MCS 258, Introduction to Differential Equations
Department of Mathematics and Computer Sciences
Methods of
Instruction
Theor.
Appl.
Lab.
Intern.
Project/Field
Work
Other
Total
Credit
28
28
-
-
-
-
56
(2 2 3)
Sem.
Spring 2010-2011
Instructor
Assoc. Prof.Dr. Thabet Abdeljawad
Schedule
Thursday: 8:40-10:30, Friday:12:40-14:30.
Office Hours
Tuesday: 13:40-15:30, Wednesday: 9:40-11:30
Prerequisite
-
Catalog
Description
Existence-uniqueness theorem of first order initial value problems. First order equations
(Separable, exact, linear, etc.). Higher order linear ordinary differential equations. Constant
coefficient equations. Reduction of order method, method of undetermined coefficients, method
of variation of parameters. Cauchy-Euler equations. Power series solutions. The Laplace
transform. Convolution integral. Solution of initial value problems using Laplace transform.
Solution of systems of linear differential equations by simple elimination and by the Laplace
transform, Fourier Analysis: Odd and Even Functions, Periodic Functions Trigonometric Series,
Fourier Series and Fourier Sine and Fourier Cosine Series for Functions of any Period function
Partial Differential Equations: Separation of Variables, Solution of the One-Dimensional Heat
Equation.
Textbook
1. Shepley L. Ross, Differential Equations.
Reference
Books
1. Dennis G. Zill, Michael R. Cullen, Advanced Engineering Mathematics
Evaluation
Criteria
Exam Dates
ECTS
Credit
Number of
Percentages
Midterm Exams
2
60
Quiz
-
Homework
-
Class Participation
Attendance
5
Final Exam
1
40
First Midterm: 25 March Friday. 17:40
Second Midterm: 29 April, Friday. 17:40.
COURSE CHART
Week Date
1
Section Covered and Comments
14 -18 Feb.
First Order Ordinary Differential Equations: Preliminaries,
Solutions Existence-Uniqueness Theorem
2
21-25 Feb.
3
28 Feb.- 4 March
Homogeneous Equations, Finding Integrating Factors, Special
Transformations (Equations Reducible to Homogeneous Equations)
4
7-11 March.
Higher Order Linear Ordinary Differential Equations: Basic Theory of
Higher Order Linear Equations, Reduction of Order Method
5
14-18 March
Homogeneous Constant Coefficient Equations, Undetermined
Coefficients Method,
6
21-25 March
Variation of Parameters Method
Exact Equations, Separable Equations, Linear Equations, Bernoulli
Equations,
First Midterm (End of March)
Cauchy-Euler Equations, Series Solutions of Ordinary Differential
Equations:
7
28 Mar.-1 Apr.
Power Series Solutions (Ordinary Point)
Power Series Solutions (Ordinary Point) (continued)
8
4-8 Apr.
Power Series Solutions (Regular-Singular Point).
9
11-15 Apr.
Laplace Transforms: Basic Properties of the Laplace Transforms,
Convolution
18-22 Apr.
10
Sat. (Holiday April 23)
11
25-29 Apr..
Inverse Laplace Transforms
Solution of Differential Equations by the Laplace Transform
Second Midterm (End of April)
12
2-6 May
9-13 May
13
Laplace Transform of piecewise functions and unit step functions
Fourier Analysis: Odd and Even Functions, Periodic Functions
Trigonometric Series, Fourier Series and Fourier Sine and Fourier
Cosine Series for Functions of any Period function
16-20 May
14
(Holiday May 19)
Partial Differential Equations: Separation of Variables, Solution of the
One-Dimensional Heat Equation
15
23-27 May
Worked Examples, Exercises