King Fahd University of Petroleum and Minerals

Department of Mathematical Sciences

Syllabus Math 260                                Second Edition (2005)

Semester 1, 2005-2006 (051)

(Coordinator: Dr. A. Shawky Ibrahim)

Course:             Math 260 (Introduction to Differential Equations and Linear Algebra)

Text Book:         Differential Equations and Linear Algebra, C. H. Edwards and D. E. Penny, Prentice

Hall, Second Edition (2005).

Objectives:         This course introduces elementary differential equations and linear algebra to students of Computer Science, Computer Engineering, System Engineering and Earth Sciences.

Week

Date

## Topic

Suggested

Homework

1

Sept 10-14

1.1

1.2

Differential Equations & Mathematical Models

Integrals as General & Particular Solutions

2, 11, 20, 30, 32, 39

4, 6, 15, 18

2

Sept. 17-21

1.4

1.5

Separable Equations & Applications

Linear First-Order Equations

1, 10, 24, 27, 33

# Saturday, September 24, 2005:  National Holiday

3

Sept 25-28

1.5

1.6

Linear First-Order Equations (contd.)

Substitution Methods & Exact Equations

4, 12, 24, 28, 32

2, 10, 22, 40, 60

4

Oct. 01-05

3.1

3.2

Introduction to Linear Systems

Matrices and Gaussian Elimination

2, 22, 24, 26

4, 8, 14, 28

5

Oct 8-12

3.3

3.4

Reduced Row-Echelon Matrices

Matrix Operations

3, 10, 24, 35

3, 10, 20, 24

# Saturday, October 15, 2005: Suggested Time for Exam I

6

Oct 15-19

3.5

3.6

Inverse of Matrices

Determinants

4, 12, 20, 28

2, 4, 12, 30, 40, 43

7

Oct 22-26

4.1

4.2

The Vector Space R3

The Vector Space Rn & Subspaces

1, 6, 13, 16, 24, 26, 30

3, 8, 16, 19

Thursday, October 27 to Friday, November 11, 2005: Id al-Fitr Vacation

8

Nov. 12-16

4.3

4.4

Linear Combination & Independence of Vectors

Bases & Dimension for Vector Spaces

1, 6, 12, 17, 26

3, 8, 13, 16, 22

9

Nov. 19-23

5.1

5.2

Second-Order Linear Equations

General Solutions of Linear Equations

1, 11, 16, 19, 25, 28, 44

2, 8, 13, 24, 26

10

Nov 26-30

5.3

5.5

Homogeneous Equations with Constant Coefficients

Method of Undetermined Coefficients

1, 4, 14, 22, 28, 33, 38

4, 12, 26, 32, 36

# Saturday, December 03, 2005: Suggested Time for Exam II

11

Dec 03-07

5.5

6.1

Method of Variation of  Parameters

Introduction to Eigenvalues

47, 52, 57, 60

2, 15, 24, 28, 36

12

Dec 10-14

6.2

6.3

Diagonalization of Matrices

Applications involving Powers of Matrices

2, 14, 25, 28

2, 10, 20, 26, 36

13

Dec. 17-21

7.1

7.2

First-Order Systems & Applications

Matrices & Linear Systems

2, 8, 13, 18, 21

2, 4, 12, 16, 20, 25

14

Dec 24-28

7.3

7.5

The Eigenvalue Method for Linear Systems

Multiple Eigenvalue Solutions

4, 9, 18, 24, 26

15

Dec 31-Jan 04

7.5

Multiple Eigenvalue Solutions (contd.)

Review

4, 10, 16, 28, 30

# Thursday, January 5, 2005 to Friday, January 20, 2006: Id al-Adha Vacation

 Saturday, January 21, 2006: Review (Last Class) Final Examinations Period from 22 to 31 of January, 2006

 The Dates of Exam I and Exam II are suggested by the College of Sciences to avoid any conflicts with other exams. The date of the final exam will be announced by the Registrar. The Final Exam is comprehensive. KFUPM policy with regard to attendance will be enforced. MATLAB will be used whenever possible.

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