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Calc III Labs

These labs were created in the Spring of 1995 by high school students participating in the University of Minnesota Talented Youth Mathematics Program (UMTYMP). The course used hypertext labs and technology-based explorations on a weekly basis, in order to better communicate the geometry of multivariate mathematics. The course was designed and taught by Geometry Center postdocs Davide P. Cervone and Frederick J. Wicklin.

As a final project for the class, students worked in groups to explore theoretical topics in mathematicas or the application of mathematics to modeling real-world phenomenon. Several groups of students created labs as part of their project; we have linked in a few of them here. When you view these documents, please bear in mind:

Student-Created Labs

Tangent Planes to Surfaces
Charles McGarraugh, Samir Murty, and Andrew Youn
A hypertext lab to explore the tangent planes and gradient vectors of 2-dimensional and 3-dimensional curves. It examines explicit, parametric, and implicit surfaces. The lab takes advantage of the graphics capabilities of Maple, and even extends them.

A Mathematical Model of Heartbeat
Martin P. Almlof, Tierre E. Christen, Sarah M. Fellows, and Apurv Kamath
A lab intended to expose students to using a planar differential equation to model the human heartbeat.

Predetor-Prey Models with Mutualism and Child-care
Etienne Benson, Elizabeth Boschee, Steve Korupp, Matt B. Lepinski
A hypertext document on the differential equations that govern population growth under mutualism and predator-prey systems with child-care.

Lagrange Multipliers
Carolyn Jones, Jenwa Hsung, and Brian Larson
A lab that explores the geometry and algebraic techniques involved in the method of Lagrange multipliers for finding extrema of a multivariable function on a bounded region. The lab includes several applications, and gives explicit instructions for using Maple to compute the extrema.

Evolutes and Involutes of Plane Curves
Erik Streed, Tim McMurry, and Chris Wyman
A lab that leads students through the background and definitions needed to understand evolutes and involutes of curves, and provides Maple code for generating these curves. The lab includes many example, and ends with some interesting relationships between the involutes and evolutes of cycloids.

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Author: Frederick J. Wicklin, Davide P. Cervone Comments to: webmaster@geom.umn.edu
Created: Jun 18 1996 --- Last modified: Jun 18 1996