In this article we examine 2 x 2 first-order systems of ordinary differential equations and show how to identify separatrices for phase plane portraits when the system has a saddle point critical value. We describe how to use a computer algebra system to generate trajectories from contour plots, when possible, and determine the equation of the…

This paper proposes an argument framework for the teaching of null hypothesis statistical testing and its application in support of research. Elements of the Toulmin (1958) model of argument are used to illustrate the use of p values and Type I and Type II error rates in support of claims about statistical parameters and subject matter research…

Scientists often have to observe and study surfaces that are impossible or impractical to see directly, such as the ocean floor or the atomic surfaces of objects. Early in the history of oceanography scientists dropped weighted cables to the bottom of the ocean. By moving across the ocean at regular intervals and keeping track of how deep the…