Mathematical Modeling

Math 485/585 - Spring 2003

• Instructor: Dr. Joceline Lega
  Office: Mathematics 511
  Phone: 621-4350
  e-mail: lega@math.arizona.edu

  Location:

  M LNG 202

  Time:

  Tuesdays and Thursdays, 11:00 am - 12:15 pm

  Office Hours:

  Tuesdays, 2-3 pm & 4-6 pm.

  Text: Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow, by Richard Haberman, published by SIAM.

  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

  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 responsibility to keep informed of any announcements, syllabus adjustments or policy changes made during scheduled classes.

  Project: Students will work in teams on a long-term project, worth 300 points. Each team will give oral progress reports on its project throughout the semester, and will turn in a final written report, due May 6th 2003 (the last day this course meets). The written part of the project will be worth 200 points and the oral presentations will count for a total of 100 points.
  

  Math 485 modeling projects should be on one of the topics listed below. The articles or web sites listed as references must make the basis of each project.

  • Modeling walking and locomotion
    • See A. Ruina's lab website at Cornell University.
  • Modeling vegetation patterns
    • Regular and Irregular Vegetation Patterns in Semiarid Vegetation by C.A. Klausmeier.
  • Predator-prey models
    • Prevention of Population Cycles by Parasite Removal by P.J. Hudson, A.P. Dobson & D. Newborn.
    • Crossing the Hopf Bifurcation in a Live Predator-Prey System by G.F. Fussmann, S.P. Ellner, K.W. Shertzer & N.G. Hairston Jr.
  • Modeling excitable systems
    • The Belouzov-Zhabotinsky chemical reaction
      • Phenomenology
      • Nonlinear kinetics group, University of Leeds
      • Pictures
      • Numerical simulations of the Barkley model
    • Reaction fronts in a surface reaction
    • Mexican waves in an excitable medium by I. Farkas, D. Helbing & T. Vicsek
  • Modeling diseases and epidemics
    • Hepatitis C Viral Dynamics in Vivo ... by A.U. Neumann et al.
    • Containing Bioterrorist Smallpox by M.E. Halloran, I.M. Longini Jr., A. Nizam & Y. Yang.
    • Modeling vaccination strategies against foot-and-mouth disease by M.J. Keeling et al.
  • Modeling collective behaviors of living organisms
    • Complexity, Pattern, and Evolutionary Trade-Off in Animal Aggregation by J.K. Parrish & L. Edelstein-Keshet.
    • Signalling and motility in Dictyostelium Discoideum
      • F. Siegert's lab, Ludwig-Maximillians University, Munich
      • C. Weijer's lab, University of Dundee

  Math 585 modeling projects may either be on one of the topics listed above or be based on the student's graduate thesis work.

  Homework: Homework problems will be assigned regularly. Quizzes based on the homework assignment will be given on a regular basis and a final homework score equivalent to 200 points, will be assigned. This score will be computed from the 10 best quiz results of the semester.
  Click here to see homework assignments

  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

  Incomplete Grades: 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.

  
  For general information on grades and the grading system, see the University Policy.

  Classroom Conduct: Students at The University of Arizona are expected to conform to the standards of conduct established in the Student Code of Conduct. Prohibited conduct includes:

  1. All forms of student academic dishonesty, including cheating, fabrication, facilitating academic dishonesty, and plagiarism.
  2. Interfering with University or University-sponsored activities, including but not limited to classroom related activities, studying, teaching, research, intellectual or creative endeavor, administration, service or the provision of communication, computing or emergency services.
  3. Endangering, threatening, or causing physical harm to any member of the University community or to oneself or causing reasonable apprehension of such harm.
  4. Engaging in harassment or unlawful discriminatory activities on the basis of age, ethnicity, gender, handicapping condition, national origin, race, religion, sexual orientation, or veteran status, or violating University rules governing harassment or discrimination.

  Students found to be in violation of the Code are subject to disciplinary action.

  Academic Integrity: Students are responsible to be informed of University policies regarding the Code of Academic Integrity. Students found to be in violation of the Code are subject to sanctions that will be determined by the severity of the infraction. The Code of Academic Integrity will be enforced in all areas of the course, including tests and homework.

  Students Who Require Reasonable Accommodations Based on Disability: Students planning to use accommodations for this course should privately identify themselves to their instructor within the first few days of class. These students must also provide the instructor with a letter of identification from the Disability Resource Center. This letter should include information about any accommodations you will need for the class, including accommodations for test taking. Students are also invited to discuss specific issues with the course instructor during regular office hours or by appointment.

  Withdrawal Dates:

  • Last day to drop without a grade (use RSVP or WebReg): February 11, 2003.
  • Withdrawal deadline (instructor's signature on a Change of Schedule form is required): March 11, 2003.

  Interesting Web Sites:

  • Mechanics
    • Computer animations

  • Meteorology and climatology
    • Global climate animations
    • Hurricane forecasting

  • Viscous fingering
    • Simulation in circular geometry
    • A paper on the selection of finger width in the absence of surface tension

  • Dendritic growth
    • Vizualization of dendritic growth
    • Dendrites in crystal growth
    • Cellular/dendritic growth

  • Population dynamics
    • Audubon's Christmas bird count
    • Iterations of the logistic map
      • From Mike Cross's web site at Caltech
      • From Pete Kernan's web site at Case Western Reserve University
    • Lab1: Modeling the growth of the U.S. population

  • Biology
    • Bacillus subtilis: colony dynamics

  • Traffic flow
    • Traffic flow simulations
    • The physics of traffic

  • PPLANE
    • PPLANE page at Rice University
    • Another source for the PPLANE JAVA applet