King Fahd University of Petroleum and Minerals |

Department of Mathematics & Statistics |

Syllabus Math 260 |

Semester II, 2010 (092) |

Coordinator: Dr. Faisal Abdul-Karim Fairag |

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

Differential Equations and Linear Algebra, C.
H. Edwards and D. E. Penny, Prentice Hall, Second Edition (2005).Text Book: |

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

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.Course Description: |

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 R^{3} |
1, 6, 13, 16, 24, 26, 30 | |||

4.2 |
The Vector Space R^{n}
& 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. |