I. COURSE DESCRIPTION:
A. Prerequisite : MATH 250 or eligibility for MATH 265 as
determined through the
SBVC assessment process.
B. Catalog and Schedule Description: An introduction to linear algebra that
complements advanced courses in calculus. Topics include systems of linear
equations, matrix operations, determinants, vectors and vector spaces.
Eigenvalues
and eigenvectors and linear transformations .
II. NUMBER OF TIMES COURSE MAY BE TAKEN FOR CREDIT: One
III. EXPECTED OUTCOMES FOR STUDENTS:
Upon completion of the course the student should be able to:
A. Solve linear equations with many unknowns;
B. Apply problems and solutions to physical world applications;
C. Know “Linear Modeling” and apply linear algebra to geometric theorems and
proofs;
D. Apply Gauss-Jordan Elimination to solve a system of equation;
E. Analyze a word problem and formulate a system of equations from which a
solution
can be found;
F. Perform the basic operations on matrices ;
G. Evaluate determinants and to apply the properties of determinants ;
H. Apply the properties of vectors to lines in three dimensions and planes;
I. Recognize the properties of a Vector Space, Subspaces, Linear Combinations ,
Linear Independence, Basis and Dimension of a vector space;
J. Recognize eigenvalues, eigenvectors and basic linear transformations of the
plane.
IV. COURSE CONTENT:
A. Systems of Linear Equations
1. Gaussian Elimination and Gauss-Jordan Elimination
2. Applications of Systems of Linear Equations
B. Matrices
1. Operations with Matrices
2. Properties of Matrix Operations
3. The Inverse of a Matrix
4. Elementary Matrices
5. Applications of Matrix Operations
C. Determinants
1. The Determinant of a Matrix
2. Evaluation of a Deteminant using Elementary Operations
3. Properties of Determinants
4. Applications of Determinants
D. Vector Spaces
1. Vectors in Rn
2. Vector Spaces
3. Subspaces of Vector Spaces
4. Spanning Sets and Linear Independence
5. Basis and Dimension
6. Rank of a Matrix and Systems of Linear Equations
7. Coordinates and Change of Basis
8. Applications of Vector Spaces
E. Inner Product Spaces
1. Length and Dot Product in Rn
2. Inner Product Spaces
3. Orthonormal Bases: Gram-Schmidt Process
4. Mathematical Models and Least Square Analysis (optional)
5. Applications of Inner Product Spaces
F. Linear Transformations
1. Introduction to Linear Transformations
2. The Kernel and Range of a Linear Transformation
3. Matrices for Linear Transformations
4. Transition Matrices and Similarity (Optional)
5. Applications of Linear Transformations
G. Eigenvalues and Eigenvectors
1. Eigenvalues and Eigenvectors
2. Diagonalization
3. Symmetric Matrics and Orthogonal Diagonalization
4. Applications of Eigenvalues and Eigenvectors
V. METHODS OF INSTRUCTION :
A. Lecture
B. Discussion
C. Collaborative Methods
VI. TYPICAL ASSIGNMENT(S):
A. At the end of each section there is a set of problems. These start with
problems that
require the student to recognize and apply the principles covered in the
section. The
problems then graduate into those requiring the application of two or more
principles
and the student must recognize the principles to apply and the correct order in
which
to apply the. Typical problem sets end with application problems in which the
student
must translate the words in the problem into appropriate mathematical symbols,
and
analyze which principles must be applied. The student must then formulate and
apply
a solution strategy.
B. Methods of Evaluation:
1. 5 Examinations and 5 quizzes
2. Each student is required to successfully complete a comprehensive final
examination
VIII. TYPICAL TEXT(S):
Larson Edwards, Elementary Linear Algebra, fourth edition, Houghton Mifflin,
2000.
IX. OTHER SUPPLIES REQUIRED OF STUDENTS: TI-85/TI-86 calculators
