Math2270 - Linear algebra, Fall 2011

Instructor: Paweł Nurowski
Homework grader: Brian Hestetune, email: brian.hestetune@aggiemail.usu.edu
Lectures: Mon-Wed-Fri 11:30, Engr203.
Office hours: Mon, Wed 2:00-3:00 p.m.

Textbook: Introduction to Linear Algebra, 4th edition, by Gilbert Strang, Wellesley-Cambridge Press.

Homework: Homework (problem sets) are due each Wednesday in class except weeks of exams. These problem sets will be posted on this web page each Wednesday. Late homework is NOT accepted. They should be folded and stapled with your name and the class (Math 2270) written on the outside. These problem sets are essential in learning linear algebra. They are not a test and you are encouraged to talk to other students about difficult problems - after you have found them to be difficult. You must write out your own solutions. Be neat to get maximum credit.

Exams: There will be three one hour exams during class. See approximate schedule below for time and content. The use of calculators, notes, etc. is not permitted during exams.

Grading Policy: There will be three midterm examinations, a final comprehensive examination, and weekly problem sets given to determine your final grade. Each midterm examination will be worth 15% of your final grade; the final examination is worth 40% of your final grade, and the weekly assignments will amount to 15% of your final grade.

A Note on Incompletes: I have a very strict, personal policy on incomplete grades: I will not give an incomplete grade unless the student has been ill for a good part of the semester and can obtain a doctor's medical certificate to authenticate the illness. NO EXCEPTIONS!

TAKE HOME EXAM 12.02.2011: CLICK HERE FOR A PDF FILE OF THE EXAM
Due: Monday Dec 5th, at 11:30 in class.

Practice exam: Click here.



Provisional Schedule:
Chapter 1: Vectors and matrices
Chapter 2: Solving linear equations
Chapter 3: Vector spaces and subspaces
TEST # 1: Wednesday, October, 5th.
Chapter 4: Orthogonality
Chapter 5: Determinants
TEST # 2 Friday, October, 28th.
Chapter 6: Eigenvalues and Eigenvectors
Chapter 10: Complex matrices
TEST # 3: Wednesday, November, 30th.
Chapter 7: Linear transformations
Chapter 8: Applications (selected topics)
FINAL EXAM: Wednesday, December 14, 9:30-11:20 am.

Topics and Assignments

 

           Week                                                                  Topics                         Assignments
Aug 29-Sep 4
1.1 Vectors and linear combinations
1.2 Lengths and dot products
1.3 Matrices
 Problem set 1.1: 2, 7, 26
Problem set 1.2: 5, 6, 7
Problem set 1.3: 4
Problem set 2.1: 12
Due: Sept 14th
Sep 5-11
2.1 Vectors and linear equations
2.2 The idea of eliminations
Problem set 2.1: 9, 10, 11, 13, 15
Due Sept. 21st
Sep 12-18
2.3 Elimination using matrices
2.4 Rules for matrix operations
2.5 Inverse matrices
2.6 Elimination=Factorization A=LU
 Problem set 2.5: 1, 22, 23, 25, 27, 30
Due Sept. 21st
Sep 19-25
2.7 Transposes and permutations
3.1 Spaces of vectors
Problem set 2.2: 5, 7, 9
Problem set 2.4: 33
Problem set 2.5: 10
Problem set 2.6: 5, 12, 16
Problem set 2.7: 20, 22
Due Sept. 28th
Sep 26 - Oct 2
3.2 The nullspace of A: solving Ax=0
***Review of Chapters 1 and 2
Problem set 2.7: 1, 9, 11, 24
Problem set 3.1: 10, 11, 12, 14, 19, 28
Due: Oct. 5th
Oct 3-9
***Test #1
3.3 The rank and the row reduced form
 
Oct 10-16
3.4 The complete solution to Ax=b
3.5 Independence, Basis, Dimension
Problem set 3.3: 2, 8, 23, 24
Problem set 3.4: 1, 2, 3, 4, 5, 21
Due: Oct. 19th
Oct 17-23
*** Vector spaces - a bonus lecture
5.1 Properties of determinants
Probem set 3.5: 1, 2, 13, 23, 25, 26, 28, 35, 38, 40
Due: Oct 26th
Oct 24 - 30
5.2 Permutations and cofactors
*** Review of Chapter 3 and 5
 
Oct 31 - Nov 6
5.3 Cramer's rule, inverses and volumes
*** Test #2
Probem set 5.1: 14, 15, 27
Problem set 5.2: 2, 15, 16
Problem set 5.3: 1, 6, 9
Due: Nov 9th
Nov 7-13
6.1 Introduction to eigenvalues
6.2 Diagonalizing a matrix
 
Nov 14 - 20
6.3 Application to Differential Equations
Probem set 6.1: 2, 3, 4, 10, 14, 24, 29
Problem set 6.2: 1, 6, 7, 15, 17, 18, 19
Problem set 6.3: 4, 8, 19, 21
Due: Nov 30th
Nov 21-27
***Second order linear differential equations with constant coefficients.
 
Nov 28 - Dec 4
***Second order linear differential equations with constant coefficients (part 2).
***Exponential of a matrix.
***Take home exam.
Problem set 6.3: 23, 24, 25, 26, 27
Due: Dec 7th
Dec 5 - 11
6.4 Symmetric matrices.
6.5 Positive definite matrices.
***Introduction to linear transformations.
 
Dec 14
 
FINAL EXAM (Wednesday, December 14)

Note the time: 9:30-11:20 a.m. !!!
 
 

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