Text: H. S. Bear, **Differential Equations: A Concise Course**

Office Hours: MWF 11-1,TR 9-11 or by appointment

Web page:

`http://www.math.wpi.edu/Course_Materials/MA2051AB05/`

- 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, including solution via the Laplace transform
- 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.

**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 10 and December 1. There will also be a comprehensive final exam in the last week of the course on Thursday, December 15. This exam will count as 35% of your final grade.

**Week 1**- Basics for a single, first order equation

Secs. 1.1, 1.2, 1.3, 1.4, 2.2, 2.4 **Week 2**- Linear equations

Secs. 3.1, 3.2, 3.3, 3.4, 3.5 **Week 3**- More on linear equations

Secs. 4.1, 4.2, 4.3 **Week 4**- Undetermined coefficients, Laplace transform

Secs. 4.4, 4.6, 5.1, 5.2, 5.3 **Week 5**- More on Laplace transform, systems of equations

Secs. 5.4, 7.1, 7.2 **Week 6**- Systems, Phase plane analysis

Secs. 7.7, Class notes **Week 7**- Overflow and Existence and Uniqueness

Secs. 6.1, 6.2, 6.3

2005-10-25