| AMATH 504 | Schedule | Instructors | Content | References | Prerequisites | Grading | Calendar | Notes | Homework |
AMATH 504
Mathematical Biology II
Spring 2008
Schedule
| SLN: | 10220 | |
| Days: | T, Th | |
| Time: | 3:30-4:50 pm | |
| Room: | Guggenheim 416 |
Instructors
| Name: | Mark Kot | |
| Office: | 415G Guggenheim Hall | |
| Phone: | (206) 543-0908 | |
| Fax: | (206) 685-1440 | |
| Email: | kot@amath.washington.edu |
| Office Hours: | M, W | |
| 1:00-2:00 pm |
| Name: | Hong Qian | |
| Office: | 415E Guggenheim Hall | |
| Phone: | (206) 543-2584 | |
| Fax: | (206) 685-1440 | |
| Email: | qian@amath.washington.edu |
| Office Hours: | TBA |
Content
Amath 504 is intended as either the third course in the Amath 422-423-504 mathematical biology sequence
or as a standalone course in advanced aspects of mathematical biology.
Topics to be covered include:
- the formulation of spatially structured models,
- reaction-diffusion equations,
- steady-state solutions,
- models of spread,
- traveling waves of invasion,
- the spread of rabies,
- integrodifference equations,
- PDEs in stochastic problems,
- random movement: the diffusion equation revisited,
- reaction-diffusion models for chemical reactions,
- the Smoluchowski theory of diffusion-controlled reactions,
- Brownian motion and stochastic differential equations,
- and Kramers theory and evolutionary stochastic dynamics.
References
Useful reference books include:
-
Allen, L. J. S. (2007)
An Introduction to Mathematical Biology
Pearson Prentice Hall, Upper Saddle River, NJ. UW Library Catalog -
Brauer, F. and Castillo-Chavez, C. (2001)
Mathematical Models in Population Biology and Epidemiology
Springer, New York, NY. UW Library Catalog -
Britton, N. F. (1986)
Reaction-Diffusion Equations and Their Applications to Biology
Academic Press, London, UK. UW Library Catalog -
Britton, N. F. (2005)
Essential Mathematical Biology
Springer, London, UK. UW Library Catalog -
Edelstein-Keshet, L. (1988)
Mathematical Models in Biology
Random House, New York, NY. UW Library Catalog Edelstein-Keshet, L. (2005)
Mathematical Models in Biology
SIAM, Philadelphia, PA. UW Library Catalog -
Keener, J. and Sneyd, J. (1998)
Mathematical Physiology
Springer, New York, NY. UW Library Catalog -
Kot, M. (2001)
Elements of Mathematical Ecology
Cambridge University Press, Cambridge, UK. UW Library Catalog -
Mangel, M. (2006)
The Theoretical Biologist's Toolbox:
Quantitative Methods for Ecology and Evolutionary Biology
Cambridge University Press, Cambridge, UK. -
Murray, J. D. (2002)
Mathematical Biology I: An Introduction
Springer, Berlin, Germany UW Library Catalog -
Murray, J. D. (2003)
Mathematical Biology II: Spatial Models and Biomedical Appications
Springer, Berlin, Germany UW Library Catalog -
Okubo, A. and Levin, S. A. (2001)
Diffusion and Ecological Problems: Modern Perspectives
Springer, New York, NY. UW Library Catalog -
Petrovskii, S. V. and Li, B.-L. (2006)
Exactly Solvable Models of Biological Invasions
Chapman & Hall/CRC, Boca Raton, FL. UW Library Catalog -
Shigesada, N. and Kawasaki, K. (1997)
Biological Invasions: Theory and Practice
Oxford University Press, Oxford, UK. UW Library Catalog
Prerequisites
Amath 422 and 423 are helpful, but not essential.
You should be comfortable with ordinary differential equations. You must be willing to learn a lot about partial differential equations.Grading
Homework accounts for 70% of the final grade.
A 10-15 page term paper accounts for 30% of your final grade Homework problems will be assigned on a regular basis and are due one week from the date of assignment. Homeworks must be done alone; they are not group projects!Calendar
Important Dates
| March 31 | - | Monday | - | First Day of Classes | |||||
| May 26 | - | Monday | - | Memorial Day (No Class) | |||||
| June 5 | - | Thursday | - | No Class | |||||
| June 9 | - | Monday | - | Papers Due ( < 12:00 pm) |
Notes
Spatial steady states: linear problems Spatial steady states: nonlinear problems Models of spread Random movement and diffusion revisited More discussions on stability and bifurcation Smoluchowski-Noyes theory of diffusion-controlled reactions
Homework
Homework problems will be assigned on a regular basis and are due one week from the date of assignment.
Homeworks constitute 70% of the final grade. Write up your homework alone, not as a group! Mark's problem #2.1 (Due: 4/10/2008) Mark's problem #2.2 (Due: 4/10/2008) Mark's problem #2.3 (Due: 4/10/2008) Mark's problem #3.1 (Due: 4/29/2008) Mark's problem #4.1 (Due: 5/06/2008) Hong's homework #1 (Due: 5/15/2008) Hong's homework #2 (Due: 5/22/2008) Hong's homework #3 (Due: 6/5/2008)
|