SALEM COMMUNITY COLLEGE Carneys Point, New Jersey COURSE SYLLABUS COVER SHEET. Action Taken (Please Check One) New Course Initiated

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1 SALEM COMMUNITY COLLEGE Carneys Point, New Jersey COURSE SYLLABUS COVER SHEET Course Title Course Number Department Linear Algebra Mathematics MAT-240 Action Taken (Please Check One) New Course Initiated (xxxxxx) Minor Updates ( ) Major Updates ( ) Endorsement Unchanged ( ) * Master Copy is Available on Diskette ( ) * Code Original Date of Syllabus November 2008 Date of Last Official Change Semester Offered Faculty Member: Spring only Wm Mays Jr. * Academic Affairs use only

2 Page 2 Salem Community College Course Syllabus Course Title: Linear Algebra Course Code: MAT-240 Lecture Hours: 4 Laboratory Hours: 0 Credits: 4 Course Description: This course is designed for students who need preparation for higher levels of mathematics. Topics include Linear equations, Matrix Algebra, Determinants, Vector Spaces, Eigenvalues and Eigenvectors, and Orthogonality and Least squares. Applications will be used extensively throughout. A TI graphing calculator is required. Prerequisite: MAT 232 or written permission of Assistant Dean of Academic Affairs Co-requisite: None. Place in the College Curriculum: This course is required in the Mathematics option of the Liberal Arts Degree. This course can be taken as a 4 credit Mathematics elective. Date of Last Revisions: November 2008

3 Page 3 Course Content Outline: I. Linear Equations in Linear Algebra A. Systems of Linear equations B. Row Reduction and Echelon forms C. Vector Equations D. The Matrix equation Ax=b E. Solution Sets of Linear Systems F. Applications of Linear Systems G. Linear Independence H. Introduction to Linear Transformations I. The Matrix of a Linear Transformation J. Linear Models in Business, Science, and Engineering II. Matrix Algebra A. Matrix Operations B. The Inverse of a Matrix C. Characterizations of Invertible Matrices D. Partitioned Matrices E. Matrix Factorizations F. The Leontief Input-Output Model G. Applications to Computer Graphics H. Subspace of R n I. Dimension and Rank III. Determinants A. Introduction to Determinants B. Properties of Determinants C. Cramer s Rule, Volume, and Linear Transformations IV. Vector Spaces A. Vector Spaces and Subspaces B. Null spaces, Column Spaces, and Linear Transformations C. Linearly Independent Sets; Bases D. Coordinate Systems E. The Dimension of a Vector Space F. Rank G. Change of Basis H. Applications to Difference Equations I. Applications to Markov Chains

4 Page 4 V. Eigenvalues and Eigenvectors A. Eigenvectors and Eigenvalues B. The Characteristic Equation C. Diagonalization D. Eigenvectors and Linear Transformations E. Complex Eigenvalues F. Discrete Dynamical Systems G. Applications to Differential Equations H. Iterative Estimates for Eigenvalues VI. Orthogonality and Least Squares A. Inner Product, Length, and Orthogonality B. Orthogonal Sets C. Orthogonal Projections D. The Gram-Schmidt Process E. Least-Squares Problems F. Applications to Linear Models G. Inner Product Spaces H. Applications of Inner Product Space

5 Page 5 Course Performance Objective #1: The student will use linear equations to solve application programs. 1. The student will solve systems of linear equations. 2. The student will write linear systems in echelon forms using row reduction. 3. The student will create and evaluate vector equations. 4. The student will define and solve a matrix equation. 5. The student will define different types of solution sets of linear systems. 6. The student will evaluate and solve application problems of linear systems. 7. The student will define linear independence. 8. The student will determine if vectors have linear independence. 9. The student will describe and evaluate linear transformations. 10. The student will apply concepts of linear equations to application problems. Course Performance Objective #2: The student will perform matrix algebra. 1. The student will perform operations on matrices. 2. The student will describe and construct the inverse of a matrix. 3. The student will describe the characteristics of invertible matrices 4. The student will determine if a matrix is invertible. 5. The student will describe how to partition a matrix. 6. The student will perform operations on partitioned matrices. 7. The student will define matrix factorization. 8. The student will solve matrix equations using matrix factorization. 9. The student will describe Leontief s Input-Output Model. 10. The student will evaluate application problems using Leontief s Input-Output Model. 11. The student will apply concepts of matrix algebra to application problems. 12. The student will define and determine the subspace of R n. 13. The student will define dimension and rank. 14. The student will apply subspace concepts to dimension and rank. Course Performance Objective #3: The student will demonstrate concepts involving determinants. 1. The student will define and determine the determinant of a matrix. 2. The student will describe the properties of determinants. 3. The student will determine if a matrix is invertible and/or linearly independent using determinants. 4. The student will describe Cramer s Rule. 5. The student will describe linear transformations using determinants. 6. The student will apply Cramer s Rule and linear transformation.

6 Page 6 Course Performance Objective #4: The student will define and evaluate vector spaces. 1. The student will define vector space and subspace. 2. The student will determine a subspace for a vector space. 3. The student will define null spaces and column spaces. 4. The student will determine the null space and column space. 5. The student will define the term bases. 6. The student will determine the bases for R n and determine which ones are linearly independent and which ones span R n. 7. The student will define and apply coordinate mapping. 8. The student will define and apply dimension of a vector space. 9. The student will define and apply rank. 10. The student will apply change of basis. 11. The student will define linear difference equations. 12. The student will apply concepts of linear difference equations to application problems. 13. The student will define probability vector, stochastic matrix, and Markov chain. 14. The student will determine probability vectors and stochastic matrices. 15. The student will apply concepts of Markov chains to application problems. Course Performance Objective #5: The student will apply Eigenvalues and Eigenvectors. 1. The student will define Eigenvalues and Eigenvectors. 2. The student will calculate Eigenvalues and Eigenvectors. 3. The student will define the characteristic equation. 4. The student will solve the characteristic equation. 5. The student will describe and perform diagonalization. 6. The student will apply linear transformation to eigenvectors. 7. The student will define and construct complex eigenvalues. 8. The student will identify a discrete dynamical system. 9. The student will apply Eigenvalues and Eigenvectors to discrete dynamical systems. 10. The student will apply concepts of Eigenvalues and Eigenvectors to application problems. 11. The student will construct iterative estimates for eigenvalues.

7 Page 7 Course Performance Objective #6: The student will evaluate and construct least squares lines. 1. The student will define orthogonal. 2. The student will define and determine the inner product. 3. The student will define orthogonal basis. 4. The student will define and apply orthogonal projection. 5. The student will describe and apply the Gram-Schmidt Process. 6. The student will define and apply the QR factorization. 7. The student will define least square lines. 8. The student will find least square solutions. 9. The student will apply least square models to application problems. 10. The student will define inner product space. 11. The student will apply inner product space to application problems. General Education Requirements: The general education goals covered in Linear Algebra are critical thinking & problem solving, quantitative skills, and science & technology. See student handbook for additional details.

8 Page 8 Outcomes Assessment: A college-wide outcomes assessment program has been put into place to enhance the quality and effectiveness of the curriculum and programs at Salem Community College. As part of this assessment program, the learning outcomes for this course will be assessed. Assessment methods may include tests, quizzes, papers, reports, projects and other instruments. Copies of all outcomes assessments are available in an electronic assessment bank maintained by the Institutional Research and Planning Office. Course Activities: Students will learn from lectures during which new material will be delivered, small group discussions, individual explorations, practice work, and discussion of assigned homework problems. Students will have the opportunity to investigate the Linear Algebra concepts using some computer software. Course Requirements and Means of Evaluation: Please refer to the instructor s syllabus addendum (to be distributed in class) for specific information regarding the course requirements and means of evaluation. Attendance: Regular and prompt attendance in all classes is expected of students. Students absent from class for any reason are responsible for making up any missed work. Faculty members establish an attendance policy for each course and it is the student s responsibility to honor and comply with that policy. Academic Honesty Policy: Students found to have committed an act of academic dishonesty may be subject to failure of this course, academic probation, and / or suspension from the college. See the Student Handbook for additional details. ADA Statement: If you have a 504 Accommodation Plan, please discuss it with your instructor. If you have any disability but have not documented it with the Disability Support coordinator at Salem Community college, you must do so to be eligible for accommodations. To contact the Disability Support Coordinator, call , or disabilitysupport@salemcc.edu to set up an appointment. To find out more information about disability support services at Salem Community College, visit Required Texts: For textbook information, please see the Salem Community College Bookstore Website. Optional Text(s): None Materials/Supplies: TI Graphing calculator. MapleSoft, Maple 11 Student Edition CD 2008 (included in textbook package in bookstore)

9 Additional Costs: As necessitated by the required materials. Page 9