AMATH 383
SLN 10209, MWF 10:30-11:20,
EEB 054
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Notes
Syllabus and Reading
- Review of analytical solution techniques for ordinary differential equations (at the level and character of AMATH 351 )
- Continuous models, carbon dating-----------------(starting Sep 29, 2 lectures)
- Modeling in physical sciences, Kepler, Newton----(Oct 6, 2 lectures)
- Harvesting models and bifurcation theory--------(Chapter 4, Wiggins and Perko 6 lectures)
- Snowball Earth and climate modelling-------------(Chapter 6, starting Friday October 18, 6 lectures)
- Models of species interaction, predator and prey--------(Chapter 7, starting Wednesday Nov 8: Reading paragraph 7.3)
- The diffusion equation and the age of the earth-------------(Chapter 11, starting Wednesday Nov 22)
- Ice ages.
- Stochastic Modelling
Reference Books
- Mathematical Modelling with Case Studies: A Differential Equation Approach Using Maple, by B. Barnes and G.R. Fulford, Taylor and Francis Publishers, 2002.
- Differential Equation Models, by M. Braun, C.S. Coleman, D.A. Drew, 1983, Springer-Verlag, NY, NY.
- Modelling with Differential Equations by David N. Burges and Morag S. Borrie.
- Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow, by Richard Haberman.
- Modeling Differential Equation in Biology, by C.H. Taubes, 2001, Prentice-Hall.
- W. E. Boyce & R. C. DiPrima, Elementary Differential Equations and
Boundary Value Problems
(8th Edition) (ISBN 0-471-43338-1)
John Wiley & Sons, 2004.
Books on bifurcations and stabililty
- Differential equations and dynamical systems Lawrence Perko New York : Springer, 2001 and earlier editions
- Introduction to applied nonlinear dynamical systems and chaos Stephen Wiggins New York : Springer, c2003 and earlier editions
Schedule and Homework
Follow links in the table below to obtain a copy of the homework in
PostScript (.ps) or 
Adobe
Acrobat (.pdf) format. You may also obtain here solutions to some of the
homework and exam problems. An item shown below in plain text is not yet
available. For additional information regarding viewing and printing the
homework and solution sets,
click here.
| Homework and Exams | Homework Due Date | Homework Problem Sets | Homework Solutions |
| First day of classes | Wednesday, September 27 | ||
| Homework#1 | due Friday, October 6 | Homework #1 (.ps, .pdf) | HW #1 Solutions (.ps, .pdf) |
| Project Proposal | Friday, October 20 | ||
| Homework#2 | due Friday, October 20 | Homework #2 (.ps, .pdf) | HW #2 Solutions (.ps, .pdf) |
| Homework#3 | due Friday, November 3 | Homework #3 (.ps, (.pdf) | HW #3 Solutions (.ps, .pdf) |
| Veteran's Day | Friday, November 10 | No class | |
| Project Outline | Wednesday, November 22 | ||
| Thanksgiving | Thursday, November 23 | No class | |
| Thanksgiving | Friday, November 24 | No class | |
| Homework#4 | due Friday, December 1st | Homework #4 (.ps, .pdf) | HW #4 Solutions (.ps, .pdf) |
| W Credit Project Draft | Monday, December 4 | ||
| Project due date | Wednesday, December 6 | ||
| Homework#5 | due Friday, December 8th | Homework #5 (.ps, .pdf) | HW #5 Solutions (.ps, .pdf) |
| Last day of classes | Friday, December 8 |
Grading
There will be no exams. There will be 5 homework assignments, each counting 10% towards the final grade. There is a term paper (50% of the final grade). If you would like to receive W (writing) credit, please so indicate on your term paper and turn in a draft on the day specified. University regulation requires the W credit paper be at least 15 pages. It will be read and returned to you for corrections.You may view your homework and exam grades on-line. grades on-line.
Term Paper Timeline
Friday October 20: Project Proposal: you submit in class one (typed) page of your project that includes: Title, one paragraph that explains why the model you are studing is important, one paragraph that describes the principles and the results you want or hope to obtain. Finally, include all possible references.Wednesday November 22: Submit a typed one or two page outline of your work and results so far.
Wednesday December 6: Project is due
Term Paper Presentations
10 min presentation of your work including time for discussion as followsWednesday December 6
Li Y.L. Epidemiology Mathematical Modeling
Ben L. Modelling of the population of Alaskan Salmon
Eric V. Modelling Casing Expansion in the Wankel Engine
Mariko F. Competing Species
? Traffic flow I
Chris H. Levels of Salinity in the Puget Sound area
Friday December 8
Ian C. Analysis of Inductive and Diffusive Waves of the Solar Dynamo
Clement Y. Modelling and Derivation of Human Mortality Tables
Harkirat S. What does Mathematics say about marriage
Brett Y. Calculation of the Mass of Binary Stars
? Traffic flow II
Entzu C. Prediction on Expected Outlook of Sales by Categories
Guidelines for Term Paper
As you will read in the documents below, you must finish a project for success in this course. You are free to follow your own interests in the choice of the topic. I will eventually post a number of possible projects and references here, which might be of a more advanced character. I reserve the right to ask you present the material of your project in front of our class.|
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| <tung@amath.washington.edu> | Sat Jan 15 15:58:59 2005 |
Important Note on Office hours
Office hours are hours during which I am guaranteed to be in my office, answering your questions and dealing with problems you may have in this course. Office hours are not time during which you do your homework in my office. Rather, you should use this time to ask questions about problems which you have tried to work out, but got stuck at some point. In other words, you should come to office hours prepared, just like you should come to class prepared.