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

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
- Signalling and motility in
*Dictyostelium Discoideum* - Bacterial aggregation
- Bacillus subtilis: colony dynamics

- Signalling and motility in
- Traffic flow
- PPLANE

Back to Dr. Lega's page