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
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.
Click Here For Pre-Calculus Graphing Projects
Calculus Graphing Projects
- 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.
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
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.
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
Presentation - I use this presentation to illustrate (in a
simplified manner) how Calculus is used in science and engineering.