Math 244 Sections 08 and 10
Linear Analysis I
Dr. Dana Paquin
Winter 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 updated course schedule. You should check this schedule frequently for updated information on topics covered in class, assigned practice problems, lab/project due dates, quiz and test dates, etc. Although you are not required to turn in the homework problems, I strongly recommend that you do at least these problems to master the material. The weekly quizzes will often contain problems that are very similar to the assigned practice problems.

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) Practice Problems
1 Monday January 4 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 January 5 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 January 7 1.5: Linear First-Order Equations 1.5: 1-25 odd
4 Friday January 8 Introduction to Maple and Wolfram Alpha Use Wolfram Alpha to practice graphing functions and finding derivatives and integrals.
5 Monday January 11 3.1: Introduction to Linear Systems 3.1: 1, 5, 13, 15, 17, 23, 25
6 Tuesday January 12 3.2: Echelon Matrices and Gaussian Elimination 3.2: 1, 9, 11, 15, 21
7 Thursday January 14 Quiz 1 on 1.1-1.5 Begin Newton's Law of Cooling Project Newton's Law of Cooling Project
8 Friday January 15 NO CLASS
Monday January 18 NO CLASS
9 Tuesday January 19 NO CLASS
10 Thursday January 21 3.2: Echelon Matrices and Gaussian Elimination

3.3: Reduced Row-Echelon Matrices

3.2: 3, 5, 7, 13, 17, 19, 25

3.3: 1-25 odd, 33, 34

11 Friday January 22 Newton's Law of Cooling Project Due Lab/Project: How do GPS Systems Work?
12 Monday January 25 3.4: Matrix Operations 3.4: 1, 9, 11, 15, 19, 23, 27, 29, 31, 33, 35, 37
13 Tuesday January 26 Quiz 2 on 3.1-3.3 3.5: Inverses of Matrices
14 Thursday January 28 3.5: Inverses of Matrices 3.5: 5, 7, 11, 17, 23, 27, 32
15 Friday January 29 Work on GPS Lab/Project
16 Monday February 1 GPS Lab/Project Due 3.6: Determinants 3.6: 1, 3, 5, 43, 50, 51, 52, 53
17 Tuesday February 2 4.1: The Vector Space R^3 4.1: 1-13 odd, 19-27 odd
18 Thursday February 4 In-class Exam 1 (on material through Section 3.6)
19 Friday February 5 NO CLASS
20 Monday February 8 4.2: The Vector Space R^n and Subspaces 4.2: 1-17 odd
21 Tuesday February 9 Quiz 3 on 4.1-4.2 4.3: Linear Combinations and Independence of Vectors 4.3: 1-21 odd
22 Thursday February 11 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!

23 Friday February 12 Maple Lab 4.5: Column Spaces and the Nullspace 4.5: 1-11 odd

Note: For problems 1-11, 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.

Monday February 15 NO CLASS
24 Tuesday February 16 5.1: Introduction: Second-Order Linear Equations

5.2: General Solutions of Linear Equations

5.1: 1-15 odd, 33-47 odd
25 Thursday February 18 Quiz 4 on 4.3, 4.4, 4.5 5.3: Homogeneous Equations with Constant Coefficients 5.3: 1-31 odd, 39

Note: For problems 1-31, you should use Wolfram Alpha (or another computational utility) to assist in finding the roots of the characteristic equation.

26 Friday February 19 Maple Lab on 4.5 Due Maple Lab: 5.4: Mechanical Vibrations
27 Monday February 22 5.5: Nonhomogeneous Equations and Undetermined Coefficients 5.5: 1, 3, 5, 9, 13, 31, 33, 35
28 Tuesday February 23 5.5: Nonhomogeneous Equations and Undetermined Coefficients

Review

29 Thursday February 25 In-class Exam 2 (on material from Section 4.1 through Section 5.5)
30 Friday February 26 Maple Lab: 5.6: Forced Oscillations and Resonance
31 Monday March 1 Maple Lab on 5.4 Due 6.1: Eigenvalues and Eigenvectors 6.1: 1-25 odd, 33, 34

For problems 1-25 odd, just find all eigenvalues and eigenvectors of each matrix.

32 Tuesday March 2 6.1: Eigenvalues and Eigenvectors Same as Monday's homework
33 Thursday March 4 Quiz 5 on 6.1
34 Friday March 5 NO CLASS
35 Monday March 8 7.1: Linear Systems of DE's

7.2: Matrices and Linear Systems

7.1 (note: these problems are on page 402 of your textbook!):

11-19 odd. For these problems, just find the solutions. You don't need to construct the direction field.

36 Tuesday March 9 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)

37 Thursday March 11 Review
38 Friday March 12 Maple Lab on 5.6 Due

LAST DAY OF CLASS

Work on 5.6 Lab
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