On 24 June 1994 at Fairchild Air Force Base, during practice for an air show, a low-flying B-52H aircraft banked its wings vertically and crashed. Emphasizing the activity of modeling drag and gravity, these notes examine the possibility of recovery with several models. First, with algebra, historical data lead to a model where in a free fall near…

Working with approximations is a common practice in physics. This paper presents an exploratory study of student understanding of some of the elementary aspects of approximations encountered in college physics. For this purpose, a questionnaire (a set of 14 multiple-choice questions) was developed to probe how students dealt with these aspects in…

We present a complete, soup to nuts, modeling activity of a falling column of water. Many colleagues have used this material in teaching applications of first order separable differential equations. We describe how the material can be presented with students collecting their own data from online videos. One can then either offer the differential…

The article addresses the problématique of where mathematization is taught in the educational system, and who teaches it. Mathematization is usually not a part of mathematics programs at the upper secondary level, but we argue that physics teaching has something to offer in this respect, if it focuses on solving so-called unformalized problems,…

In this article, the author reports results in their efforts to model sublimation of carbon dioxide and the associated kinetics order and parameter estimation issues in their model. They have offered the reader two sets of data and several approaches to determine the rate of sublimation of a piece of solid dry ice. They presented several models…

An aspect of Galileo's classical trajectory that persists in a simple resistance model is noted. The resistive model provides a case study for the classroom analysis of limiting behaviour of an implicitly defined function. (Contains 1 note.)

"Use of mathematical representations to model and interpret physical phenomena and solve problems is one of the major teaching objectives in high school math curriculum" [National Council of Teachers of Mathematics (NCTM), "Principles and Standards for School Mathematics", NCTM, Reston, VA, 2000]. Commonly used pre-calculus textbooks provide a…

This article first notes the misinterpretation of a common thought experiment, and the misleading comment that "systems tend to flow from less probable to more probable macrostates". It analyses the experiment, generalizes it and introduces a new tool of investigation, the simplectic structure. A time-symmetric model is built upon this structure,…

We introduce a model of radiative transfer in circumstellar dust shells. By assuming that the shell is both isothermal and its thickness is small compared to its radius, the model is simple enough for students to grasp and yet still provides a quantitative description of the relevant physical features. The isothermal model can be used in a…

This paper deals with a brief introduction to major remarkable discoveries of the "soliton" and the "inverse scattering transform" in the 1960s. The discovery of the soliton (or the solitary waves) began with the famous physical experiments of the Scottish Engineer and Naval Architect John Scott Russell in the Glasgow-Edinburgh…

A course in differential equations for mathematics and physics students is designed to encourage students to models of situations in the sciences. (SD)

Some ways to link calculus instruction with the mathematical models used in physics courses are presented. The activity of modelling is presented as a major tool in synchronizing physics and mathematics instruction in undergraduate engineering programs. (MP)

A Mathematica[TM] package is described that uses simulations and animations to illustrate key concepts in harmonic oscillation and electric circuits for students not majoring in physics or mathematics. Students are not required to know the Mathematica[TM] environment: a user-friendly interface with buttons functionalities and on-line help allows…