AMATH 383
SLN 10200, MWF 10:30-11:20, Guggenheim Hall 416
(Prerequisites: AMATH 351 or MATH 307)

Introduction to Continuous Mathematical Modeling

Instructor:
Katie Oliveras
Guggenheim 412
oliveras AT amath.washington.edu
Office Hours: 1:00 - 2:00 Thurs GUG 415L
12:30 - 1:30 Fri GUG 415L

Syllabus / Lectures : Grading : Homework : Term Paper : Computer Usage : 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 a course in ordinary differntial equations.

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.

Syllabus and Lecture Notes

The syllabus for the course can be found here, though much all of the information in the syllabus can be found on this webpage.

Below is a general outline for the course, and is subject to change depending on class interests.

Review of solutions to ODEs (notes)
Building A Mathematical Model (notes)
Scaling Laws and Dimensional Analysis (notes)
1-D Models (Exponential, Population, and Physical Models) (Exponential Model notes) (Physical Science Models) (1D Population Models)
2-D Models (Predator-Prey, Competition/Cooperation, and Conflict Models) (2D Models/Predator Prey) (Competition Models) (Conflict Model) (Marriage Model)
3-D and Higher Models (3D Overview)
Modeling with Partial Differential Equations (Bridge Collapse, Traffic Flow if time permits)

Lecture notes, and tutorials will be posted here online as they are made available.

Grading

There will be no exams (for better or worse, but mostly for better). You grade will be composed of 8 homework assignments (counting for 70% of you final ), and a final term paper (counting for the remaining 30%). Typically, I assign a 2.7 to the class average, however this is subject to change if the course standard deviation is small.

Schedule and Homework

Assignments are due at the beginning of class on the due date, and will generally be returned in class one week later. Late assignments will not be accepted unless you have prior approval from me. Every assignment 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.

Below is a tentative list of assignments and due dates. This list is subject to change. Any changes will be announced in class.

Assignment	Date Assigned	Date Due	Homework Assignments	Homework Solutions
Homework 1	October 1	October 8	HW1.pdf excel file	HW1Sols.pdf
Topic Proposals Due		October 10
Homework 2	October 8	October 15	HW2.pdf	HW2Sols.pdf
Homework 3	October 19	October 26	HW3.pdf	HW3Sols.pdf
Final Proposal Due		November 2
Homework 4	October 29	November 5	HW4.pdf pplane7.m
Happy Halloween		October 31	You know you want to wear your costume to class!
Homework 5	November 10	November 19	HW5.pdf
Homework 6	November 19	November 26	HW6.pdf Reading Material
Final Outline		TBA
NO CLASS		November 23	THANKSGIVING. Be thankful that there is no class!
Rough Draft Due		December 3
Homework 7	November 28	December 7	HW7.pdf
Final Paper Due		December 10

Term Paper

A major feature of this introductory mathematical modeling course is that students develop course projects and write term papers on those projects. These term papers are to be turned in during the final examination week.

This course is listed as an optional W (writing) credit class. If you would like to receive a W credit, please indicate so on all of your assignments relating to your term paper. 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 Universityâ€™s writing credit can be found at

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

Guidelines for the final paper can be found here (guidelines.pdf), and you can also find a running list of topic references and suggestions here (topics.pdf)

Below is a list of final project related assigments and their due date.

Date	Assignment Due
Oct 10, 2007	Project Proposals - Just a list of 2-3 ideas that you would like to explore. Include a 1-2 sentence description of each one. If you are having problems thinking of a topic, write a paragraph of your interests, and perhaps I could lead you towards a topic
Oct 26, 2007	Project Proposal - Finalize your topic choice, and write a rough outline of what you plan to discuss. Include at least two references (outside of the course textbook), and an informal half page about your ideas. (2.5% of your final project grade)
Nov 16, 2007	Finalize your outline for your paper. Include a 1-2 page description of your mathematical model. This doesn't have to be the final version of your model. If you are having problems with the modeling, please make an appointment with me a week before this is due. (2.5% of your final project grade)
Dec 3, 2007	Rough Draft Due. This should be a close version of your final paper. I will skim your paper and give general feedback on your model, as well as your . If you are taking the class for W credit, I will give you additional feedback outside of content. (5% of your final project grade)
Dec 10, 2007	Final Paper due by 5pm. Location for paper drop-off will be announced later.

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.

Software is also available for purchase from the University Bookstore at Student prices.

<oliveras@amath.washington.edu>

Friday October 19, 2007 5:00 pm