Text: Paul Davis, **Differential Equations: Modeling with
MATLAB**

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)

- 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.

**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.

**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

2004-10-26