Fall04
The Battle of Trafalgar: handout, excel worksheet , historical situation (diagram depicting the actual battle from Military History June 1986 p25)
Some basic population models: handout, US Population (excel)
Take a look at some real predator-prey data: Moose & Wolves
Modified Logistic model and harvesting, phase lines, and bifurcation diagrams: Maple Examples
Maple References:
An exciting action scene in a movie is going to be filmed, and you are the
stunt coordinator! A stunt person on a motorcycle will jump
over an elephant and land in a pile of cardboard boxes to cushion their fall.
You need to protect the stunt person, and also use
relatively few cardboard boxes (lower cost, not seen by camera, etc.).
Your job is to:
determine what size boxes to use
determine how many boxes to use
determine how the boxes will be stacked
determine if any modifications to the boxes would help
generalize to different combined weights (stunt person & motorcycle) and
different jump heights
Note that, in "Tomorrow Never Dies", the James Bond character on a motorcycle
jumps over a helicopter.
2000-Problem A:
Dedicated to the memory of Dr. Robert Machol, former chief scientist of the
Federal Aviation Agency
To improve safety and reduce air traffic controller workload, the Federal
Aviation Agency (FAA) is considering adding software to the
air traffic control system that would automatically detect potential aircraft
flight path conflicts and alert the controller. To that end, an
analyst at the FAA has posed the following problems.
Requirement A: Given two airplanes flying in space, when should the air traffic
controller consider the objects to be too close and to
require intervention?
Requirement B: An airspace sector is the section of three-dimensional airspace
that one air traffic controller controls. Given any
airspace sector, how do we measure how complex it is from an air traffic
workload perspective? To what extent is complexity
determined by the number of aircraft simultaneously passing through that sector
(1) at any one instant? (2) during any given interval
of time?(3) during a particular time of day? How does the number of potential
conflicts arising during those periods affect complexity?
Does the presence of additional software tools to automatically predict
conflicts and alert the controller reduce or add to this
complexity?
In addition to the guidelines for your report, write a summary (no more than two
pages) that the FAA analyst can present to Jane
Garvey, the FAA Administrator, to defend your conclusions.
Cyclists have different types of wheels they can use on their bicycles. The two basic types of wheels are those constructed using wire spokes and those constructed of a solid disk (see Figure 1) The spoked wheels are lighter, but the solid wheels are more aerodynamic. A solid wheel is never used on the front for a road race but can be used on the rear of the bike.
Professional cyclists look at a racecourse and make an educated guess as to what kind of wheels should be used. The decision is based on the number and steepness of the hills, the weather, wind speed, the competition, and other considerations. The director sportif of your favorite team would like to have a better system in place and has asked your team for information to help determine what kind of wheel should be used for a given course.
Figure 1: A solid wheel is shown on the left and a spoked wheel is shown on the right.
The director sportif needs specific information to help make a decision and has asked your team to accomplish the tasks listed below. For each of the tasks assume that the same spoked wheel will always be used on the front but there is a choice of wheels for the rear.