Course Syllabus

Ohio Northern University

College of Arts and Sciences

Department of Mathematics

                                                                                                                                    Date:   Fall/Winter, 05-06 

 

Course MATH- 272   Name:  Introduction to Linear Algebra                              _            

 

Credit hours   4   Lecture hours/week    0   Lab hours/week         

 

Instructor   Staff                                                                           

 

Usual student level   Sophomore                                                  

 

Course required of students in  Chemistry, Engineering, and Mathematics  

 

Course frequency per year   Fall, Winter                         

 

Average enrollment per year   120                                                   

 

This course has a prerequisite  MATH-164 or consent of the instructor                                    

 

This course is a prerequisite for  MATH-332, MATH-336, MATH-361 and MATH-461         

 

Catalogue description

 

Linear systems of equations and Gauss elimination. Vector spaces. Linear Transformations and their Matrices. Eigenvalues and eigenvectors.  Applications of eigenvalues.

 

Course Objectives

 

To introduce the student to the essential concepts of matrix algebra, to give the student an informal and concrete introduction to linear algebra and to equip the student with the basic mathematical tools necessary to solve significant linear algebra problems on a computer.

 

 

Textbook Linear Algebra and It’s Applications, updated 3rd edition, by David C. Lay

 

 

Outline of content follows:

(See attached)

 

 

Course Outline

MATH-272

Introduction to Linear Algebra

1. Linear Equations in Linear Algebra.                                                 9 hours           
Systems of Linear Equations.
Row Reduction and Echelon Forms.
Vector Equations.
The Matrix Equation Ax = b.
Solution Sets of Linear Systems.
 Linear Independence.
Introduction to Linear Transformations.
The Matrix of a Linear Transformation.
 

2. Matrix Algebra.                                                                                 5 hours

Matrix Operations.
The Inverse of a Matrix.
Characterizations of Invertible Matrices.
Subspaces of Rn.
Dimensions and Rank.

3. Determinants.                                                                                   3 hours
Introduction to Determinants.
Properties of Determinants.
Cramer's Rule, Volume, and Linear Transformations.


4. Vector Spaces.                                                                                 5 hours

Vector Spaces and Subspaces.
Null Spaces, Column Spaces, and Linear Transformations.
Linearly Independent Sets; Bases.
Coordinate Systems.
The Dimension of Vector Space
Rank.
Change of Basis.

 

5. Eigenvalues and Eigenvectors.                                                        9 hours
Eigenvectors and Eigenvalues.
The Characteristic Equation.
Diagonalization.
Eigenvectors and Linear Transformations.
Complex Eigenvalues.
Discrete Dynamical Systems.
Applications to Differential Equations.(OPTIONAL)

6. Orthogonality and Least-Squares. (OPTIONAL)                                 4 hours

Inner Product, Length, and Orthogonality.
Orthogonal Sets.
Orthogonal Projections.
The Gram-Schmidt Process.
 

Total of 35 hours. Review and examination 5 hours.

 

NOTES:    

1)         There are many applications throughout the course. To maintain a pace to cover the topics, some applications will probably need to be omitted. It is expected that in total about 6 hours will be spent on the applications of the instructor’s choice.

2)         It is expected that technology will be incorporated into the course where appropriate.