M369 Fall 2006 Course: Linear Algebra
Instructor: Dr. Iuliana Oprea
Department of Mathematics, Colorado State University
office:Weber 123, phone:1-6751,
url: http://www.math.colostate.edu/~juliana

email juliana'at'math.colostate.edu

General information Prerequisites
Textbook
Homework and quizzes Exams
Review Sheet 1, Review Sheet 2
Sample final exams
Review Session for the final exam, Dr. Painter:
SUNDAY,   10 Dec 06    6:30 - 8:00 pm  Weber 130 ( usual room), or Weber 117 in case of a large crowd.
Grading scheme
Course syllabus

General information

Prerequisites

Prerequisites for this course are MCC161 (or M161) and M229. If you have taken equivalent courses elsewhere please see the instructor before registering.

Textbook:
Steven J. Leon "Linear algebra with applications" 7th edition, Prentice Hall 2006.

Recommended (on-line free text book with solutions to all exercises):
Jim Hefferon, Linear Algebra: http://joshua.smcvt.edu/linalg.html

Homework and quizzes

There will be weekly homework, mainly set from the textbook. The homework must be handed in  Wednesday at the beginning of the lecture.
There will usually be a short quiz  on Friday. This will test the concepts we have covered that week, including Friday's lecture.
Grader for HW: Yung Zou, Weber 17

Exams

There will be two midterms and one final exam. These will be held in the same room as the lectures.

If you are unable to attend any of these exams because of a legitimate reason (for example, it clashes with an exam for another course), then you must let the instructor know at least one week in advance.

Grading scheme

Your final grade will be determined from a score out of 600. The homework and quizzes will count for 200 points, the midterms will count for 100 points each, and the final exam will count for 200 points.
90% - 100% A;  80% - 89% B; 70% - 79% C; 60% - 69% D; 0%  - 59%  F

Course syllabus

The syllabus below will be updated as the semester progresses.

Week

Material covered (with page numbers)

Homework

Aug 21-25

 Chapter 1 : Matrices and systems of equations
  • Systems of linear equations (1-11)
  • Row echelon form (13-25)
  • Matrix algebra (30-57)
  • Elementary matrices (61-69)
Chapter 2 : Determinants
  • The determinant of a matrix (90-96)
  • Properties of determinants (98-103)

 HW1 - due Wednesday 30 August ; graded problems are printed in red colour

Chapter 1:
Section 1: 1b, 2b, 3d, 5b, 6f
Section 2: 1,2,5f
Section 3: 1d, 2, 10, 12
Section 4: 10g, 11
Chapter 2:
Section 1: 3, graded: 3g

Aug 28-Sep 1

Chapter 3 : Vector spaces

  • Definition and examples (115-121)
  • Subspaces (123-131)
  • Linear Independence

 HW2, due Wed September 6
Chapter 3
Section 1: 3, 10, 11
Section 2:  1abc, 2, 9, 10
Section 3: 1ace, 2bd, 5

Sep 4-8
No class Monday

  • Basis, Dimension
  • Change of Basis

HW3, due Wed September 13
Chapter 3
Section 3: 6ac, 7bd, 8, XC: 16 +TBA
Section 4: 4,5,6,10,14
Section 5: 1b, 2b, 3b,5, 6.
Sep 11-15
  • Change of Basis - continued
  • Row Space - Column Space
 HW4, due Wed September 20
Chapter 3
Section 5: 8,9
Section 6: 2ab, 3, 5abc, 6,7,10,14,18,19.
Sep 18-22
 Chapter 4: Linear Transformations
  • Linear transformation
  • Matrix representations of linear transformations
 HW5, due Wed September 27
Chapter 4
Section 1: 1 a,e; 3, 4, 5ac, 6ac, 9a, 17ab, 18,23
Section 2:  2ac, 3b, 6, 14, 18ac
Sept 25-29
  • Similarity
Chapter 5: Orthogonality
  • The scalar product
 HW6, due Friday September 29
Chapter 4
Section 3: 1 a,d; 2, 3, 9
Sep 30 - Oct 5
  • review
  • exam 1
  • The scalar product (continued) 
 HW7, due Wednesday 11 October
Chapter 5
Section 1: 1a, 3c, 4, 8c, 9
Section 2: 1c, 2(Xcredit). 3, 4
Oct 9-13  
  • Orthogonal subspaces
  • Least Squares Problems
 HW8 due Wednesday 18 October
Chapter 5
Section 3: 1b,c, 2, 5, 11 (9=Xcredit).
Section 4: 1,2,3,7,8,16
Oct 16-20
  • Inner Product Spaces
  • Orthonormal sets
  • Gram-Schmidt Orthogonalization
 HW9 due Wednesday 25 October
Chapter 5
Section 5: 1c,d; 2,3,5,8, 15,16,21
 
Oct 23-27
  • Gram-Schmidt Orthogonalization
  • Least squares polynomial approximation
 HW10 due Wednesday 1 November
Chapter 5 Section 6: 1-6
and
p1: find the least squares linear approx. of f(x) = sqrt(x) on [-1,1]
p2: find the least squares quadratic approx. of f(x) = sqrt(x) on [0,1]
Oct 29-Nov 3
 Chapter 6: Orthogonality
  • Eigenvalues and eigenvectors of a linear operator
 HW11 due Wednesday 8 November
Chapter 6
Section 1:  1) a,d,g,k; 2,10,11,13
Section 3: 1)a,c; 2,3
Section 1(again): 19, 26
Nov 6-10
  • Eigenvalues and eigenvectors of a linear operator, diagonalization
  • applications to ODEs
 HW12
Chapter 6
Section 2:  1) a,b, 2) a,b
Nov 13-17
  • Revision, Midterm, Hermitian Matrices
 
 Thanksgiving break
Nov 27-Dec 1
  • SVD, Canonical Forms
 Last HW, due Wed 6 December:
S4: 1,2,3,4: S5: 1,2,5; S6: 1
Last Week
Review:  Mo: Chapters 1-3; W: chapters 4,5; F: Chapters 5,6