Math 244
Linear Analysis
Dr. Dana Paquin
Spring 2009




Course materials such as the syllabus, lecture notes, Maple files, quizzes and quiz solutions, computer lab assignments, etc. are posted on the Course Materials page in Blackboard.

The following is an updated course schedule. You should check this schedule frequently for updated information on topics covered in class, suggested practice problems, assignment due dates, quiz and test dates, etc. The suggested practice problems listed on this page are problems that I recommend that you do in addition to the homework assignments that you are required to turn on. The weekly quizzes will often contain problems that are very similar to (or exactly the same as) the suggested practice problems.

Classes on Monday and Friday will meet in the Learning Commons computer lab, 035-0111B (first floor of Kennedy Library). Classes on Tuesday and Thursday will meet in 186-C201.

Class Date Quiz/Test/Assignment Due Topics Covered (lecture notes, Maple files, quiz solutions, and other materials are posted on the Course Materials page in Blackboard) Problems To Be Turned In Suggested Practice Problems
1 Monday March 30 Note: no class on Tuesday, March 31. Introduction to Math 244

The Computer Algebra System Maple

Viewable html version of the Some Basic Maple Commands worksheet

1.1: Differential Equations and Mathematical Modeling

Download and work through the "Getting Started: Some Basic Maple Commands" Maple worksheet posted in the "Computer Lab Assignments and Maple Files" folder on the Course Materials page in Blackboard.

Viewable html version of the Some Basic Maple Commands worksheet

2 Thursday April 2 1.1: Differential Equations and Mathematical Modeling

1.2: Integrals as general and particular solutions

HW 1 Due on Tuesday April 7:

1.1 # 8, 16, 22, 32, 38

1.1: # 1, 3, 7, 13, 15, 17, 19, 25, 27, 33, 37, 39, 43
3 Friday April 3 1.2: Integrals as general and particular solutions

Derivatives, integrals, and differential equations in Maple

1.3: Slope fields and solution curves

Viewable html file for working with derivatives, integrals, and differential equations in Maple

HW 1 Due on Tuesday April 7:

1.2 # 10, 16, 20, 26

1.2: 1, 3, 5, 7, 9, 11, 13, 19, 25, 29, 31
4 Monday April 6 1.3: Slope fields and solution curves

Slope fields in Maple

HW 2 Due on Friday April 10:

1.3: 6, 8 (do these problems by hand)

1.3: 5, 7
5 Tuesday April 7 HW 1 Due

Quiz 1

1.4: Separable Equations and Applications
6 Thursday April 9 1.5: Linear First-Order Equations HW 3 Due on Tuesday April 14:

1.4: 2, 12, 14, 22, 36, 39

1.4: 1, 11, 17, 19, 23, 37, 47
7 Friday April 10 HW 2 Due 2.4: Numerical Approximation: Euler's Method HW 3 Due on Tuesday April 14:

2.4: 6 (do this problem by hand)

2.4: 5 (by hand)
8 Monday April 13 2.4: Numerical Approximation: Euler's Method

In-class work on Maple Lab 1

9 Tuesday April 14 HW 3 Due

Quiz 2 (covers material through Section 1.4)

1.5: Linear First-Order Equations HW 4 Due on Friday April 17:

1.5: 2, 8, 14, 20, 22

1.5: 1-25 every other odd
10 Thursday April 16 3.1: Introduction to Linear Systems HW 5 Due on Tuesday April 21:

3.1: 12, 16, 20, 26, 33

3.1: 1, 5, 13, 15, 17, 23, 25
11 Friday April 17 HW 4 Due

Maple Lab 1 Due

3.1: Introduction to Linear Systems

3.2: Matrices and Gaussian Elimination

HW 5 Due on Tuesday April 21:

3.2: 6, 10, 14, 16, 18, 24

3.2: 1, 7, 13, 17, 19, 25
12 Monday April 20 3.2: Matrices and Gaussian Elimination
13 Tuesday April 21 HW 5 Due

Exam 1

14 Thursday April 23 3.3: Reduced Row-Echelon Matrices HW 6 Due on Tuesday April 28:

3.3: 8, 14, 16, 32

3.3: 1, 3, 7, 13, 17
15 Friday April 25 3.3: Reduced Row-Echelon Matrices

3.4: Matrix Operations

HW 6 Due on Tuesday April 28:

3.4: 4, 7, 8, 10, 14, 18, 23, 27, 31

3.4: 1, 9, 11, 15, 19, 29, 37
16 Monday April 27 Matrix Operations in Maple

3.5: Inverses of Matrices

17 Tuesday April 28 HW 6 Due

Quiz 3

3.5: Inverses of Matrices HW 7 Due on Friday May 1:

3.5: 4, 10, 18, 26, 30, 32

3.5: 5, 7, 11, 17, 23, 27, 35
18 Thursday April 30 3.6: Determinants HW 8 Due on Tuesday May 5:

3.6: 2, 4, 6, 41, 50

3.6: 1, 3, 5, 43
19 Friday May 1 HW 7 Due

Quiz 4

4.1: The Vector Space R^3 HW 8 Due on Tuesday May 5:

4.1: 2, 6, 10, 20, 26

4.1: 1, 5, 13, 21, 25
20 Monday May 4 In-class work on Maple Lab 2
21 Tuesday May 5 Quiz 5 (covers material through Section 3.6)

HW 8 Due

4.3: Linear Combinations and Independence of Vectors HW 9 Due on Friday May 8:

4.3: 6, 8, 12, 14, 18, 20

4.3: 3, 5, 9, 11, 13, 15, 17, 19, 21
22 Thursday May 7 4.3: Linear Combinations and Independence of Vectors

4.4: Bases and Dimension for Vector Spaces

23 Friday May 8 Quiz 6 (covers material through Section 4.3)

HW 9 Due

4.4: Bases and Dimension for Vector Spaces HW 10 Due on Tuesday May 12:

4.4: 2, 6, 8, 16, 22

4.4: 1, 3, 5, 7, 15, 17, 21, 23
24 Monday May 11 Maple Lab 2 Due 4.5: Row and Column Spaces HW 11 Due on Friday May 15:

4.5: 2, 4, 6, 8, 12.

Find a basis for the row space, column space, AND THE NULLSPACE of each matrix. Note that your answer for the row space may not match the answer given in the back of the book. Also find the dimension of each space, and verify that the Row Rank Equals Column Rank and Rank-Nullity Theorems are satisfied.

4.5: 1, 3, 5, 7, 9, 11.

Find a basis for the row space, column space, AND THE NULLSPACE of each matrix. Note that your answer for the row space may not match the answer given in the back of the book. Also find the dimension of each space, and verify that the Row Rank Equals Column Rank and Rank-Nullity Theorems are satisfied.

25 Tuesday May 12 Quiz 7 (covers material through Section 4.4)

HW 10 Due

5.1: Introduction: Second-Order Linear Equations

5.2: General Solutions of Linear Equations

HW 11 Due on Friday May 15:

5.1: 2, 12, 14, 16, 34, 36, 40

5.1: 1, 9, 13, 35, 39
26 Thursday May 14 5.3: Homogeneous Equations with Constant Coefficients HW 12 Due on Friday May 22:

5.3: 8, 10, 12, 18, 24, 40

5.3: 1, 7, 11, 17, 25, 39
27 Friday May 15 Quiz 8 (covers material through Section 5.2)

HW 11 Due

In-class Maple Lab: Review of Properties of Matrices
28 Monday May 18 In-class work on Lab Assignment 3, Part I

5.4: Mechanical Vibrations

Study for Exam 2

Work on Lab Assignment 3

29 Tuesday May 19 Exam 2

Exam 2 will be on Sections 3.3-3.6, 4.1, 4.3-4.5, and 5.1-5.2.

Work on Lab Assignment 3
30 Thursday May 21 5.5: Nonhomogeneous Equations and Undetermined Coefficients HW 13 Due on Tuesday May 26:

5.5: 1, 2, 3, 4, 6, 11, 31

5.5: 5, 9, 15, 19, 33
31 Friday May 22 HW 12 Due

Note: No class on Monday May 25

5.6: Forced Oscillations and Resonance

In-class work on lab Assignment 3

Work on Lab Assignment 3
32 Tuesday May 26 Quiz 9 (covers material in Sections 5.3 and 5.5)

HW 13 Due

6.1: Introduction to Eigenvalues Read Section 6.1 in your text and start working on the homework from Section 6.1 (see below)
33 Thursday May 28 6.1: Introduction to Eigenvalues

6.2: Diagonalization of Matrices

HW 14 Due on Tuesday June 2:

6.1: 2, 12, 16, 22, 24

NOTE: For these problems, just find the eigenvalues and associated eigenvectors for each matrix.

6.1: 1-25 odd
34 Friday May 29 In-class work on Maple Lab 3
35 Monday June 1 Maple Lab 3 Due

6.2: Eigenvalues and Diagonalization of Matrices HW 15 NOT to be turned in (do these problems to prepare for the final):

6.2: 2, 6, 10, 14, 16

6.2: 1-27 odd
36 Tuesday June 2 Quiz 10 (on Section 6.1)

HW 14 Due

7.1: Linear Systems of DE's

7.2: Matrices and Linear Systems

37 Thursday June 4 7.3: The Eigenvalue Method for Linear Systems HW 16 NOT to be turned in (do these problems to prepare for the final):

7.3 (note: these problems are on page 427 of your textbook!): 2, 3, 4 (just find the solutions, don't need to construct the direction field or solution curves), 17, 18

38 Friday June 5 Review



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