## MA 2051A Ordinary Differential Equations B term 2005

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

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/MA2051AB05/`

## 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, 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.

## 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.
• 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.

### Material to be covered

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
William W. Farr
2005-10-25