MTH 244/4
Differential Equations
Spring 2007/URI

TextOrdinary Differential Equations by Finizio and Ladas, Simon and Schuster, Third Edition

Exams and Grading: Your grade will be based on three tests, a final exam, Maple projects, and quizzes as follows:

 Three tests at 100 points each 300 points Final exam 150 points Quizzes 150 points Maple 100 points Total 700 points

Calculators and Computers: As in Calculus Courses you will need a programmable graphing calculator. You are encouraged to use the CAS (computer algebra system) such as Maple, Livemath, and Scientific Notebook and online programs that can be found on Internet. We will give a brief introduction to such resources. Some Maple notebooks will be provided and demonstrated in the class. Third exam will be Maple-aid exam.

Course Description: In MTH 244 we study ordinary differential equations in greater details than in the calculus courses. This subject has wide applications in the physical sciences, engineering, bio-medical sciences, and economics, as well as leading to many advanced areas of mathematics itself. You will find that there are new algebraic ideas to master.

The homework problems are the core of this course. An important purpose of the problems is to make you think through and master the ideas of the subject so that you can confidently apply your knowledge in new situations. You will learn a great deal from honest hard work on a problem, even if you don't succeed in solving it. Read the text material before working on the problems.
The exams will reflect the variety of the homework problems. It is important that you give these problems adequate time and effort.

The topics that will be covered are:

Exact solutions of first order differential equations (homogeneous, linear, Bernoulli, differential equations with total differential)

Existence and uniqueness theorems for differential equations

Linear differential equations – general theory

Systems of linear differential equations

Laplace transform and applications in solving linear differential equations

Solving linear differential equations with method of series

Numerical solutions of  ordinary differential equations

Online information: www.math.uri.edu/courses and  www.math.uri.edu/~kulenm

Instructor: Dr. M. Kulenovic, Tyler 216,  X44436,                            e-mail: kulenm@math.uri.edu

Office hours: MTW:  1- 2     Time: MWF: 12-12: 50          Room: Wales 224

### Syllabus

 Sections Homework Problems Exams/Events 1.1 5,9,11,14,18,25 1.2 3,7,10 1.3 1,11,19, 24,33 1.4 5,7,17,31,35,41,44,45 1.5 1,5,11,15,23,25,29,32,41 1.6 1,7,12,19,23,29 1.7 3,7,12 1.8 1,5 2.2 3,7,8,30,33,41 2.3 1,7,11 2.4 5,7,11,19,35 2.5 5,20,23,35,47 2.7 7,11,19,31,37 2.8 5,7,14,29 Exam 1 2.9 5,10,14 2.10 7,11,19,23 2.11 1,7,14,23,29,41 2.12 5,7,11,23 3.1 5,7,11,29 3.2 5,7,11,19 3.3 5,7,19,23,29,35 4.2 4,7,14,28,31,49 4.3 5,7,28,31 5.2 7,11,19 Exam 2 5.3 7,11,14 5.4 4,7,19,20 5.5 7,11,23,29 6.1 1,7,11 6.2 4,5,7 7.2 4,5,7 7.3 2,4,7 Exam 3

Sample Maple notebooks:

HTML format:

Maple  format:

Series Solutions of ODE

Numerical Methods for ODE

Interesting Java applets for Differential Equations

Interactive Differential Equations set of applets for Differential Equations

Elementary Differential Equations
by Douglas Meade - nice collection of Maple programs

Complete Maple animation of  free and forced harmonic oscillations

Complete Maple animation of two pendulums coupled by spring

Complete Maple animation of bouncing ball

Complete Maple Animation of Gyroscopic Motion

Dynamics Lab a Maple package for simulation of dynamical systems