King Fahd University of Petroleum and Minerals

Department of Mathematics and Statistics

SYLLABUS

Semester II: 2007-2008(072)

(Instructor: Dr. Faisal Fairag)

Course #:

MATH 202

Title:

Elements of Differential Equations

Textbook:

A First Course in Differential Equations by D.G. Zill, 8th Edition

Course Description:

Special functions. Besselís functions and Legendre polynomials. Vector analysis including vector fields, divergence, curl, line and surface integrals, Greenís, Gaussí and Stokesí theorems. Systems of differential equations. Sturm-Liouville theory. Fourier series and transforms. Introduction to partial differential equations and boundary value problems.

 

Week

Date

Sec.

Topics

Homework††††††††††††††††††††††††††††††††††††††††††

(CAS)

1

Feb 12-16*

1.1

1.2

Definition and Terminology

Initial-Value Problems

4, 7, 8, 9, 10, 13, 16, 20, 27, 28, 30

2, 12, 20, 22, 27

(55)

--

2

Feb 18-22

2.2

2.3

Separable Variables

Linear Equations

1, 21, 24

8, 14, 20, 22, 23, 27, 45

(5,7)

(ex 4)

3

Feb 25-Mar 01

2.4

2.5

Exact Equations

Solutions by Substitutions

5, 13, 16, 18, 30, 37

2, 5, 8, 15, 25, 27, 29, 31, 42(a), 43, 44

(5,9)

--

4

Mar 04-08

2.1

1.3

 

 

3.1

Solution Curves (light coverage)

Mathematical Models (reading): Growth and Decay, Newtonís Law of Cooling and Mixtures

Linear Models

4, 6, 10, 13, 18, 21, 26, 30

See Sec.# 3.1

 

 

3, 6, 13, 14, 15, 19, 20, 21, 23

--

 

 

 

--

5

Mar 11-15

4.1

4.1.1

4.1.2

Linear Equations: Basic Theory

Initial-Value and Boundary-Value

Homogeneous Equations

 

3, 10, 12, 13

15, 21, 23, 28

 

--

††††††††† --

EXAM I on Wednesday, March 15, 2006.

6

Mar 18-22

4.1.3

4.2

Nonhomogeneous Equations

Reduction of Order

33, 36, 37(b,e)

1, 3, 12, 14, 19

--

--

7

Mar 25-29

4.3

 

4.5

 

Homogeneous Linear Equations with Constant Coefficients

Undetermined Coefficients Ė Annihilator Approach

4, 9, 12, 15, 20, 34, 40, 49, 50, 51

 

8, 13, 22, 24, 34, 41, 48, 64, 67, 73

(57)

 

--

 

Midterm Break: Sat-Sun, April 01-02, 2006

8

Apr 03-05

4.6

4.7

Variation of Parameters

Cauchy-Euler Equation (Both Methods)

6, 11, 13, 24, 25, 28

3, 5, 10, 11, 14, 16, 19, 31, 34, 37, 39

--

(44)

9

Apr 08-12

6.1

6.1.1

6.1.2

Solutions About Ordinary Points

Review of Power Series

Power Series Solutions

 

1, 10, 11

15, 17, 20, 22, 32

 

--

--

10

Apr 15-19

6.2

Solutions about Singular PointsÓ

3, 10, 13, 14, 19, 20, 27

(ex 5)

EXAM II: Wednesday, April 19, 2006.

11

Apr 22-26

App II

 

Matrices and Linear Systems(review)

The Eigenvalue Problem

14, 15, 19, 23, 27, 29, 31, 33, 39, 43

47, 49, 52, 53, 55

--

--

12

Apr 29-May 03

8.1

8.2

Preliminary Theory

Homogeneous Linear Systems

4, 5, 8, 14, 15, 17, 23, 25

--

13

May 06-10

8.2.1

8.2.2

8.2.3

Distinct Real Eigenvalues

Repeated Eigenvalues

Complex Eigenvalues

3, 7, 10, 13

19, 21, 23, 25, 27

33, 34, 36, 39, 41, 45

(ex 2)

--

--

14

May 13-17

8.3

8.3.2

8.4

Nonhomogeneous Linear Systems

Variation of Parameters

Matrix Exponential

 

11, 12, 23, 32

1, 5, 9, 2, 6, 4, 8

 

(35 (a,b))

(27(a))

15

May 20-24, + May 27**

Pace Adjustment, Review

 

 

*Thursday: Normal Saturday Classes.††† **Last day of classes: Sunday, May 28, 2006.



Ó Some statements about Besselís equation and Legendreís equation should be included in the final remarks about Series Solutions.See the introductory paragraph of Section 6.3 in page 259.