Text: Linear Algebra (Third Edition) by David Lay
Instructor: M. Kulenovic
Office: Lippitt Hall
200A
Phone: 8744436 Email: mkulenovic@mail.uri.edu
Online information: www.math.uri.edu/courses
or www.math.uri.edu/~kulenm
Office Hours: MF at 10, W at 2, and by arrangement.
Students who require accommodations and who have
documentation from Disability Services (8742098) should make
arrangements with me as soon as possible.
Topics: vectors, matrices, linear systems, linear transformations,
vector spaces, determinants, eigenvalues, eigenvectors.
There are many applications of linear algebra to problems in many areas
of math and science. We will look at applications in order to
motivate the study of linear algebra.
Calculators: The recommended calculator is TI89 or TI92. TI83, TI84 and TI86 could be also used.
Grading: Your grade will be based on three tests, a final exam, and
classwork as follows:
Three tests at 100 points each  300 points 
Final exam  150 points 
Classwork  150 points 
Maple Projects 
100 points 
Total  700 points 
Tests and the final exam: The tests will be given in the class. A comprehensive final exam will be given during the final exam period. Time and place will be announced later. The exams will reflect the variety of the homework problems. The best way to prepare for the exams, and to develop confidence in your ability to solve problems, is to work on the homework problems as suggested. Some problems may be done in class or as homework, as your instructor chooses. No makeups for exams will be given unless you have a University sanctioned excuse.
Classwork: The distribution of the 150
points will be decided by your instructor. It will include quizzes and
class participation.
Makeups: No makeup quizzes will be
given. Instead, your lowest quiz grade will be dropped.
Homework: Homework plays a central role
in the class and in your understanding of the material. It is fair to
say
that most of the learning that you achieve during any math course is
from
your homework.
Read the textbook: An important part of your
mathematical education is acquiring the knack of learning mathematics
on your own, from books. You may not be used to reading
mathematics texts, but you
will be actively encouraged to read this one. By reading the text
before
class, even if you don’t understand everything the first time, you will
have a better chance of making good use of your time in class.
Reading
the text after class is a good way of reinforcing the material in the
lecture,
nailing down what questions you need to ask in the next class, and
learning
material that was not gone over during class time. The text is
well written, with the beginning linear algebra student in mind. Linear algebra is much easier if you
keep up with the classe and homework. You also retain the
material longer and better if you review material frequently rather
than just studying at exam time.
Syllabus
Week  Sections  Suggested Homework Problems  Exams/Events 
Systems of Linear
Equations 
1.1 
2,7,11,15,19,29  
Row Reduction and Echelon Forms 
1.2  1,3,7,11,19,25,29,31  
Vector Equations  1.3  1,5,9,11,13,17,25  
The Matrix Equation Ax = b 
1.4  1,7,9,15, 21,23,25,29,37  
Solution Sets of Linear Systems  1.5  1,5,11,15,19,27,31,35  
Linear Independence 
1.7 
1,5,7,11,19,23,29,31  
Introduction to Linear Transformations  1.8  1,5,7,9,11,19,25,35  
The Matrix of a Linear Transformation  1.9  1,5,7,9,15,19,37  
Matrix Operations  2.1  1,5,9,17,23,31  
The Inverse of a Matrix 
2.2  1,3,7,8,11,13,17,19,29,31,35  
Characterizations of Invertible Matrices  2.3  1,5,7,11,17,27,33 

Subspaces of R^{n} 
2.8 
5,7,11,17,23,29,37  
Dimension and Rank  2.9  3,5,7,11,13,23,29  
Introduction to Determinants 
3.1 
1,5,9,11,15,19,29,35  Exam 1 
Properties of Determinants 
3.2  1,5,7,11,19,23,29,31,35,41,43 

Cramer's Rule  3.3  1,5,7,9,11,15,19,25  
Vector Spaces and Subspaces  4.1  1,5,7,11,15,21,31 

Null Spaces, Column Spaces 
4.2 
1,5,7,11,15,19,23,31,37  
Linearly Independent Sets: Bases  4.3  1,5,7,9,11,19,21,23,31  
The Dimension of a Vector Space  4.5  1,7,11,17,21,22,29  
Rank  4.6  1,5,11,19,21,29,31  
Change of Basis  4.7  1,5,7,11,19  
Applications to Difference Equations  4.8  1,5,7,11,19,23,31  
Applications to Markov Chains  4.9  1,5,7,11,15,21  
Eigenvectors and Eigenvalues 
5.1 
1,3,5,7,11,13,15,23,27 
Exam 2 
The Characteristic Equation  5.2 
1,5,7,9,11,15,23 

Diagonalization 
5.3 
1,5,7,11,17,29  
Eigenvectors and Linear Transformations  5.4  5,7,11,17,19,31  
Discrete Dynamical Systems  5.6  1,5,11,15  
Inner Product, Length, and Orthogonality  6.1  1,5,17,23 

Orthogonal Sets 
6.2 
1,5,7,11,15,19,21,29 

Orthogonal Projections  6.3  1,5,7,11,15,17,19 

The GramSchmidt Process 
6.4  1,5,11,13,19 

Review  Exam 3 
Maple
worksheet on matrix exponential and systems of differential equations
Handout
on matrix exponential and systems of differential equations
Here are some useful links for linear algebra:
Jim Baglama's web page for MTH 215 with PDF of lectures
Linear
Algebra Toolkit
S.
Smith's Math 310 Home page
Math
Archives  Linear & Matrix Algebra
STAT/MATH
Center  Linear Algebra with Maple
Open
Directory Project  Linear Algebra
Notes on Linear
Algebra
Practice
Linear Transformations