Modeling Across the Mathematics Curriculum

After having taught Calc I and Calc III recently, now I find myself teaching Calc II, integral calculus, in the fall.  So again I am looking for projects. These ideas are on Dave Martin's Real teaching means real learning blog. A project that combines creating images on GeoGebra with functions and then calculating the areas created.  I think students would like the GeoGebra part, but there is little motivation for the need of calculating the areas.  Another page talking about the same project with some nice pics. Can Kobe Bryant jump over a moving car ?  A video shows him doing it.  Can we use calculus, including integration, to investigate this? Explain mathematically explaining everything you know about an irregularly shaped symmetrical object such as a bottle or a vase. Include detailed drawings and calculations. Create a video of an object in free-fall .  You must throw your object, and calculate the velocity of the object when it left your hand.  Appropriate measure

The following are some modeling projects that come from textbooks.  They may include topics that are typically covered in a particular multivariable calculus classroom, but for me would be additional topics. The Hall Effect :  This is the end-of-chapter project in Chapter 10 of Sullivan/Miranda's Calculus Early Transcendentals . "The Hall effect is the production of a voltage difference (the Hall voltage) across an electrical conductor, transverse to an electric current in the conductor and to an applied magnetic field perpendicular to the current." (from Wikipedia)  The project leads students through calculations that involve force, magnetic field, velocity, and electric field as vectors. Road Safety :  This is the end-of-chapter project in Chapter 11 of Sullivan/Miranda's  Calculus Early Transcendentals . The project investigates the forces on a vehicle under various road curve secenarios.  The model is described with vector functions for position, velocity, an

I keep running across references to 3D printing as projects in multivariable calculus.  On the one hand, this is a modeling project in that the code has to be written in order to produce a physical printout.  OTOH, it may be that it has all be done before. Regardless, here are the references I have found in my travels.j John Zweck , UT Dallas, has code and images of 3D printouts of sample curves. The Harvey Mudd multivariable calculus project page has references to programs for 3D printing. Triply Periodic Minimal Surfaces has a seemingly unending list of surfaces to be studied and printed.

Here are some projects I found online.  Again, my emphasis is on projects that have a modeling aspect to them. Thermoclines:   An article by Bruder and Kohler about a calc lab to investigate thermoclines.  Data is collected and students use a fitting program to fit a multivariable function to the data.  The lab only requires items that can be obtained from our supply room or a hardware store.  While the article is about the pedagogy, there is enough information for students to execute the lab on their own. Amusement park rides :  Although the mathematical details of this project are a little fuzzy, the description in the article below provides an opportunity for a project using physics and parametric curves.  The students in the article built rides from a set with motors.  There would have to be a financial outlay to do this.  "An AP Calculus Classroom Amusement Park" by Sarah Ferguson, The Mathematics Teacher , Vol. 109, No. 7 (March 2016), pp. 514-519. Helical stairw

As I find various websites with project suggestions, I see more and more overlap, but the specific interests of the faculty authors provides diverse options. These suggestions are from a multivariable projects page from Bryn Mawr.   There were many projects suggested there, but these are the ones that were unique from the ones in part 1 (the beginning) and part 2. Cobbs-Douglas production formula :  "In economics, the Cobb–Douglas production function is a particular functional form of the production function, widely used to represent the technological relationship between the amounts of two or more inputs, particularly physical capital and labor, and the amount of output that can be produced by those inputs." from Wikipedia Ruled surfaces :  "A ruled surface is a surface that can be swept out by moving a line in space. It therefore has a parameterization of the form. (1) where is called the ruled surface directrix (also called the base curve) and is the director c

The blog Continuous everywhere and differentiable nowhere , (CEDN) by a high school math teacher in Brooklyn, New York, has a list of Calc III projects.  Here are the ones I felt were modeling projects.  See the blog site for more details, including the overall assignment sheet. Volume of an n -dimensional sphere :  Define a sphere in 2D, 3D, 4D, etc.  Find the formula for the volume of an n -dimensional sphere.  Strangely, as the dimension increases, the volume of given radii decreases.  This is related to the problem with data modeling in multidimensions when the measure is a distance.  The higher the dimension, a larger percentage of points are more than a fixed distance from a given point.  Study this weirdness.  Resource: Rogawski, Section 15.3. Fluid dynamics and hurricane modeling :  This blogger recommends studying material from Anton, pp. 1883-7, on fluid dynamics and how that study can be used to model hurricanes. Lissajous Curves :  The prospect is to study Lissajous cu