## MA 2051A Ordinary Differential Equations B term 2004

Text: Paul Davis, Differential Equations: Modeling with MATLAB

Professor: W. Farr, 105A Stratton, X5496, E-mail - bfarr
Office Hours: MWF 11-1,TR 9-11 or by appointment
Web page: `http://www.math.wpi.edu/Course_Materials/MA2051AB04/`
PLA: Tom Howard (e-mail - thoward)

## Goals for this Course

• Understand the basic concepts of differential equations.
• Be proficient at solving the following types of differential equations.
• single linear first order
• linear second order equation with constant coefficients
• first order systems with constant coefficients
• Understand the general theory of existence and uniqueness of solutions of differential equations
• Understand and be able to analyze the qualitative behavior of a single nonlinear autonomous differential equation
• Be able to interpret the phase plane for an autonomous, noonlinear system of two differential equations.
• Be able to develop and interpret results from simple models.

## Course Structure

This course meets four times a week for lectures, where the basic concepts will be introduced. There is also one conference section per week. In these sessions you will work in small groups, aided by a Peer Learning Assistant.
• Homework
The homework assignments will be given on class and listed on the course web page. Completing these exercises is essential to your mastery of the material. Homework will be collected each Thursday in lecture and selected problems will be graded. Late homework will not be accepted without prior arrangement with the instructor. Homework scores will count as 15% of your final grade.

• Exam
There will be two hour exams during the term. Each will count 25% of your final grade. Tentative dates are November 11 and December 2. There will also be a comprehensive final exam in the last week of the course on Thursday, December 16. This exam will count as 35% of your final grade.

### Material to be covered

Week 1
Basics for a single, first order equation
Secs. 4.1-4.4
Week 2
Existence and Uniqueness, Modeling with first order equations
Secs. 4.5, 4.6, 2.1, 2.2
Week 3
More modeling, qualitative theory for a single, first order equation
Secs. 2.3, 2.4, 3.2, 3.3
Week 4
Second order equations with constant coefficients
Secs. 5.1, 5.2, 6.1, 6.2, 6.3, 6.4
Week 5
More on second order equations
Secs. 6.5, 6.6, 6.7
Week 6
Systems, Phase plane analysis
Secs. 7.1, 7.2, 8.1
Week 7
Solving systems in two dimensions
Secs. 8.2, 8.3
William W. Farr
2004-10-26