Matthias Kawski Department of Mathematics Arizona State University |
These projects have been developed and tested in third semester calculus classes at ASU (the first two projects have been class-tested sveral times, while the third one is new in fall 1997). (Visit the homepage for the fall 1997 class.) The partial support by the Foundation Coalition through the Center for Innovation in Engineering Education is gratefully acknowledged.
All three projects are designed as multi-week team projects. They assume that the students already have some experience working in teams, and that they have access to a computer algebra system (CAS), such as MAPLE.
| The main purpose of this project is to practice working with parameterized curves at more depth than usual text-book exercises. As a side benefit, students are introduced to more extensive work with a computer algebra system (CAS). Motivation are programming of a pen-plotter or of a welding-robot. Ultimately, the benefits are reaped in vector calculus when students are much more at ease with (setting up) line-integrals. |
Summaries of project reports This page has been edited in 2009, some broken links have been removed.
Click on the picture for an animation |
The main purpose of this project is to practice working with
iterated integrals and connect these to
credible applications.
The main task is to analyze how fast various rolling objects roll down an inclied plane. This involves integrating the equations of motion, setting up and evaluating several integrals (to find the moments of inertia), and interpreting the findings. The most critical component that we added to this classical exercise is to move from a physics point of view to an engineering point of view: Use the findings to construct a rolling object that will win a competition at the end of the project. |
Summaries of project reports: Broken links have been removed in 2009.
Pictures: Winners, Runners-up, Winning design, LP-wheels, Gumbo-wheels. What is in the cookie-can?
The main purpose in this very ambitious project is to learn
using Green's theorem at the interface of vector
calculus, differential equations and control.
Unlike many other projects that tie the integral theorems
of vector calculus to either one of the traditional, but
narrow applications of electro magnetics or fluid dynamics,
this project takes a much broader view.
This project derives its charm from its use of mathematical tools to understand rather counterintuitive motions of very tangible bodies (falling cats, -- picture from www.ds.mei.titech.ac.jp/cat.gif -- and gymnasts), and that it is intimately related to current research efforts worldwide (compare this 1997 publication by the National Research Council, which may be read on-line). While technically actually rather straightforward, this project nonetheless requires a CAS in order to keep track of a multitude of terms. | |
The object under investigation is a planar assembly of three linked rigid bodies, governed by conservation of (zero) angular momentum, and subject only to the torques exerted by actuators at the internal joints. The task is to explicitly derive the equations of motion (simple vector analysis and line integrals), reformulate the differential equation as a control problem governed by a nonintegrable differential form (vector field). |
Summaries of project reports: Broken links have been removed in 2009.