Calculus Labs

For those revisiting this page, you might notice there is some shuffling going on. My school has recently had a technology refresh, so I'm trying to adapt and reorganize everything this semester. The biggest difference is that we no longer have TI-InterActive!, so I'm rewriting the existing activities to be less "software specific". I'm hoping to eventually include some sample data for each activity that requires an experiment... for those times when the equipment chooses not to cooperate!

If the mess is too much for you, click here to go back to the AP Calculus page.

Below are the labs and activities that we will be tackling in AP Calculus. Most files require either MS Word (*.doc) or Maple (*.mws). Some have been given as a PDF file so you can preview the documents from home using the Adobe Acrobat Reader.

Your calculator can be a great help in many of these labs, especially if you have updated operating systems, certain programs, and tools. Here are a few links you might find helpful:

	TI Connect - This is a little program that essentially allows your calculator to communicate and swap files with your computer (and yes... that includes games, too).
	TI-89 OS - You can download the latest operating system for the TI-89 Titanium (currently v3.10). Installation requires TI Connect. If you are using the older TI-89 calculator, it's latest OS (v2.09) can be downloaded here.
	DataMate - This is a handy little application for the TI-89 that makes the use of the CBL probes easier to set up.

Click the link to download the desired file to a disk or your student directory at school. You can then open the downloaded file and record your results directly into the document. Please save your changes under a different (but recognizable) filename... something like Boyles_Law_Group1.doc. Submit your final report as instructed in class.

One suggestion that might help - print a blank copy before class to review and make notes on as you go through the activity. You can then later (often as a group) type up and submit a final document.

Boyle's Law Lab Infinite Limits Sample Data	This lab verbally, graphically, and analytically investigates infinite limits as applied to the relationship between pressure and volume known as Boyle's Law.
Ball Drop Rectilinear Motion Balldrop.tii or Balldrop.pdf Balldrop Data.tii	This lab verbally, numerically, and analytically investigates the relationships among position, velocity, and acceleration. The Balldrop Data.tii file contains data from an actual experiment (to be used if performing the experiment is not possible). To be updated soon!
Weather Sinusoidal Curves and the Chain Rule Weather.tii or Weather.pdf	This lab verbally, numerically, graphically, and analytically investigates sinusoidal patterns demonstrated in weather data. Also to be updated soon.
Bouncing Wagon Activity Implicit Differentiation	This activity graphically and analytically investigates the properties of the implicitly-defined "bouncing wagon" curve. Its grading rubric is also included. Although I've seen the equation in other places, this particular activity is adapted from Exercise 22 on page 244 in James Stewart’s Calculus: Concepts and Contexts, 2nd ed.
Graph Behavior Project Graph Behavior	This project allows each student to choose from a variety of functions and explore its characteristics in detail. The current version allows for students to select their own functions not already listed. A grading rubric is also included.
Euler's Method Activity Euler's Method and Slope Fields	This activity numerically, graphically, and analytically investigates the solutions of a differential equation using slope fields and Euler's method. This particular activity is adapted from Exercise 25 on page 521 in James Stewart’s Calculus: Concepts and Contexts, 2nd ed.
Cootie Lab Logistic Modeling Sample Data	This lab verbally, graphically, and analytically investigates logistic behavior as applied to the spread of a disease through a population over time.

With the Maple activities, all questions should be answered in the space provided (add more lines with Ctrl-J if necessary). Please remove all output from the worksheet before submitting. The first activity is actually a brief introduction to Maple.

Maple Introduction Some of the Basics Maple Introduction	This activity introduces the first-timer to the Maple environment.
Maple Activity #1 Functions and Graphing Maple 1	This activity introduces methods of defining, graphing, and analyzing functions in Maple.
Maple Activity #2 Derivatives and Graphs Maple 2	This activity uses the CAS in Maple to perform several calculations related to differential calculus.
Maple Activity #3 Implicit Differentiation and Graphs Maple 3	This activity uses the CAS in Maple to perform several calculations related to implicit differentiation and the graphs of relations.
Maple Activity #4 Integration Maple 4	This activity uses the CAS in Maple to perform several calculations related to integral calculus.
Maple Activity #5 Differential Equations Maple 5	This activity uses the CAS in Maple to perform several calculations related to differential equations.