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