Introduction to Mathematical Modeling

All students in the School of Engineering and Science with and interest in the application of Mathematics to real-life problems, and have a mathematical background equivalent to either Engineering and Science Mathematics 1B (Multivariable Calculus, ODE), Engineering and Science Mathematics 3A or 3B, or Analysis I (better: Analysis II) should consider taking this course as a home school elective. Students of Computational Science can take this course as part of their first or second year major requirement.

The following topics are covered:

- Discrete growth models: Optimal harvesting, tumor cell growth

- From the discrete to the continuous I: Predator-prey models, Temperature-dependent sex determination in crocodiles, Dynamics of marital interaction

- From the discrete to the continuous II: Random walks and diffusion, Models for animal dispersion and chemotaxis

- Parameter estimation and optimal initialization of models

- Basic data processing, analysis, and visualization techniques, in particular the discrete Fourier transform.

Lectures (subject to change!)

Tu 9:45-11:00 in East Hall 2

F 9:45-11:00 in East Hall 2

• E. J. D. Murray: Introduction to Mathematical Biology I: An Introduction, 3rd edition, Springer, 2002.
• F. C. Hoppenstaedt, C. S. Peskin: Modeling and Simulation in Medicine and the Life Sciences, 2nd edition, Springer, 2002.

• To be announced later

Homework and modeling projects (including some numerical simulations) are handed out and collected roughly every two weeks. The solutions to homework needs to be turned in on the due date by noon to Room 106 in Research I, or to the mailbox in Research I (near Room 40). Don't forget to indicate name and course on the paper. If necessary, other arrangements will be announced by the instructor. Project work needs to be submitted in the same way. Code (Matlab (preferably), Octave, or C/C++) and simulation results should be documented, and sent in a single email to P. Oswald . You should be able to present and explain project and homework solutions.

Homework is your individual work. Collaborative project work in groups of two or three is permissible provided:

• Each member of a group maintains and submits their own version of the project solution.
• You state who you collaborated with (or at the beginning of a written project submission or as comment in the source code submission).
• Each member of the group is able to explain the project solution without help from others.

You may consult books and internet resources, provided you always quote the source.

• The final grade will be computed from the weighted average of percentages of maximal scores with the weights

  Homework:	25%
  Projects:	25%
  Two Midterm Exams (weeks 7 or 8, and 13):	Each 25%

  
  according to the following table:

  Cutoff score:	95%	90%	85%	80%	75%	70%	65%	60%	55%	50%	45%	40%
  IUB Points:	1.0	1.33	1.67	2.0	2.33	2.67	3.0	3.33	3.67	4.0	4.33	4.67