Jordan University of Science and Technology
Faculty of Department of Mathematics and Statistics
Second Semester 2006/ 2007
Course Syllabus
Course Information
Course Title
Ordinary Differential Equations
Course Code
Prerequisites
Math 203
Math 102
Course Website
NA.
Instructor
Coordinator: Dr. Sofian Obeidat
Office Location
M6
Office Phone #
Office Hours
23860
Sunday, Tuesday, Thursday : 1:05-2:05
Monday, Wednesday : 3:30-4:15.
E-mail
[email protected]
Teaching
Assistant(s)
NA.
Course Description
Introduction, classification, first order differential equations. Applications. Differential equations of higher
order and their solutions. Applications. Solutions by series near ordinary points. Solving IVPS using
Laplace transform. Linear systems of differential equations.
Textbook
Title
Fundamentals of Differential Equations.
Author(s)
R. Nagle, E. Saff and A. Snider.
Publisher
Addison-Wisley.
Year
2000.
Edition
Fifth.
Book Website
Other references
1. D. G. Zill, A First Course in Differential Equations with Applications,
PWS-Kent
2. Rainville and Bedient, Elementary Differential Equations, Macmillan.
Assessment
Assessment
Expected Due Date
First Exam
18/3/2007
Percentage
30%
Second Exam
30%
Final Exam
40%
Course Objectives
Percentage
1.
To demonstrate the usefulness of ordinary differential equations for modeling
physical phenomena.
5%
2.
To introduce different classifications of ordinary differential equations.
10%
3.
To introduce different forms of differential equations and show how to solve
them using analytical methods.
60%
4.
To introduce systems of differential equations in normal form and show how
to solve them.
10%
5.
To discuss some applications on differential equations.
15%
Teaching & Learning Methods
Lectures and class discussion
Learning Outcomes: Upon successful completion of this course, students will be able to
Related Objective(s)
Will be able to
Reference(s)
1st
2,3&5
Solve different forms of
differential equations.
order
Chapter 1,2
2,3&5
Solve some linear second order
differential equations.
Chapter 2,3
2&3
Solve some nth order linear
differential equations.
Chapter 4
3
Solve some linear second order
initial value problems using
Laplace transform.
Chapter 5
3
Solve some linear second order
differential equations using series
methods.
Chapter 6
4
Solve a linear system of
differential equations in normal
form.
Chapter 7
Useful Resources
Online resources on differential equations.
Course Content
Week
Chapter in Textbook
Topics
1
Introduction.
1.1
1.2
2
Solutions and Differential Equations and Initial
Value Problems.
Existence and Uniqueness Theorem.
1.2
First Order Differential equations and Separable
Equations.
3
4
5
Linear Equations, Exact Equations and Special
Integrating Factors.
Bernoulli Equation, Homogeneous Equations
and Clairaut Equation.
Higher order Differential Equations.
Linear Differential Operators.
Fundamental Solutions of Differential Equations.
7
8
9
10
Homogeneous Linear Equations with Constant
Coefficients.
Cauchy_Euler Equations and Reduction of
Order.
Auxiliary Equations with Complex Roots.
Methods of Undetermined Coefficients.
Methods of Variation of Parameters
Mechanical Vibrations and Simple Harmonic
Motion.
2.6
2.6
4.2
4.3
4.5, 4.6
4.4
4.6, 6.2
4.7, 4.8, 4.9
4.1, 4.11, 4.12
Damped Free and Forced Vibrations.
Definition of Laplace Transform .
Properties of Laplace Transform and Its Inverse.
11
2.2, 2.4, 2.5
Substitutions and Transformations.
Orthogonal Trajectories.
6
2.3
Solving Initial Value Problems Using Laplace
Transform.
7.2, 7.3, 7.4
7.5
8.2
Power Series.
12
Radius Of Convergence and Ordinary and
Singular Points.
8.2, 8.3
13
Series Solution of Differential Equations.
14
Review of Matrices and Vectors.
Linear Systems in Normal Form.
8.3, 8.4
9.3
15
Homogeneous Systems with constant
Coefficients.
Non_homogeneous Linear Systems.
9.4
9.5, 9.6
9.7
Additional Notes
The students need to do many exercises in order to be able to understand how to solve different types of
differential equations. In addition, it is good for the students to review previous exams and try to solve them.