Ma 232 Linear Algebra
Fall 2008 darinka.dentcheva@stevens.edu
__________________________________________________________________
Objective
The objective of this course is to introduce the students to linear algebra and demonstrate some of its applications. This course builds a foundation for many other courses in mathematics, as well as computational engineering, quantitative methods in finance and management.
Time and Place
Lectures
take place on Mondays, Thursdays and Fridays, 2—2:50 pm. in Babio 210.
Mondays and Thursdays 3:00--4:00 pm. or by appointment,
Peirce 302.
Tel: (201)
216-8640, Fax: (201) 216-8321
Course Material
Linear Algebra and its Applications, Gilbert Strang, Fourth Edition, Thompson Brooks/Cole, 2006, ISBN-13: 978-0-03-010567-8; ISBN-10: 0-03-010567-6.
Not all sections will be covered.
Graded work
Homework
assignments will be given in most of the weeks to help you understand and apply
the concepts and the theoretical results. In addition, two midterm exams and a
final exam will be conducted. The solutions will be discussed in class.
The grade
will be assigned according to the final score, which will be computed as
follows:
Score
= 0.2 average(homework) + 0.2
exam 1 + 0.2 exam 2 + 0.4 final exam.
Final grade (tentative, subject to change)
|
Score |
[90, 100] |
[75, 90) |
[60,75) |
[50,60) |
|
Grade |
A |
B |
C |
D |
Plan of lectures
|
Lecture |
Date |
Topic |
|
1 |
Aug 25 |
Linear equations. Geometry. |
|
2 |
Aug 28 |
Matrices and operations with matrices |
|
3 |
Aug 29 |
Gaussian elimination |
|
4 |
Sep 4 |
Examples Assignment 1 |
|
5 |
Sep 5 |
Triangular factors. Row exchanges and permutations |
|
6 |
Sep 8 |
Inverses and transposes. The Gauss-Jordan procedure |
|
7 |
Sep 11 |
Special matrices (HW1 due) Assignment 2 |
|
8 |
Sep 12 |
Vector spaces and subspaces |
|
9 |
Sep 15 |
Examples |
|
10 |
Sep 18 |
Linear independence (HW2 due) Assignment 3 |
|
11 |
Sep 19 |
Basis and dimension |
|
12 |
Sep 22 |
The four fundamental subspaces for a system of linear equations. |
|
13 |
Sep 25 |
Homogeneous and non-homogeneous systems of equations (HW3 due) Assignment 4 |
|
14 |
Sep 26 |
Fundamental relations. Existence of an inverse of a matrix |
|
15 |
Sep 29 |
Applications |
|
|
Oct 2 |
Exam 1 (HW4 due) Study guide 1 Sample Exam |
|
16 |
Oct 3 |
Linear transformations |
|
17 |
Oct 9 |
Matrix representation of some linear transformations Assignment 5 |
|
18 |
Oct 10 |
Orthogonal vectors and subspaces |
|
19 |
Oct 14[1] |
Projections onto lines. Schwarz inequality |
|
20 |
Oct 16 |
Projections onto subspaces (HW5 due) Assignment 6 |
|
21 |
Oct 17 |
Projection and least squares problems |
|
22 |
Oct 20 |
Orthogonal basis |
|
23 |
Oct 23 |
Gram-Schmidt orthogonalization procedure (HW6 due) |
|
24 |
Oct 24 |
Examples Assignment 7 |
|
25 |
Oct 27 |
Some functional spaces |
|
26 |
Oct 30 |
Determinants. Basic properties. |
|
27 |
Oct 31 |
Formulae and expansion in cofactors (HW7 due) Assignment 8 |
|
28 |
Nov 3 |
Cramer’s rule |
|
29 |
Nov 6 |
Review (HW8 due) |
|
|
Nov 7 |
Eigenvectors and eigenvalues |
|
30 |
Nov 10 |
Diagonalization of a matrix Assignment 9 |
|
31 |
Nov 13 |
Exam 2 Study
guide 2 Sample Exam |
|
32 |
Nov 14 |
Examples |
|
33 |
Nov 17 |
Positive definite matrices and quadratic forms |
|
34 |
Nov 20 |
Test for positive definiteness. |
|
35 |
Nov 21 |
Matrix norm and condition number |
|
36 |
Nov 24 |
Computation of eigenvalues |
|
37 |
Dec 1 |
Markov processes and matrices |
|
38 |
Dec 4 |
Two-person games |
|
41 |
Dec 5 |
Review |