Math 260 Syllabus (022)
Dept. Math. Sci., KFUPM
K. M. Furati
Course: Math 260 Introduction to Differential Equations and Linear Algebra (303)
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. Nonhomogeneous differential equations. Methods of undetermined coefficients and variation of parameters. Systems of differential equations. Nonhomogeneous systems.
Corequisite: Math 201.
Wk 
Dates 
Sec 
Topics 
Suggested Homework^{*} 
1 
Feb 2326 
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 15 
1.4 1.5 
Separable Equations & Applications Linear First Order Equations 
2, 12, 17, 24, 30 
3 
Mar 8Mar 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 1519 
3.1 3.2 
Introduction to Linear Systems Matrices and Gaussian Elimination 
4, 22, 24, 28 2, 8, 12, 28 
5 
Mar 2226 
3.3 3.4 
Reduced RowEchelon Matrices Matrix Operations 
4, 8, 10, 20, 35 2, 10, 20, 29, 36 
6 
Mar 29Apr 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. 5Apr. 9 
4.1 4.2 
The Vector Space R^{3} The Vector Space R^{n} and Subspaces 
2, 8, 12, 18, 22 2, 8, 16, 20, 28 
8 
Apr 1216 
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 1923 
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 2630 
5.3 5.5 
Homogeneous Equations with Constant Coefficients Undetermined Coefficients 
2, 4, 24, 28, 34 4, 12, 26, 32 
11 
May 37 
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 1014 
6.2 6.3 
Diagonalization of Matrices Applications involving Powers of Matrices 
4, 16, 26, 28, 32 2, 10, 20, 34 
13 
May 1721 
7.1 7.2 
First Order Systems & Applications Matrices and Linear systems 
2, 6, 12, 18 4, 10, 14, 20, 23 
14 
May 2428 
7.3 7.5 
The Eigenvalue Method for Linear Systems Multiple Eigenvalue Solutions 
2, 6, 18, 26, 38 
15 
May 31Jun 4 
7.5 
Multiple Eigenvalue Solutions (Contd.) 
2, 11, 12, 16, 26 
16 
Jun 7 

Review 
