Math 260 Syllabus (022)

Dept. Math. Sci., KFUPM

K. M. Furati

 

Course:           Math 260 Introduction to Differential Equations and Linear Algebra (3-0-3)

Textbook:       Differential Equations and Linear Algebra, C. H. Edwards and D. E. Penney, Prentice Hall 2001.

Objectives:     This course introduces elementary differential equations and linear algebra to students of CCSE.

Course Description: Systems of linear equations. Rank of matrices. Eigenvalues and eigenvectors. Vector spaces, subspaces, bases, dimensions. Invertible matrices. Similar matrices. Diagonalizable matrices. Block diagonal and Jordan forms.  First order differential equations: separable and exact. The homogeneous differential equations with constant coefficients. Wronskian. Non-homogeneous differential equations. Methods of undetermined coefficients and variation of parameters. Systems of differential equations. Non-homogeneous systems.  

Corequisite:    Math 201.

 

Wk

Dates

Sec

 

Topics

Suggested Homework*

1

Feb 23-26

1.1       1.2

Differential Equations & Mathematical Models                            

Integrals as General and Particular Solutions

2, 10, 21, 30, 34, 40         

2, 6, 14, 22, 33

2

Mar 1-5

1.4      1.5

Separable Equations & Applications                       Linear First Order Equations

2, 12, 17, 24, 30

3

Mar 8-Mar 12

1.5      1.6

Linear First Order Equations (Contd.)      Substitution Methods and Exact Equations

4, 10, 24, 26, 33                    2, 8, 14, 22, 38, 47

4

Mar 15-19

3.1     3.2

Introduction to Linear Systems                            Matrices and Gaussian Elimination

4, 22, 24, 28                         2, 8, 12, 28

5

Mar 22-26

3.3     3.4

Reduced Row-Echelon Matrices                             Matrix Operations

4, 8, 10, 20, 35                2, 10, 20, 29, 36

6

Mar 29-Apr 2

3.5     3.6

Inverses of Matrices                                     Determinants

4, 14, 22, 26, 32                  2, 4, 10, 20, 28, 50

Exam I.  Sunday, March 30, 6:30 pm.

7

Apr. 5-Apr. 9

4.1     4.2

The Vector Space R3                                                    The Vector Space Rn and Subspaces

2, 8, 12, 18, 22                 2, 8, 16, 20, 28

8

Apr 12-16

4.3     4.4

Linear Combination and Independence                    Bases and Dimension for Vector Spaces

2, 6, 10, 20, 24                 2, 8, 12, 18, 22

9

Apr 19-23

5.1     5.2

Second Order Linear Equations

General Solutions of Linear Equations.

2, 12, 16, 19, 26               4, 10, 14, 24, 26

10

Apr 26-30

5.3     5.5

Homogeneous Equations with Constant Coefficients Undetermined Coefficients

2, 4, 24, 28, 34                4, 12, 26, 32

11

May 3-7

5.5     6.1

Variation of Parameters                                  Introduction to Eigenvalues

48, 54, 57, 60                                           2, 16, 24, 30, 36

Exam II.  Tuesday, May 6, 6:30 pm.

12

May 10-14

6.2     6.3

Diagonalization of Matrices                           Applications involving Powers of Matrices

4, 16, 26, 28, 32              2, 10, 20, 34

13

May 17-21

7.1     7.2

First Order Systems & Applications                    Matrices and Linear systems

2, 6, 12, 18                      4, 10, 14, 20, 23

14

May 24-28

7.3     7.5

The Eigenvalue Method for Linear Systems        Multiple Eigenvalue Solutions

2, 6, 18, 26, 38

15

May 31-Jun 4

7.5

Multiple Eigenvalue Solutions (Contd.)

2, 11, 12, 16, 26

16

Jun 7

 

Review