Description:

This sophomore-level introduction to linear algebra uses a matrix-oriented approach, with an emphasis on problem solving and applications. The course focus is on matrix arithmetic, systems of linear equations, properties of Euclidean n-space, eigenvalues and eigenvectors, orthogonality and vector spaces. The use of technology is a major feature of the course. 3 hrs. lecture/wk.

Associated Costs: These are additional (out-of-pocket) expense considerations that students should expect in addition to the course tuition, fees, and textbooks. $0 to $100.

Supplies: Refer to the instructor’s course syllabus for details about any supplies that may be required.

Textbook(s): For information see - http://bookstore.jccc.net

Course Fees: NONE

Course Objectives:

Upon successful completion of this course the student should be able to:

1. Solve systems of linear equations using Gaussian methods, matrices, and vectors.
2. Determine how the functional properties of linear transformations correspond to the properties of matrix multiplication.
3. Perform basic operations involving determinants.
4. Determine the solution set of a homogeneous system of linear equations, the span of a finite set of vectors, the null space and range of a linear transformation; apply their properties.
5. Calculate eigenvalues and eigenvectors; use their properties to describe diagonalizable matrices.
6. Construct a basis of perpendicular eigenvectors for a given matrix or linear transformation.
7. Extend previous concrete concepts to the more general context of an abstract vector space.

Content Outline & Competencies:

I. Matrices, Vectors, and Systems of Linear Equations
   A. Define matrices and vectors. 
   B. Manipulate linear combinations, matrix-vector products, and special
matrices. 
   C. Solve systems of linear equations. 
   D. Perform Gaussian elimination.  
   E. Find the span of a set of vectors. 
   F. Determine linear dependence and independence. 

II. Matrices and Linear Transformations 
   A. Perform matrix multiplication.  
   B. Construct inverse matrices with elementary matrices. 
   C. Find the inverse of a matrix.  
   D. Describe the relationship between linear transformations and
matrices. 
   E. Determine the composition and invertibility of linear
transformations. 

III. Determinants 
   A. Perform cofactor expansions. 
   B. Use the properties of determinants.

IV. Subspaces and Their Properties 
   A. Define subspaces associated with matrices. 
   B. Construct a basis for a subspace.
   C. Determine the dimension of a subspace.
   D. Determine the dimension of subspace associated with a matrix. 
   E. Perform rotation of coordinate systems. 
   F. Construct matrix representations of linear operators. 

V. Eigenvalues, Eigenvectors, and Diagonalization 
   A. Determine eigenvalues and eigenvectors. 
   B. Construct the characteristic polynomial of a matrix. 
   C. Perform the diagonalization of matrices. 
   D. Perform the diagonalization of linear operators.

VI. Orthogonality 
   A. Describe vectors with geometry. 
   B.Construct orthonormal vectors. 
   C. Perform least-squares approximation.
   D. Produce orthogonal projection matrices. 
   E. Create orthogonal matrices and operators. 
   F. Formulate symmetric matrices.   

VII. Vector Spaces 
   A. Define vector spaces and their subspaces. 
   B. Determine dimension and isomorphism. 
   C. Develop linear transformations; find matrix representations. 
   D. Define inner product spaces. 

ADDITIONAL TOPICS OF INTEREST (time permitting)
Systems of linear equations in applications
Matrix multiplication in applications
LU decomposition of a matrix
Eigenvalues in applications
Singular value decomposition of a matrix
Rotations of R3 in computer graphics applications

Methods of Evaluation of Competencies:

Evaluation of student mastery of course competencies will be accomplished using the following methods:

Unit Exams, Unit Papers and/or Unit Projects   40% - 80%
Homework, Quizzes and/or Small Projects         0% - 50%
Final Exam**                                   10% - 40%

**The final exam must count at least as much as any unit exam, unit paper
or unit project. In any course where unit exams are not proctored, the
instructor may require that the student score at least a 70% on the final
exam to earn a ‘C’ for the course. At the instructor's discretion, the
grade on all or any part of the final exam may replace any lower test
score.

Caveats:

1. The majority of mathematics courses are sequential. Students must earn a grade of C or higher in a prerequisite mathematics course to progress to its subsequent mathematics course.
2. In accordance with the assertion made on your billing statement, during the first two weeks of the semester, if a student is found not to have successfully fulfilled the prerequisite(s) for this course, the student will be dropped from the course. He/she will be allowed to enroll in the appropriate lower level math course on a space available basis with an even exchange of tuition. After the first two weeks, students who have not met the prerequisite(s) will be dropped from the course with no refund of tuition.

Disabilities:

If you are a student with a disability, and if you will be requesting accommodations, it is your responsibility to contact Access Services. Access Services will recommend any appropriate accommodations to your professor and his/her director. The professor and director will identify for you which accommodations will be arranged.

JCCC provides a range of services to allow persons with disabilities to participate in educational programs and activities. If you desire support services, contact the office of Access Services for Students With Disabilities (913) 469-8500, ext. 3521 or TDD (913) 469-3885. The Access Services office is located in the Success Center on the second floor of the Student Center.