MTH 244/4
Differential Equations
Spring 2007/URI
Text: Ordinary 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:
Solving First and Second Order ODE
Maple format:
Solving First and Second Order ODE
Links for Differential Equations:
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