MTH 215/URI
LINEAR ALGEBRA
Fall 2014

Text:   Linear Algebra (Fourth Edition) by David Lay

Instructor: M. Kulenovic           Office:  Lippitt Hall 202D
Phone:  874-4436    Email:  mkulenovic@mail.uri.edu

Online information: www.math.uri.edu/courses or www.math.uri.edu/~kulenm
Office Hours: M: 11-12, 3-4, W:  11 - 12 and by appointment.

Lectures: Bliss Hall MWF: 12-12:50

Students who require accommodations and who have documentation from Disability Services (874-2098) 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 TI-89 or TI-Inspire. The calculators TI-83, TI-84 and TI-86 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:
 

Two 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


The Matrix Equation Ax = b

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


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 Rn

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


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

Exam 1


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

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 Gram-Schmidt Process

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
MITOpenCourseware