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# Syllabus for Differential Equations and Linear Alg

## I. MTH 237 Linear Algebra – 3 Semester Hours.

(See Course Detail in Supplement)

## II. Course Description

This course introduces the basic theory of linear equations and matrices, real
vector spaces, bases and dimension, 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.

## III. Prerequisite

C or higher in MTH 126, Calculus II.

## IV. Textbook

Elementary Linear Algebra, 9th edition, by Howard Anton; John Wiley and
Sons Publishing Company, Inc., 2005. (For sections covered, see Course
Detail in Supplement.)

## V. Course Objectives

The objective of this course is to provide an understanding of concepts,
develop competent skills, and demonstrate applications in the theory of
elementary linear algebra. This course seeks to further the student’s
introduction to the more rigorous techniques and thought processes of
advanced mathematics.

## VI. Course Outline of Topics

(See Course Detail in Supplement)

A. This course shall include the following topics as a minimum:
1. Introduction to systems of linear equations
2. Gaussian elimination and Gauss-Jordan elimination
3. Applications of systems of linear equations
4. Operations with matrices
5. Properties of matrix operations
6. The inverse of a matrix
7. Elementary matrices
8. Applications of elementary matrices
9. Determinant of a matrix
10. Evaluation of a determinant using elementary operations
11. Properties of determinants
12. Applications of determinants
13. Vectors in n-space
14. Vector spaces
15. Subspaces
16. Spanning sets and linear independence
17. Basis and dimension
18. Rank of a matrix
19. Rank and systems of equations
20. Coordinates and change of basis
21. Applications of vector spaces
22. Length and dot product in n-space
23. Inner product spaces
24. Orthonormal base: Gram-Schmidt process
25. Math models and least squares analysis
26. Applications of inner product spaces
27. Introduction to linear transformations
28. The kernel and range of a liner transformation
29. Matrices for linear transformations
30. Transition matrices and similarity
31. Applications of linear transformations
32. Eigenvalues and Eigenvectors
33. Diagonalization
34. Symmetric matrices and orthogonal diagonalization
35. Applications of Eigenvalues and Eigenvectors

B. Optional topics may include the following:
1. Quadratic forms

## VII. Evaluation and Assessment

(See Grading Plan and Grade Scale in Supplement)

Evaluation and assessment techniques may include any or all of the
following: Exams, projects, homework, computer assignments, and
participation.

Grades will be given based upon
A = 90% – 100%, B = 80% – 89%, C = 70% – 79%, D = 60% – 69%, and F = below 60%.

## VIII. Attendance

Students are expected to attend all classes for which they are registered.
Students who are unable to attend class regularly, regardless of the reason
or circumstance, should withdraw from that class before poor attendance
interferes with the student’s ability to achieve the objectives required in the
course. Withdrawal from class can affect eligibility for federal financial aid.

## IX. Statement on Discrimination/Harassment

The College and the Alabama State Board of Education are committed to
providing both employment and educational environments free of
harassment or discrimination related to an individual’s race, color, gender,
religion, national origin, age, or disability. Such harassment is a violation of
State Board of Education policy. Any practice or behavior that constitutes
harassment or discrimination will not be tolerated.

## X. Americans with Disabilities

The Rehabilitation Act of 1973 (Section 504) and the Americans with
Disabilities Act of 1990 state that qualified students with disabilities who
meet the essential functions and academic requirements are entitled to
reasonable accommodations. It is the student’s responsibility to provide
appropriate disability documentation to the College.

## MTH 237, LINEAR ALGEBRA (Lecture-Based)

2. COURSE DETAIL

a. Course name, number and credit hours:
MTH 237 Linear Algebra—3 Semester Credit Hours.

b. *Section number and reference/synonym number:

c. *Class meeting time (days, time, location):

d. Textbook:
Elementary Linear Algebra, 9th edition, by Howard Anton; John Wiley and
Sons Publishing Company, Inc., 2005. (Chapters 1, 2, 3, 4, 5, 6, 7, 8, and 9.5.)

e. Organization of Topics

CHAPTER 1 SYSTEMS OF LINEAR EQUATIONS AND MATRICES
1.1 Introduction to Systems of Linear Equations
1.2 Gaussian Elimination
1.3 Matrices and Matrix Operations
1.4 Inverses; Rules of Matrix Arithmetic
1.5 Elementary Matrices and a Method for Finding A-1
1.6 Further Results on Systems of Equations and Invertibility
1.7 Diagonal, Triangular, and Symmetric Matrices

CHAPTER 2 DETERMINANTS
2.1 Determinants by Cofactor Expansion
2.2 Evaluating Determinants by Row Reduction
2.3 Properties of the Determinant Function
2.4 A Combinatorial Approach to Determinants (Optional)

CHAPTER 4 EUCLIDEAN VECTOR SPACES
4.1 Euclidean n-Space.
4.2 Linear Transformations from Rn to Rm
4.3 Properties of Linear Transformations from Rn to Rm
4.4 (Omit)

CHAPTER 5 GENERAL VECTOR SPACES
5.1 Real Vector Spaces
5.2 Subspaces
5.3 Linear Independence
5.4 Basis and Dimension
5.5 Row Space, Column Space, and Nullspace
5.6 Rank and Nullity

CHAPTER 6 INNER PRODUCT SPACES
6.1 Inner Products
6.2 Angle and Orthogonality in Inner Product Spaces
6.3 Orthonormal Bases; Gram-Schmidt Process; QR-Decomposition
6.4 Best Approximation; Least Squares
6.5 Change of Basis
6.6 Orthogonal Matrices

CHAPTER 7 EIGENVALUES, EIGENVECTORS
7.1 Eigenvalues and Eigenvectors
7.2 Diagonalization
7.3 Orthogonal Diagonalization

CHAPTER 8 LINEAR TRANSFORMATIONS
8.1 General Linear Transformations
8.2 Kernel and Range
8.3 (Omit)
8.4 Matrices of General Linear Transformations
8.5 Similarity
8.6 (Omit)

CHAPTER 9 ADDITIONAL TOPICS
9.1 (Omit)
9.2 (Omit)
9.3 (Omit)
9.4 (Omit)
9.5 Quadratic Forms (Optional)
9.6 (Omit)
9.7 (Omit)
9.8 (Omit)
9.9 (Omit)

f. Course Sequencing Statement:
This course is a prerequisite for differential equations at some
institutions.

g. Course Applicability Statement:
This course is required for the mathematics Associate of Science Degree
program. Students should consult the current College Catalog for other
courses required in their major/program of study.

h. Course Transferability Statement:
This course usually transfers to institutions where linear algebra is
taught at the sophomore level. It usually will not transfer to institutions
that teach linear algebra as a junior level course. For specific information
on the transferability of this course, please contact the institution to
which you plan to transfer.

3. COURSE SUPPORT MATERIALS

a. *Laboratory manual(s) and/or additional notes/materials/supplies:
b. CD/DVD: CD/DCD lecture presentations that accompany the textbook may be
available for viewing online or in the Mathematics Learning Center.
c. Library and LRC resources and services are accessible on-line

4. INSTRUCTIONAL METHODS
Instructional methods may include, but not be limited to, lectures, class
discussions, student presentations, CD/DVD lecture presentations, and
computer-generated material. The facilities of the Mathematics Learning
Center may be utilized.

5. *GRADING PLAN
To include information on the number and type of evaluation methods
(exams, quizzes, labs, homework, papers, etc.) with point or percentage
values for each

6. GRADE SCALE

A – Excellent (90% – 100%)
B – Good (80% – 89%)
C – Average (70% – 79%)
D – Poor (60% – 69%)
F – Failure (Below 60%)

7. *WEEKLY OR DAILY LIST OF ASSIGNMENTS
To include required submissions of course requirements as shown in the
Grading Plan. (Note: Instructors should ensure that at least one major
course requirement (exam/paper/project) has been completed, graded, and
returned for student review prior to the end of the withdrawal period).

8. *DATE, TIME, AND LOCATION OF FINAL EXAM

9. ATTENDANCE POLICY

Class attendance is required. The attendance policy is set by the college
and is in effect from the first time a class meets. If a student registers during
the drop/add period, attendance is counted from the first class meeting
following registration. Students whose absences exceed twice the number of
weekly class meetings in a regular 15-week semester can be involuntarily
dropped from the class roll by the instructor with a grade of W (withdrawal).
The maximum number of absences for an eight-week mini semester is two
(2); for 10-week or five-week summer courses, three (3); and for weekend
courses, two (2). Distance education students can be involuntarily
withdrawn by the instructor if the student has not communicated with the
instructor by phone, email, or in person within the first two weeks of a
semester.

Students are responsible for activities missed during any absence, and makeup
work will be governed by the instructor as stated in the course syllabus.
It is the student’s responsibility to keep a record of his/her absences and to
understand specific policies detailed in each course syllabus.
Communication with the instructor concerning absences is essential.
Appeals of involuntary withdrawals are made at the divisional level to the
division chairperson.

Military personnel who are involuntarily called to active duty for unscheduled
and or emergency situations and those individuals called for jury duty will be
excused. Official documentation will be required. College-related events
such as field trips, athletic competitions, and drama productions, which are
documented by the college, will also be excused. Official documentation will
be required.

Each course syllabus will contain a makeup policy, a statement of the
maximum number of absences allowed in the course and if the
instructor will be assigning the grade of W if the maximum number of
absences is exceeded.

10. *MAKEUP POLICY/HOW TO MAKE UP MISSED WORK

11. WITHDRAWAL POLICY

Effective from the day after the Drop/Add period through the last day of
classes (prior to final examinations), students may withdraw and receive a
grade of W or faculty may initiate a withdrawal and assign a grade of W if the
student exceeds the number of absences in the college’s attendance policy.

12. DISCRIMINATION/HARASSMENT STATEMENT

The College and the Alabama State Board of Education are committed to
providing both employment and educational environments free of
harassment or discrimination related to an individual’s race, color, gender,
religion, national origin, age, or disability. Such harassment is a violation of
State Board of Education policy. Any practice or behavior that constitutes
harassment or discrimination will not be tolerated.

13. DISABILITY STATEMENT

If you have a disability that might require special materials, services, or
assistance, please contact Calhoun’s Disability Services Office in the
Chasteen Student Center, Second Floor, Room 220 (Decatur Campus) or call
(256) 306-2630 or (256) 306-2635.

14. *GENERAL COMMENTS BY INSTRUCTOR

a. Children are not allowed to attend classes with students or faculty. No
minors should be left unattended in any building of Calhoun Community
College.

b. Calhoun Community College will communicate campus-wide information
via SPACE student e-mail. You have a SPACE e-mail account, which you
can access from www.calhoun.edu. Your username is: first initial, last
name, and last four digits of your student ID number (Example:
jsmith1234). Your initial password is 'cal'
. You will be prompted to
change the password.

c. Notice—Student Schedules/Grades:
Calhoun Community College will no longer mail a student’s schedule or
grades. Students may obtain schedule and grade information
(transcripts) through the Calhoun Web Site at www.calhoun.edu and
clicking on the Web Advisor link. A student user name and password is
needed to access Web Advisor.

d. *

*To be completed by the instructor for this course.

THIS SYLLABUS IS EFFECTIVE SPRING SEMESTER, 2009.