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MONTH
or WEEK
| DAY
| Topic, Event
| Section;
Homework
Problems
| Assigned
Proof
|
| JANUARY
|
Chapter 1: Vectors & Matrices
§7.1: Complex Vectors & Matrices |
| |
| WEEK 1
| 14-18 January
|
|
| Mon 14
| Course Introduction
Syllabus, Objectives
|
|
|
|
|
| Vector operations
| §1.1 #1,4,5,6,8,9,14,20
| §1.1 #11
|
|
| Tue 15
| The Dot Product
| §1.2 #2,5,7,9,10,12-17,19-21
| §1.2 #11
|
|
| Thu 17
| Proof Techniques
| §1.3 #1,5,8,14,19
|
|
| Fri 18
| Proof Techniques
|
| §1.3 #4
|
| WEEK 2
| 21-25 January
|
|
| Mon 21
|  Martin Luther King Day Holiday
No class meeting
|
|
| Tue 22
| Matrix Operations
| §1.4 #1(d),(h),(j), 2(H),(K),(M), 3(a), 14
| §1.4 #13
|
|
| Thu 24
| Matrix Multiplication
| §1.5 #1(a),(i),(n), 2(b),
7-9,13,19,20,21(b),23,26
| §1.5 #14(b)
|
|
| Fri 25
| Complex Vectors & Matrices
| §7.1 #1,3(a),(c),(d),(f),(i), 6-9
| §7.1 #10
|
Chapter 2: Systems of Linear Equations
§10.1: Elementary Matrices |
| |
| WEEK 3
| 28 January - 1 February
|
|
| Mon 28
| Gaussian Elimination
| §2.1 #1(a),(e)(g),2(b),(c),3,5,8,9
| §2.1 #10
|
|
| Tue 29
| Reduced Echelon Form
| §2.2 #1,2(a),(d),(f),3,4(a),5(b),7,8,12,13
| §2.2 #11(a),(c),(d)
|
|
| Thu 31
| Equivalent Systems, Rank and Row Space
| §2.3 #1,2,5(e),(f),6(a),7,
8(a)-(c),9(d),13,16,19,21
| §2.3 #18
|
| FEBRUARY
|
|
| Fri 1
| Inverses of Matrices
| §2.4 #2(a),(b),(d), 3(c),(d),(e), 4(a),(b),
6(a), 8, 10(a),(b), 13,14,20
| §2.4 #18
|
| WEEK 4
| 4 - 8 February
|
|
| Mon 4
| Matrix Inverses, continued
|
|
|
|
| Tue 5
| Elementary Matrices
| §10.1 #1,2(a),7,8,9
| §10.1 #3
|
|
| Thu 7
| REVIEW of Chapters 1 & 2 and §§7.1, 10.1
| §1.1 #26
§1.2 #23
§1.3 #25
§1.4 #15
§1.5 #27
§7.1 #11
§2.1 #11
§2.2 #14
§2.3 #22
§2.4 #21
§10.1 #10
|
|
| Fri 8
| Hour Exam 1: Chapters 1 & 2 and §§7.1, 10.1.
Objectives for Hour Exam 1.
|
Chapter 3: Determinants and Eigenvalues
§7.2: Complex Eigenvalues and Eigenvectors |
| |
| WEEK 5
| 11-15 February
|
|
| Mon 11
| Introduction to Determinants
| §3.1 #1(c),(i), 2(a),(b), 3(c), 5(a),(b),
9(a),(b), 10,11(a),(b), 12,16
| §3.1 #14
|
|
| Tue 12
| Determinants and Row Reduction
| §3.2 1,2(c),(d), 3(c),(d), 4(a),(c), 5,7,8,11
|
|
|
| Thu 14
|
|
| §3.2 #12
|
|
| Fri 15
| Further Properties
| §3.3 2(c),(d), 4(c), 8,15,16,21
| §3.3 #19
|
| WEEK 6
| 18-22 February
|
|
| Mon 18
| Eigenvalues and Diagonalization
| §3.4 1(d),(e), 2(b),(c), 3(a),(c),(g),(h),
4(a),(b),(g), 5(b),(c), 6,12,15,16,22,23
|
|
|
| Tue 19
| Eigenvalues, continued
|
| §3.4 #20
|
|
| Thu 21
| Complex Eigenvalues and Eigenvectors
In-Class Exercise:
2x2 Real Matrices with Complex Eigenvalues
[PostScript] [Acrobat]
Work in teams of 2-3.
| §7.2 1(c),2(c),3,4
| §7.2 #4(c)
|
| Chapter 4: Finite Dimensional Vector Spaces |
| |
|
| Fri 22
| Introduction to Vector Spaces
| §4.1 #3,6,12,14,18
| §4.1 #11
|
| WEEK 7
| 25-29 February
|
|
| Mon 25
| Subspaces
| §4.2 #1,2,5,7(d),11,13,14
|
|
|
| Tue 26
| Subspaces, continued
|
| §4.2 #18
|
|
| Thu 28
| Span
| §4.3 #1(b),(c),(f), 4,6,7,10,14,23,25
| §4.3 #24
|
|
| Fri 29
| Linear Independence
In-class Exercise: [PostScript] [Acrobat]
| §4.4 #1-4,7,9,12,13,16,22,26,27
|
|
| MARCH
|
| WEEK 8
| 3 - 7 March
|
|
| Mon 3
| Linear Independence, continued
|
| §4.4 #19
|
|
| Tue 4
| REVIEW of Chapters 3 & §§4.1-4.
|
|
|
|
| Thu 6
| Hour Exam 2: Chapter 3 & §§4.1-4.
Objectives for Hour Exam 2.
|
|
| Fri 7
| Basis and Dimension
| §4.5 #1(a),(d), 4,7,12-14,18,19,23
|
|
| WEEK 9
| 10-14 March
|
|
| Mon 10
| Basis and Dimension, continued
|
| §4.5 #15
|
|
| Tue 11
| Constructing Special Bases
| §4.6 #1,7,11,13,19
| §4.6 #15(a)
|
|
| Thu 13
| Coordinatization
| §4.7 #1(a),(b),(e),(f),(h),(i),
2(a),(c),(e),(g), 5,6
|
|
|
| Fri 14
| Coordinatization, continued
|
| §4.7 #7(b)
|
SPRING RECESS
17 - 21 MARCH |
Chapter 5: Linear Transformations
§7.3: Complex Vector Spaces |
| |
| WEEK 10
| 24-28 March
|
|
| Mon 24
| Introduction to Linear Transformations
| §5.1 1,5,7,8,12-14,
16,17,22,23,27,28
|
|
|
| Tue 25
| Linear Transformations, continued
Appendix B: Functions
| Appendix B #2,4-8,10,11
| §5.1 #18
|
|
| Thu 27
| The Matrix of a Linear Transformation
| §5.2 2, 3(a)-(c), 6(c),7(b),8(b),
11,12, 13(c),(d), 17,18,21,23
|
|
|
| Fri 28
| Matrix of Linear Transformation, continued
|
| §5.2 #27
|
| WEEK 11
| 31 March - 4 April
|
|
| Mon 31
| The Dimension Theorem
| §5.3 #1,3,6,7,9,11,13
| §5.3 #17
|
| APRIL
|
|
| Tue 1
| Isomorphism
| §5.4 #1,3,5,7,10,11,12,14,27
|
|
|
| Thu 3
| Isomorphism, continued
|
| §5.4 #20
|
|
| Fri 4
| Diagonalization of Linear Operators
| §5.5 #1(e),(f), 4,5,7,8,10,15,16
|
|
| WEEK 12
| 7-11 April
|
|
| Mon 7
| Diagonalization, continued
|
| §5.5 #13
|
|
| Tue 8
| Complex Vector Spaces
| §7.3 #2
| §7.3 #4
|
|
| Thu 10
| REVIEW of Chapters 4 & 5
| §4.5 #13
§4.7 #6
§5.2 #14
§5.5 #10
|
|
|
| Fri 11
| Hour Exam 3: Chapters 4 & 5
Objectives for Hour Exam 3.
|
| WEEK 13
| 14-18 April
|
Chapter 6: Orthogonality
§§7.4-5: Orthogonality in C^n,
Inner Product Spaces
§§8.10 & 8.3: Least Squares Problems |
| |
|
| Mon 14
| Orthogonal Bases, Gram-Schmidt algorithm
| §6.1 #1, 3(a)(b), 4(a),(b),
5(b)(d), 7(a)(b), 9-11, 15
|
|
|
| Tue 15
|
|
| §6.1 #12
|
|
| Thu 17
| Orthogonal Complement
| §6.2 #1(b)(d)(f), 2(b)(d), 4(a)(b), 5,
7-9, 10(b)(c), 11-13, 18, 21, 22
|
|
|
| Fri 18
|
|
| §6.2 #14
|
| WEEK 14
| 21-25 April
|
|
| Mon 21
| Orthogonal Diagonalization
| §6.3 #1, 3(a)(c)(d)(f), 6,7,9,11,12
| §6.3 #10
|
|
| Tue 22
| Least Squares
| §8.10 #1,4
|
|
|
| Thu 24
|
|
| §8.10 #5
|
|
| Fri 25
| Least squares polynomials
| §8.3 #1,2,4(b),6,9
| §8.3 #8
|
| WEEK 15
| 28 April - 2 May
|
|
| Mon 28
| Orthogonality in C^n
| §7.4 #4,5,11,12,14
| §7.4 #7(b)
|
|
| Tue 29
| Inner product spaces over a field
| §7.5 #1-4,7-8,12,16,25,29
| §7.5 #11
|
| MAY
|
|
| Thu 1
| REVIEW
|
|
|
|
| Fri 2
| REVIEW
|
|
|
FINAL
EXAMS
| 5 - 9 May
|
|
|
|
| Fri 9
| FINAL EXAM
7:30 - 9:30am, 4 Carver
Objectives for final exam.
|
|
