Mathematical Modeling

Spring Semester 1998
MATH 471.01 (3 credits), Tu_Th, 2:30PM-3:45PM, Wickersham 109

Instructor:

Dr. Buchanan
Office: Wickersham 113, Phone: 872-3659, FAX: 871-2320
Office Hours: 1PM-2PM (M_W_F), 1:30PM-2:30PM (Tu_Th), or by appointment
Email: Robert.Buchanan@millersville.edu

Readings:

There is no textbook for this course. Periodically, reading assignments will be made and material placed on reserve in Ganser Library. Many assignments will require students to search the published literature, electronic databases, and internet resources for information relevant to mathematical modeling.

Coverage:

Topics in this course will include (but are not limited to):

Allometry, shape, and form
- Organ sizes and body weights of animals
- Geometry of blood vessels
- Design of blades in cutting tools
Pharmacokinetic modeling
- One compartment linear models
- Two compartment linear models
- Non--linear Michaelis-Menten processes
- Physiologically--based modeling
Chemical reaction dynamics
Population biology and mathematical ecology
- Cleaning pollution from a lake
- Mutual competition between two species
- Predator--prey interactions
- Pioneer--climax interactions
Traffic dynamics
- Paths of turning and towed vehicles
- Braking to avoid collisions
- Driving in tunnels
- Shocks and rarefactions in traffic flow
Optimal control and utility
- Energy allocation in plants
- Energy consumption during animal migration
- Employment levels in a company
- Harvesting and stocking strategies
- Temperature control in reptiles
Elections and voting
Games and chance and skill
Birth and death
- Branching processes
- Inventory control
- Traffic junctions and turn lanes
- Justification for pedestrian crossings

Prerequisites:

A grade of C- or better in MATH 365 (Ordinary Differential Equation) is the prerequisite for this course.

Attendance:

Students are expected to attend all class meetings. If you must be absent from class you are expected to complete class requirements (presentations and/or homework assignments) prior to the absence. In the event you are absent from or late to class, you are still responsible for all assignments made, material covered, and handouts given.

Homework:

The major part of the learning that takes place in this class occurs while working on homework problems and projects. Students are expected to do their homework and participate in class. Frequently throughout the semester, some homework problems will be assigned to be handed in for grading. Students should submit all homework by the date due. Late homework without valid excuse will not be accepted. Discussion between students on homework assignments is encouraged, but homework submitted for grading should be written up separately.

If you feel that an error was made in the grading of homework, you should explain the error on a separate sheet of paper and return both it and the original homework to me within two class periods after the assignment is returned to you.

Grades:

Students' performance will be measured along three axes: homework, in-class presentations, and a final project. The final project represents a solo mathematical modeling assignment resulting in a written report and public presentation during Math Awareness Week. Students will also have several opportunities to practice their presentation skills on smaller projects in the friendly environment of their peers in the course. Course grade will be calculated as follows.

Homework	1/3
Project	1/3
Presentations	1/3

The course letter grades will be calculated as follows.

90-100	A
80-89	B
70-79	C
60-69	D
0-59	F

Final Word:

Math is not a spectator sport. What you learn from this course and your final grade depend mainly on the amount of work you put forth. Here is a list of the qualities a student in this course should possess.

Creativity, originality, inventiveness, curiosity, willingness to experiment, and use of imagination.
Initiative, independence, effort, perseverance, and self discipline.
Skill development, effective retention and use of mathematics learned in previous courses, presentation skills.
Quality of finished work.
Willingness to challenge oneself and others.
Ability to take criticism and input.
Outside work - expect to spend a minimum of 12 hours per week outside of class on activities related to this course.
Participation in class discussions and critiques.
Commitment to the course.
Respect for your classmates and professor.

Page maintained by: Robert.Buchanan
Robert.Buchanan@millersville.edu

Last updated: