Differential equations are widely used tools for modelling the world around us, making a course in differential equations a natural place for students to connect concrete mathematical applications to abstract concepts. Since students grasp the concepts better by applying them, introducing differential equations through modelling becomes essential.…

This paper describes a new lab experiment where students explore the magnetic force on a permanent magnet placed inside a short solenoid. This lab is the fourth experiment performed in the second semester of the calculus-based introductory physics course at Washington University in St. Louis. The experiment is performed using a speaker (which…

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…

The Department of Physics at EKU [Eastern Kentucky University] with support from the National Science Foundations Course Curriculum and Laboratory Improvement Program has successfully converted our entire introductory physics sequence, both algebra-based and calculus-based courses, to an activity-based format where laboratory activities,…

It is shown how the same physically appealing method can be applied to find analytic solutions for two difficult and apparently unrelated problems in optics and electrostatics. They are: (i) the diffraction of a plane wave at a perfectly conducting thin half-plane and (ii) the electrostatic field associated with a parallel array of stripes held at…

This paper describes two uses of the software package TEMATH (Tools for Exploring Mathematics) with calculus students: (1) as a demonstration tool in the classroom to visually explore with students the many mathematical models introduced in a first year calculus course; and (2) as a part of a lab where students use a set of laboratory explorations…

A pair of experiments, appropriate for the lower division fourth semester calculus or differential equations course, are presented. The second order differential equation representing the equation of motion of a simple pendulum is derived. The period of oscillation for a particular pendulum can be predicted from the solution to this equation. As a…

To help students understand the real-world applications of calculus, our calculus students all take part in a lab. This is not another "computer lab" but a lab where the students perform experiments and then collect and analyze the data. The students are able to verify for themselves many of physical claims that are left as theory in…

A laboratory experiment, based on a simple electric circuit that can be used to demonstrate the existence of real-world "related rates" problems, is outlined and an equation for voltage across the capacitor terminals during discharge is derived. The necessary materials, setup methods, and experimental problems are described. A student laboratory…

This paper presents an application of integration to the field of hydraulics. An integral relation for the time required to drop the fluid contained in a cylindrical tank from one level to another using a hole in the tank wall is derived. Procedures for constructing the experimental equipment and procedures for determining the coefficient of…