King Fahd University of Petroleum and Minerals Department of Mathematics & Statistics Syllabus Math 260 Semester II, 2010 (092) Coordinator: Dr. Faisal Abdul-Karim Fairag

 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. 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.

 W Date Section Topic Homework 1 Feb 20-Feb 24 3.1 Introduction to Linear Systems 2, 22, 24, 26 Part I: Linear Algebra 3.2 Matrices and Gaussian Elimination 4, 8, 14, 28 3.3 Reduced Row-Echelon Matrices 2 Feb 27-Mar 03 3.3 Reduced Row-Echelon Matrices 3, 10, 24, 35 3.4 Matrix Operations 3, 10, 20, 24 3.5 Inverse of Matrices 4, 12, 20, 28 3 Mar 06-10 3.6 Determinants 2, 4, 12, 30, 40, 43 4.1 The Vector Space R3 1, 6, 13, 16, 24, 26, 30 4.2 The Vector Space Rn & Subspaces 3, 8, 16, 19 4 Mar 13-17 4.3 Linear Combination & Independence of Vectors 1, 6, 12, 17, 26 4.4 Bases & Dimension for Vector Spaces 3, 8, 13, 16, 22 5 Mar 20-24 4.5 Row and Column Spaces 1, 7, 13, 15, 17, 25, 26 6.1 Introduction to Eigenvalues 2, 15, 24, 28, 36 Review (Exam-1) 6 Mar 27-31 Review (Exam-1) Exam -1 (Sund Mar 28)  6pm B54  ( 3.1 - 4.5 ) 6.2 Diagonalization of Matrices 2, 14, 25, 28 7 Apr 03- 07 6.3 Applications involving Powers of Matrices 2, 10, 20, 26, 36 7.5 Jordan form (pp 454-457) 8 Apr 10-14 7.5 Jordan form (pp 454-457) 37, 38, 41, 43 1.1 Differential Equations and Mathematical Models 2, 12, 22, 30, 36, 40 PartII: Differential Equations 1.2 Integrals as General & Particular Solutions (page: 10-11) 4, 6, 15, 18 Apr 17-21 Midterm Midterm Vacation Midterm Vacation 9 Apr 24-28 1.4 Separable Equations & Applications 1, 10, 24, 27, 33 1.5 Linear First-Order Equations 4, 12, 24, 28, 32 Review (Exam-2) 10 May 01-05 Review (Exam-2) Exam -2 (Sund May 2)  6pm B54  ( 6.1 - 1.5 ) 1.6 Substitution Methods & Exact Equations 2, 10, 22, 40, 60 2.4 Euler's Method 3, 7, 12 11 May 08-12 5.1 Second-Order Linear Equations 1, 11, 16, 19, 25, 28, 44 5.2 General Solutions of Linear Equations 2, 8, 13, 24, 26 12 May 15-19 5.3 Homogeneous Equations with Constant Coefficients 1, 4, 14, 22, 28, 33, 38 5.5 Method of Undetermined Coefficients 4, 12, 26, 32, 36 13 May 22-26 7.1 First-Order Systems & Applications 2, 8, 13, 18, 21 7.2 Matrices & Linear Systems 2, 4, 12, 16, 20, 25 14 May 29-Jun2 7.3 The Eigenvalue Method for Linear Systems 4, 9, 18, 24, 26 7.5 Multiple Eigenvalue Solutions 15 Jun 5-9 7.5 Multiple Eigenvalue Solutions (contd.) 4, 10, 16, 28, 30 Review Jun-19 Final Exam (sat 7pm) comperhenxive

 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. MATLAB will be used whenever possible. KFUPM attendance policy will be enforced.