Course Syllabus
Ordinary Differential Equations
SYLLABUS FOR MATH 2318
(Revised December 2014)
Catalog Description: MATH 2320 Topics include systems of linear equations, vector spaces,
matrices, linear mappings, and determinants. Prerequisite: MATH 2413.
3 credit (3 lecture).
Prerequisites: MATH 2413.
Course Intent: This course provides the background in sciences for further study in mathematics
and its applications.
Audience: This is a sophomore level mathematics course, which requires a background
consisting of Calculus I and II.
Course Objectives: Upon completion of this course, a student should be able to:
1. Determine if a system of equations is consistent and find its general solution.
2. Row reduce a matrix to reduced echelon form.
3. Apply solution methods of linear system for various problems.
4. Solve the equation Ax = b where A is an m x n matrix and x is in ℜn .
5. Write the solution set of a given homogeneous system in parametric vector form.
6. Determine if the columns of a given matrix form a linearly dependent set.
7. Find all x in ℜn that are mapped into the zero vector by the transformation x → Ax.
8. If T is a linear transformation, find the standard matrix of T.
9. Matrix algebra including the inverse of a matrix.
10. Recognize various characterizations of nonsingular matrices.
11. Compute the products of matrices, which are partitioned conformably.
12. Compute the determinant of a given matrix.
13. Combine row reduction and cofactor expansion to compute a given determinant.
14. Solve a system of equations using Cramer’s rule (Optional).
15. Determine a subspace from a vector space.
16. Determine a null space and a column space.
Math 2318
17. Find bases for vector spaces.
18. Use an inverse matrix to find [ x ]β for the given x and β.
19. Find the dimension of the subspace spanned by the given vectors.
20. Given an m x n matrix, find the rank and nullity of the matrix.
21. Change the coordinates of a vector from a basis to a standard basis.
22. Given a matrix and an eigenvalue, find the basis for the corresponding eigenspace.
23. Find the characteristic polynomial of a given matrix.
24. Use the Diagonalization Theorem to find the eigenvalues of a matrix A.
25. Find the β-matrix of a transformation.
Textbook: Elementary Linear Algebra: Applications Versions, 10th Edition Anton & Rorres
ISBN-13: 9780470432051
Course Outline: Instructors may find it preferable to cover the course topics in the order listed
below. However, the instructor may choose to organize topics in any order, but all material must
be covered.
APPROXIMATE TIME
REFERENCE
TEXT
UNIT I - Systems of linear equations and Matrices
Sections: 1.1  1.7
UNIT II - Determinants
Sections: 2.1, 2.2, 2.3,
UNIT III - Euclidean Vector Spaces
Sections: 3.1, 3.2
UNIT IV - General Vector Spaces
Sections: 4.1  4.11
UNIT V - Eigenvalues and Eigenvectors
Sections: 5.1, 5.2
UNIT VI - Linear Transformations
(4 hours)
Sections: 8.1  8.5
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Math 2318
Departmental Policies:
1. Each instructor must cover all course topics by the end of the semester. The final exam is
comprehensive and questions on it can deal with any of the course objectives.
2. Each student should receive a copy of the instructor’s student syllabus for the course during
the first week of class.
3. A minimum of three in class tests and a comprehensive final examination must be given.
The final examination must be taken by all students.
4. All major tests should be announced at least one week or the equivalent in advance.
5. The final exam must count for at least 25 to 40 percent of the final grade.
6. The final course average will be used in the usual manner (90-100 ”A”; 80-89 “B”; 70-79
“C”; 60-69 “D”; Below 60 “F”).
7. Either an open book or a take home major test may be given at the discretion of the
instructor.
8. Any review sheet should be comprehensive and the student should not feel that classroom
notes, homework, and tests may be ignored in favor of the review sheet for any examination.
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Math 2318
Resource Materials: Any student enrolled in Math 2318 at HCCS has access to the Academic
Support Center where they may get additional help in understanding the theory or in improving
their skills. The Center is staffed with mathematics faculty and student assistants, and offers
tutorial help, video tapes and computer-assisted drills. Also available is a student’s Solutions
manual which may be obtained from the Bookstore.
Suggested Methods: It is helpful to begin each class with questions concerning the material
discussed and the assigned homework problems. In presenting new material, it is suggested that
an explanation be followed by students working examples in class. Students should be encouraged
to work the review exercises at the end of each chapter. Also, they should be encouraged to visit
the Academic Support Center at their respective colleges.
Americans with Disabilities Act (ADA)
Any student with a documented disability (e.g. physical, learning, psychiatric,
vision, hearing, etc.) who needs to arrange reasonable accommodations must contact the
Disability Services Office at his or her respective college at the beginning of each semester.
Faculty members are authorized to provide only the accommodations requested by the Disability
Support Services Office. Persons needing accommodations due to a
documented disability should contact the ADA counselor for their college as soon as
possible. Also, interested students may wish to consult the Disability Support Services
Student Handbook which may be found online.
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