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# Projects and Experiments Using Pre-Calculus and Calculus

Pre-Calculus Graphing Projects

These projects use Graphmatica, a shareware program. We have a site license for this program (it was only about \$300 at the time and it was a one-time fee) and students also can download their own trial copy at http://graphmatica.com/. I would suggest you try out the software first. It is extremely easy to use and allows students to print out their graphs.  A basic information sheet on using graphmatica is given here. Note that I have no affiliation or partnership with the owners of Graphmatica.

Calculus Graphing Projects

Incline Experiment - To do this, for each student I had to manufacture 1"x2" wood sticks with a groove ripped on one side for a marble to roll down. I marked off the sticks at 1ft, 2ft, and 3ft. I had a small group so this was manageable. Students did this project at home. This is a variation of a free fall lab but takes less room and allows more precise time measurements since the fall is slowed.  Note that solid wood sticks tend to warp - plywood or plastic would hold up better.

Corner-Pipe Problem - This lab reproduces a classic calculus text problem.  What I like about this lab is that it seems to provide valuable insight into the analytical solution. I glued pieces of wood onto thin plywood to create the corners.  Then, I provided students with a "pipe" made of two plastic drinking straws, one inserted into the other so the length could be adjusted to a point where the "pipe" clears the corner. You may need to provide some hints on the analytic solution.  Also, once you obtain the minimization equation, you may want to have students solve using  a numerical or graphical solution since the algebraic solution is quite difficult (but do-able).

Newton's Law of Cooling - This lab is fairly self-explanatory. The first time I provided thermometers to students but several got broken.  So thereafter, I did the temperature measurements in class (during lecture) and had students finish the project.

Flow Rate Project - This project required the use of inexpensive funnels plugged or taped off at the bottom (I used duct tape) and marked off as shown in the diagram.  Each student received a funnel and did the project on their own. Another nice representation of a classic text problem.

Oil Tank Project - This project was inspired by an episode of my own. My oil tank measurement float disconnected and fell to the bottom of my tank.  So I had to design my own stick using the same math as outlined in the project.  No special equipment needed. Note that I checked student results of Part I to make sure they were on the right track before having them do Part II.

Differential Equations

Car Suspension System Project  - I developed this project on my first sabbatical using my actual vehicle from the time. It is a nice example of a second-order system.  It requires the use of Graphmatica.

PowerPoint Presentation

Pre-Calculus PowerPoint Presentation - I use this presentation to illustrate (in a simplified manner) how Calculus is used in science and engineering.