**Rainbow Lab**- How are rainbows formed? Why do they only occur when the sun is
behind the observer? If the sun is low on the horizon, at what angle
in the sky should we expect to see a rainbow? This lab helps to
answer these and other questions by examining a mathematical model of
light passing through a water droplet.
**Numerical Integration Lab**-
The fundamental theorem of calculus tells us that if we know the rate
of change of some quantity, then adding up (or integrating) the rate
of change over some interval will give the total change in that
quantity over the same interval. But often scientists do not know a
formula for a function, but can only experimentally know the value of
the function at discrete times. Is it possible to "integrate" this
discrete data? If so, how?
**Beams, Bending, and Boundary Conditions Lab**-
Beams hold up the roof over your head and give support to the walls
surrounding you. Beams are literally all around us. Engineers use
beams to support and strengthen structures ranging from silos
to bridges to towering skyscrapers. In this lab, we will explore the
mathematics associated with the static deformation of beams. We will
begin with the geometric concepts of centroids and moments of inertia,
and then learn how different methods of supporting a beam contribute
to the beam's ability to support loads.
**Modeling Population Growth**-
Populations grow according to the number of individuals that are
capable of reproduction. At the same time, their growth is limited
according to scarcity of land or food, or the presence of external
forces such as predators. In this module, we examine simple
differential equations that model populations. We also introduce and
explore powerful techniques for the geometric analysis of
differential equations: phase space, equilibria, and stability.

Comments to: webmaster@www.geom.uiuc.edu

Created: Jan 26 1995 ---
Last modified: Thu Jul 18 18:24:51 1996