Mathematical
Modeling
Math 485/585 - Spring 2002
- Instructor:
Dr. Joceline Lega
- Office: Mathematics 511
- Phone: 621-4350
- e-mail:
lega@math.arizona.edu
- Location:
- M LNG 411
- Time:
- Tuesdays and Thursdays, 11:00 am - 12:15
pm
- Office Hours:
-
Tuesdays 4:30-5:30 pm
-
Thursdays 2-3:45 pm
-
or by appointment.
- Text:
Mathematical Models: Mechanical Vibrations, Population Dynamics, and
Traffic Flow, by Richard Haberman, published by SIAM.
- Project:
Each student will work on a semester-long modeling project, worth 300 points.
The written part of the project will be worth 200 points and the oral
presentation 100 points.
Possible modeling projects:
- Modeling walking and locomotion (see web site below to get an
idea of what can be done)
- Modeling vegetation patterns
- Modeling neural dynamics
- Modeling special chemical reactions (e.g. the Belouzov-Zhabotinsky
reaction, see below)
- Modeling bacterial dynamics
- Homework:
Homework will be assigned regularly. The nature of each assignment will vary.
Possible types of assignments include
- writing a brief report on topics discussed in class
- solving assigned problems
- progress report on the semester-long project
Reports should be typed. Selected homework will be graded and a final of
score of 200 points will be assigned.
Click here to see homework assignments
- Attendance:
Students are expected to attend every scheduled class,
and to be familiar with the University Class Attendance policy as it
appears in the General Catalog. It is the student's responsability to
keep informed of any announcements, syllabus adjustments or policy
changes made during scheduled classes.
- Grades:
The total number of points available on the project and homework
is 500. Grades will be no lower than those set forth in the following
table:
| 450 < points | 90% to 100% | A |
| 400 < points < 449 | 80% to 90% | B |
| 350 < points < 399 | 70% to 80% | C |
| 300 < points < 349 | 60% to 70% | D |
| points < 300 | 0% to 60% | E |
The grade of I will be awarded if all of the following conditions are
met:
- The student has completed all but a small portion of the required
work.
- The student has scored at least 50% on the work completed.
- The student has a valid reason for not completing the course on time.
- The student agrees to make up the material in a short period of time.
- The student asks for the incomplete before grades are due, 48
hours after the final exam.
- Course contents:
- Topics
- Nature of mathematical modeling
- Mecanical vibrations
- Population dynamics
- Reaction-diffusion equations
- Traffic flow
- Techniques
- Dimensional analysis
- Phase plane analysis
- Solutions of systems of differential equations
- Simple solutions of partial differential equations
- Method of characteristics
- Interesting web sites:
- Mechanics
- Meteorology and climatology
- The Belouzov-Zhabotinsky chemical reaction
- Viscous fingering
- Dendritic growth
- Population dynamics
- Biology
- Traffic flow
- PPLANE
Back to Dr. Lega's page