Linear Analysis I

Dr. Dana Paquin

Spring 2010

Course materials such as the syllabus, lab and project assignments, quizzes and quiz solutions, exam information, etc. are posted in Blackboard.

The following is an

Class | Date | Quiz/Test/Assignment Due | Topics Covered (lab and project
assignments, quizzes and quiz solutions, exam information and other
materials are posted on the Course Materials page in
Blackboard) |
Problems |

1 | Monday March 29 | Introduction to
Math 244 1.1: Differential Equations and Mathematical Modeling 1.2: Integrals as general and particular solutions |
1.1: 1, 3, 7, 13, 15, 17, 19, 25, 27, 33, 37, 39 1.2: 1, 3, 5, 7, 9, 11, 13, 19, 25, 29, 31 | |

2 | Tuesday March 30 | 1.3: Slope
fields and solution curves 1.4: Separable Equations and Applications | 1.3: 3, 5, 7, 21 1.4: 1, 3, 5, 7, 11, 17, 19, 23, 27, 35, 37, 47 | |

3 | Thursday April 1 | 1.5: Linear First-Order Equations | 1.5: 1-23 odd | |

4 | Friday April 2 | Introduction to
Maple and Wolfram Alpha Lab 1: Slope Fields andGraphing in Maple |
Work on Lab 1 Use Wolfram Alpha to practice graphing functions and finding derivatives and integrals. | |

5 | Monday April 5 | 3.1: Introduction
to Linear Systems 3.2: Echelon Matrices and Gaussian Elimination | 3.1: 1, 5, 13, 15, 17, 23, 25 | |

6 | Tuesday April 6 | Quiz 1 on 1.1-1.5 This
will be a | 3.2: Echelon Matrices and Gaussian Elimination | 3.2: 1-25 odd |

7 | Thursday April 8 | NO CLASS | ||

8 | Friday April 9 | NO CLASS | ||

9 | Monday April 12 | 3.3: Reduced Row-Echelon Matrices | 3.3: 1-25 odd, 33, 34 | |

10 | Tuesday April 13 | Coffee To Go Project
Due Quiz 2 on 3.1, 3.2 This will be an Tuesday's office hours will be on Monday April 12 from 2:15 to 3:30 pm (this week only) | 3.4: Matrix Operations, Part 1 | 3.4: 1-4 |

11 | Thursday April 15 | 3.4: Matrix Operations, Part 2 | 3.4: 9, 11, 15, 19, 23, 27, 29, 31, 33, 35, 37 | |

12 | Friday April 16 | Lab: How do GPS Systems Work? | ||

13 | Monday April 19 | NO CLASS | ||

14 | Tuesday April 20 | 3.5: Inverses of Matrices | 3.5: 5, 7, 11, 17, 23, 27, 32 | |

15 | Thursday April 22 | Quiz 3 on 3.3, 3.4
This will be a | 3.5:
Inverses 3.6: Determinants | 3.6: 1, 3, 5, 43, 50, 51, 52, 53 |

16 | Friday April 23 | Work on GPS Lab | ||

17 | Monday April 26 | GPS Lab Due | 3.6:
Determinants Review | |

18 | Tuesday April 27 | In-class Exam 1 (on material through Section 3.6) | ||

19 | Thursday April 29 | 4.1: The
Vector Space R^3 4.3: Linear Combinations and Independence of Vectors | 4.1: 1-13 odd, 19-27 odd 4.3: 1-21 odd | |

20 | Friday April 30 | Vectors Lab: Linear Combinations and Linear Independence | ||

20 | Monday May 3 | 4.3: Linear
Combinations and Independence of Vectors 4.4: Bases and Dimension for Vector Spaces | 4.3: 1-21 odd | |

21 | Tuesday May 4 | Vectors Lab Due Quiz 4 on 4.1, 4.3 (linear independence/dependence and linear combinations)
This will be a | 4.4: Bases and Dimension for Vector Spaces | 4.4: 1-7 odd, 15-25 odd Read Example 5 in Section 4.4 for an example of how to do numbers 15-25! |

22 | Thursday May 6 | 4.2:
Subspaces 4.5: Column Spaces and the Nullspace | 4.2: 1-17
odd 4.5: 1-11 odd Note: For problems 1-11 in Section 4.5, find a basis for the column space, AND THE NULLSPACE of each matrix. You do NOT have to find a basis for the row space. Also find the dimension of the column space and nullspace, and verify that the Rank-Nullity Theorem is satisfied. | |

23 | Friday May 7 | Lab: Column Space and Nullspace | ||

24 | Monday May 10 | Column Space and Nullspace Lab Due | 5.1: Introduction: Second-Order Linear Equations | 5.1: 1-15 odd, 33-47 odd |

25 | Tuesday May 11 | Quiz 5 on 4.2, 4.4,
4.5 This will be an | 5.3: Homogeneous Equations with Constant Coefficients | 5.3: 1, 3, 5, 7, 11, 13, 15, 19, 21,
25, 27 39 Note: For problems 1-31, you may use Wolfram Alpha (or another computational utility) to assist in finding the roots of the characteristic equation. |

26 | Thursday May 13 | 5.3: Homogeneous Equations with Constant Coefficients | 5.3: 9, 17, 23, 29, 31, 33-36, 40, 42 | |

27 | Friday May 14 | Maple Lab: 5.4: Mechanical Vibrations | ||

28 | Monday May 17 | NO CLASS | ||

29 | Tuesday May 18 | Mechanical Vibrations Lab Due | 5.5: Nonhomogeneous Equations and Undetermined Coefficients | 5.5: 1, 3, 5, 9, 13, 31, 33, 35 |

30 | Thursday May 20 | Review | ||

31 | Friday May 21 | In-class Exam 2 (Sections
3.6, 4.1-4.5, 5.1, 5.3, 5.5) The exam will be in the | ||

32 | Monday May 24 | 6.1: Eigenvalues and Eigenvectors | 6.1: 33, 34, 35 Review the definitions of eigenvector/eigenvalue and the proofs of Properties 1-3 from today's class. | |

33 | Tuesday May 25 | 6.1: Eigenvalues and Eigenvectors | 6.1: 1-25 odd For problems 1-25 odd, just find all eigenvalues and eigenvectors of each matrix. | |

34 | Thursday May 27 | Quiz 6 on 6.1 This
will be a | ||

35 | Friday May 28 | Maple Lab: 5.6: Forced Oscillations and Resonance | ||

35 | Monday May 31 | NO CLASS | ||

36 | Tuesday June 1 | Forced Oscillations Lab Due | 7.1: Linear Systems of DE's | 7.1 (note: these problems are on page 402 of your textbook!): 1, 3, 11-19 odd |

37 | Thursday June 2 | 7.3: The Eigenvalue Method for Linear Systems | 7.3 (note: these problems are on page 427 of your textbook!): 1-5 (just find the solutions, don't need to construct the direction field or solution curves), 17, 18 | |

38 | Friday June 3 | LAST DAY OF CLASS | Review |

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