MTH 215/URI
LINEAR
ALGEBRA
Fall
2013
Text: Linear Algebra (Fourth Edition) by David Lay
Instructor: M. Kulenovic
Office: Lippitt Hall 202D
Phone: 8744436 Email: mkulenovic@mail.uri.edu
Online information: www.math.uri.edu/courses
or www.math.uri.edu/~kulenm
Office Hours: MWF at 1112 and by appointment.
Lectures: Kelley Hall MWF: 1212:50
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. . You are encouraged to use the CAS (computer algebra system) such as Mathematica and Scientific Notebook and online programs that can be found on Internet. We will give a brief introduction to such resources. All Mathematica notebooks needed will be provided in SAKAI and demonstrated in the class.
Grading: Your grade will be based on two tests, a final exam,
and classwork as follows:
Three tests at 100 points each 
200 points 
Final exam 
150 points 
Classwork 
150 points 
Mathematica Projects 
100 points 
Total 
600 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 class 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 
1,3,5,11,19,25,29 

Vector Equations 
1.3 
1,5,7,11,13,19,23 


1.4 
1,7,9,15, 21,23,37 

Solution Sets of Linear Systems 
1.5 
1,5,11,15,19,27,35 

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 


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 


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 


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 
Exam 1 

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 


5.1 
1,3,5,7,11,13,15,23,27 

The Characteristic Equation 
5.2 
1,5,7,9,11,15,23 


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 


6.4 
1,5,11,13,19 
Exam 2 
Review 

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
Open Directory
Project  Linear Algebra
Notes on Linear Algebra
Practice
Linear Transformations