AMATH 383
SLN 10054, MWF 12:00-1:00, Loew Hall 102
(Prerequisites: AMATH 351 or MATH 307)

Introduction to Continuous Mathematical Modeling

Instructor:
Katie Oliveras
Condon 810A
oliveras AT amath.washington.edu
office hours: Mon and Wed 2:00 - 3:00 and by appointment.

Course Description : Textbook : Syllabus / Lectures : Grading : Homework : Term Paper : Online Grades

Course Description

This course is an introductory survey of applied mathematics with emphasis on modeling of physical and biological problems in terms of differential equations. We will discuss formulation of the problem, derivation of the solution, and interpretation of the results.

Prerequisites: AMATH 351, MATH 307, or equivalent.

Textbook

We will be using Topics in Mathematical Modeling by K.K. Tung (List Price $45.00). You can find it at the University Bookstore or at various online dealers.

Lectures

A copy of the syllabus can be found here

You can find the notes for 3D and higher ODEs here
You can find the handwritten notes covering marriage (conflict model) here
You can find the handwritten notes covering competition models, non-dimensionalization, and null clines here
Lecture notes are available here and cover up through the July 16,2007 lecture. Some figures from the last few lectures are not available in the notes yet.

A more accurate description of modeling a chemical process can be found here. The notes have been changed to reflect this addition.

• Review of AMATH 351 (June 18)
• Chapter 4 - Differential Equation Models
• Chapter 5 - Modeling in the Physical Sciences
• Chapter 6 - Nonlinear Population Models
• Additional Reference - Bifurcation Theory - Advanced Ideas in Nonlinear Stability
• Chapter 9 - Interactions, Predator-Prey Models
• Chapter 10 - Marriage and Divorce
• Chapter 11 - Chaos in Deterministic Continuous Systems

Grading

There will be no exams (for better or worse, but mostly for better). You grade will be composed of 6 homework assignments (each counting for 10% of your final grade), and a term paper (counting for the remaining 40%).

Please note, that if you would like to receive a W (writing) credit, please indicate so on your term paper, and turn in a draft on the day specified. It will be read, and returned to you for corrections. University regulations requires the W credit paper 10-15 pages long (not including figures or biblography). More information about the University’s writing credit can be found at

http://www.washington.edu/students/ugrad/advising/ged/gedw.html

Homework

Homework is due at the beginning of class on its due date. Late homework is not accepted unless you have prior approval from me. Every homework that you turn in should include a header with your name, student number, due date, course, and the homework number as a title.

The grader is instructed to deduct points for messiness.

Assignment	Assigned Date	Due Date	Homework Sets	Homework Solutions
Homework 1	Wed. Jun. 20	Wed. Jun. 27	HW1.pdf (updated)	HW1Sols.pdf
Proposal Ideas		Fri. Jun. 29
Homework 2	Fri. Jun. 29	Fri. Jul. 13	HW2.pdf	HW2Sols.pdf
Project Proposal		Mon. Jul 16
Homework 3	Fri Jul. 13	Fri. Jul. 20	HW3.pdf problems from the book	HW3Sols.pdf
Homework 4	Mon. Jul. 23	Mon. Jul. 30	HW4.pdf EXTRA CREDIT! Work problem #2 with F' = F(2 - 2F - G) G' = G(1 - G - F)
Homework 5	Wed. Aug 1	Wed. Aug 8	HW5.pdf main.m solveODE.m Water wheel video
EXTRA CREDIT	Monday Aug. 6	Fri Aug 10	Using the code in the appendix of the book, write a matlab script to solve the Lorenz equations. Then investivage what happens for different r values. Include 3 graphs, and include a paragraph explaination for the difference. You are encouraged to play around with the parameters and see what happens.
Homework 6	Wed Aug 8	Wed Aug 15	HW6.pdf
Final Paper

Term Paper

A major feature of this introductory mathematical modeling course is that students develop course projects and write term papers on those pro jects. These term papers are to be turned in on the last day of lectures.
Guidelines for the final paper can be found here guidelines.pdf
You can also find a running list of topic references and suggestions here topics.pdf

Date	Assignment Due
June 29, 2007	Project Proposals - Just a list of 2-3 ideas that you would like to explore
July 16, 2007	Project Proposal - Finalize your topic choice, and write a rough outline of what you plan to discuss. Include at least one reference (outside of the course textbook), and an informal half page about your ideas. This counts for 15 points out of the 200 points for your final project
Aug 3 2007	Finalize your outline for your paper, and include a brief 1/2 - 1 page summary of your finding so far
August 13, 2007	Draft Due for W credit
August 17, 2007	Final Paper due by 1pm to Condon Hall Room 810A.

Computer Usage

The use of computer software such as Matlab, Maple, Mathematica, etc. might be useful in gaining intuition into systems that we will be examining. All of these programs are available in the Math Sciences Computing Center located in the basement of the Communications Building in Room B-022. Hours are M-F 8:30 - 5:00. Software is also available for purchase from the University Bookstore at Student prices.

<oliveras@amath.washington.edu>

Mon June 18, 2007 10:58 am