Metropolis algorithm. This method is illustrated with reference to the harmonic oscillator but is particularly useful when the partition function cannot be evaluated; an example using a one-dimensional spin system…

A common example of real-world motion that can be modeled by a differential equation, and one easily understood by the student, is the simple pendulum. Simplifying assumptions are necessary for closed-form solutions to exist, and frequently there is little discussion of the impact if those assumptions are not met. This article presents a…

A mathematics module in the undergraduate programme for first year engineers aims to enable those with low mathematical qualifications to understand and use efficiently calculus and related topics. The teaching approach is designed to develop student's fluency, understanding and responsibility through creating an inquiry community, encouraging…

This discussion uses a more difficult reaction as the prototype to derive the standard equation for chemical equilibrium. It can be used by students who can understand and use partial derivatives. (CW)

Suggests an approach to understanding the integrals associated with teaching electricity and magnetism at the college level. Categorizes integrals that are commonly used, explains the significance of paired usage and presents a method for introducing concepts. Provides a review of symbols and for integrals in college textbooks. (CW)