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Student Information Plan
Math 2318
Linear Algebra
INSTRUCTOR:
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TEXT: Linear Algebra and its Applications (2nd Edition) by David C. Lay
Course Description: Topics included in this course are systems of linear equations and matrices,
vector spaces and linear transformations, eigenvectors and eigenvalues, determinants, and
orthogonality.
Objectives: This course is designed to develop the understanding of linear algebra as it is used
in science, engineering, economics and other subjects. In addition, it will prepare mathematics
students for the study of the many subjects depending on it. The level of abstraction involved is
an excellent preparation for more advanced courses.
Course Outline:
A. Linear Equations in Linear Algebra
1. Systems of Linear Equations
2. Row Reduction and Echelon
Forms
3. Vector Equations
4. The Matrix Equations Ax=B
5. Solutions Sets of Linear Systems
6. Linear Independence
7. Introduction of Linear
Transformations
8. The Matrix of a Linear
Transformation
9. Linear Models in Business,
Science and Engineering
B. Matrix Algebra
1. Matrix Operations
2. The Inverse of a Matrix
3. Characterizations of Invertible
Matrices
4. Partitioned Matrices
5. Matrix Factorizations
6. Iterative Solutions of Linear
Systems
7. The Leontief Input-Output Model
8. Applications to Computer Graphics
9. Subspaces of |Rn
C. Determinants
1. Introduction
2. Properties of Determinants
3. Cramer’s Rule, Volume, and
Linear Transformations
D. Vector Spaces
1. Vector Spaces and Subspaces
2. Null Spaces, Column Spaces, and
Linear Transformations
3. Linearly Independent Sets; Bases
4. Coordinate Systems
5. The Dimension of a Vector Space
6. Rank
7. Change of Basis
8. Applications of Difference
Equations
9. Applications of Markov Chains
E. Eigenvalues and Eigenvectors
1. Eigenvalues and Eigenvectors
2. The Characteristic Equation
3. Diagonalization
4. Eigenvectors and Linear
Transformations
5. Complex Eigenvalues
6. Discrete Dynamical Systems
7. Applications to Differential
Equations
8. Iterative Estimates for Eigenvalues
F. Orthogonality and Least Squares
1. Inner Product, Length and
Orthogonality
2. Orthogonal Sets
3. Orthogonal Projections
4.
5.
6.
7.
8.
The Gram-Schmidt Process
Least-Squares Problems
Applications of Linear Models
Inner Product Spaces
Applications of Inner Product
Spaces
G. Symmetric Matrices and Quadratic
Forms
1. Diagonalization of Symmetric
Matrices
2. Quadratic Forms
3. Constrained Optimization
4. The Singular Value Decomposition
5. Applications of Image Processing
and Statistics
Grading:
A. Methods of Evaluation
1.
2.
3.
4.
Homework
Quizzes
Exams
Comprehensive Final Exam
B. Grading System
Course Average
90- 100
80- 89
70- 79
60-69
below 60
Grade
A
B
C
D
W, I or F
Attendance. Regular attendance in class is expected. If an absence is unavoidable, the student
is responsible for completing all work missed during the absence. Any work missed and not
subsequently completed will affect the grade of the student regardless of the reason for the
absence. Your instructor may initiate administrative withdrawal procedures for a student who
exceeds course absence standards. Withdrawal from class may affect enrollment in other
courses, insurance eligibility, financial aid, and/or veteran’s benefits. It should be noted that
ceasing to attend class does not terminate enrollment. Therefore, a student who ceases to attend
class without officially withdrawing from that class, may receive a failing grade.
Classroom Behavior. It is expected that students will behave in a mature and courteous
manner. Disruptive behavior during class will not be tolerated. Students are expected to be
attentive, take notes, ask pertinent questions, arrive on time, and not leave until the class is
dismissed. Conflicts which arise between the scheduled class time and the student=s personal
schedule must be resolved by the student.
Academic Honesty is Assumed. A student found guilty of scholastic dishonesty is subject to
disciplinary action. Violations such as plagiarism, cheating on tests, and collusion are described
in the ACC Student Handbook. Consequences are at the discretion of the instructor and range
from receiving a 0 on the assignment/test to failing the course to expulsion from the College.
Camcorders and any other video recording devices are prohibited in the classroom. Audio
recording may be allowed ONLY WITH THE PERMISSION OF THE INSTRUCTOR.
Cellphones are not to be used and are not to ring during class. Cellphones are not to be out
during tests. IF there are special circumstances, arrangements must be made with the instructor.
ADA Compliance. This College will adhere to all applicable federal, state, and local laws,
regulations, and guidelines with respect to providing reasonable accommodations as required to
afford equal educational opportunity. It is the policy of Alvin Community College to provide
reasonable accommodations for qualified individuals who are students with disabilities. It is the
student’s responsibility to contact the Counseling Center in a timely manner to arrange for
appropriate accommodations.