GENERAL COURSE SYLLABUS
TITLE OF
COURSE: Linear Algebra (MTH 237)
DIVISION: Mathematics,
Science, and Technology
COURSE
DESCRIPTION: This course introduces the basic theory of
linear equations and matrices, real vector spaces, bases and dimensions, linear
transformations and matrices, determinants, eigenvalues and eigenvectors, inner
product spaces, and the diagonalization of symmetric matrices. Additional topics may include quadratic forms
and the use of matrix methods to solve systems of linear differential
equations. This course is offered upon
sufficient enrollment.
HOURS: Credit: 3 Contact:
3 Lecture: 3 Clinical: 0 Lab: 0
PREREQUISITE(S): MTH 126
COREQUISITE(S): None
REQUIRED TEXTBOOK(S): Elementary
Linear Algebra, 5th edition, by Larson, Edwards, and Falvo,
Houghton Mifflin Company, 2004.
SUPPLIES: Rectangular graphing
paper and a graphing calculator are highly recommended.
GENERAL EDUCATION OBJECTIVE: All associate degree
graduates should be able to use the mathematical concepts, notations, and
manipulations needed in their field of study or occupation. (3)
COURSE
OBJECTIVE(S): Upon successfully completing Linear Algebra,
the student should be able to:
1. Use elementary row operations,
elementary matrices and matrix algebra to solve systems of linear equations.
2. Do matrix operations, find inverses for
matrices (where possible), use matrix algebra, find the transpose of a matrix
and use matrices to solve systems of equations.
3. Find determinants and use properties of
determinants to determine if a matrix is nonsingular.
4. Perform vector operations, use
properties of vector operations, and determine vector subspaces, spanning sets
and bases of vector spaces.
5. Show that a set of vectors forms a basis
for a set and find the dimension of a subspace.
6. Find inner products and find a basis for
a given inner product space.
7. Find the standard matrix for a given
linear transformation and use this matrix to find the image of a given vector.
8. Find real eigenvalues and eigenvectors of 3 x 3 real matrices with at
least one rational eigenvalue.
9. Diagonalize
symmetric matrices.
- Course Grade Evaluation: (Minimum of 4
measurements)
A comprehensive
final exam will be given and counted toward the student’s final average. Make-up examinations, as such, will not
generally be given.
- Evaluation of General Educational
Objectives: Student
success on the General Educational Objective (3) is measured by student
performance on each of the course objectives, which require use of mathematical
concepts, notations, and manipulations.
Performance on each course objective will be evaluated using
appropriate problems from the final exam.
Results will be tallied for each course objective.
- Use of Findings: Instructors
will analyze data gathered from the assessment(s) for each course
objective and changes will be made based on identified weaknesses. The math department will meet once every
five years to discuss findings and implement strategies to improve
department and student performance.
OUTLINE OF COURSE TOPICS:
I.
Systems
of Linear Equations
A.
Introduction
to Systems of Linear Equations
B.
Gaussian
Elimination and Gauss-Jordan Elimination
C.
Applications
of Systems of Linear Equations
II.
Matrices
A.
Operations
with Matrices
B.
Properties
of Matrix Operations
C.
The
Inverse of a Matrix
D.
Elementary
Matrices
E.
Applications
of Matrix Operations
III.
Determinants
A.
The
Determinant of a Matrix
B.
Evaluation
of a Determinant using Elementary Operations
C.
Properties
of Determinants
D.
Introduction
to Eigenvalues
E.
Applications
of Determinants
IV.
Vector
Spaces
A.
Vectors
in 
B.
Vector
Spaces
C.
Subspaces
of Vector Spaces
D.
Spanning
Sets and Linear Independence
E.
Basis
and Dimension
F.
Rank
of a Matrix and Systems of Linear Equations
G.
Coordinates
and Change of Basis
H.
Applications
of Vector Spaces (Optional)
V.
Inner
Product Spaces
A.
Length
and Dot Products in
B.
Inner
Product Spaces
C.
Orthonormal
Bases: Gram-Schmidt Process
D.
Mathematical
Models and Least Squares Analysis(Optional)
E.
Applications
of Inner Product Spaces(Optional)
VI.
Linear
Transformations
A.
Introduction
to Linear Transformations
B.
The
Kernel and Range of a Linear Transformation
C.
Matrices
for Linear Transformations
D.
Transition
Matrices and Similarity
E.
Applications
of Linear Transformations(Optional)
VII.
Eigenvalues
and Eigenvectors
A.
Diagonalization
B.
Symmetric
Matrices and Orthogonal Diagonalization
C.
Applications
of Eigenvalues and Eigenvectors(Optional)
AMERICANS WITH DISABILITIES
ACT POLICY: It is the policy of
ATTENDANCE POLICY:
Because class attendance is considered to be essential to the accomplishment of
course objectives, excessive absences are discouraged. At no time should a
student miss more than 20% of the class meetings for a course. These absences
also include any absences accrued during late registration. Failure to adhere
to the 20% policy may result in a failing grade based on academic performance.
Students should discuss with the instructor what is considered “excessive” for
a particular course. Any variation of this policy must be approved through the
Chief Instructional Officer. A student who is absent due to required
participation in a school activity must be allowed to make up work, according
to guidelines issued by individual instructors.
WITHDRAWAL POLICY: A student who is unable to complete a course
is expected to withdraw from that course by the end of 60% of class
meetings. A student who withdraws by the
date published in the schedule will receive a grade of “W” for the course. This withdrawal is done only by student
request. The
grade of “W” is allowed regardless of the student’s grades to the point of
withdrawal.
After the designated date of class withdrawal, the approval
of the Chief Instructional Officer is required prior to allowing a student to
withdraw. The determination of “WP” (withdrawal passing) or “WF” (withdrawal
failing) will be made by the instructor for the course and is based on the
student’s grades to the point of withdrawal.