COURSE SYLLABUS (Formally the CIS)

Transcription

1 COURSE SYLLABUS (Formally the CIS) COURSE NUMBER AND TITLE: MATH Linear algebra COURSE (CATALOG) DESCRIPTION: An introductory course in linear algebra. Topics include system of linear equations, Gauss- Jordan elimination, matrices, determinants, vector in N-space, subspaces, linear independence, basis and dimension of a vector space and Eigen value problems. MAJOR COURSE REQUIREMENTS: LEARNING OBJECTIVES: Perform elementary row operation with matrices. 1. Solve systems of linear equations using Gauss-Jordan elimination. 2. Detect inconsistent systems. 3. Calculate the matrix inverse. 4. Apply vector space properties of R n. 5. Verify that subsets are subspaces. 6. Calculate bases and dimensions of subspaces. 7. Perform linear transformation R n to R m. 8. Calculate nullity and rank of a matrix. 9. Find the eigenvalues and eigenvectors for a given matrix. 10. Solve problems using elementary operations with determinants. 11. Find the characteristic polynomial and the eigenvalues for a given matrix. 12. Expand the determinants using cofactor method. 13. Solve system of equations using Cramer s rule. 14. Evaluate the determinants through reduction to triangular form. 15. Calculate wronskian. I. STUDENT LEARNING OUTCOMES A. Matrices and Systems of Linear Equations (Scans 6C) 1. Define echelon form of a matrix and Gauss-Jordan elimination method. 2. Solve system of linear equations using Gauss-Jordan elimination. 3. Define consistent and inconsistent systems of equations. 4. Solve consistent systems of linear equation. 5. Define rules for various matrix operations. 6. Add, subtract and multiply Matrices.

2 7. Define linear independence and nonsingular matrices and solving related problems 8. Perform matrix inverses. B. The Vector Space R n (Scans 6C) 1. Describe properties of Vector Space R n. 2. Solve problems using the properties of R n. 3. Define subspaces. 4. Identify subspaces. 5. Calculate bases of subspaces. 6. Calculate dimension of subspaces. 7. Identify orthogonal bases. 8. Perform linear transformation R n to R m. C. The Eigenvalues Problem (Scans 6C) 1. Define the relation between determinants and Eigenvalues problems. 2. Solve dertminants using the rules of elementary operations. 3. Calculate Eigenvalues from characteristic polynomials 4. Define Eigenvalues and Eigenvectors. D. Determinants (Scans 6C) 1. Solve determinants using cofactor expansion. 2. Perform elementary operations to reduce determinants to triangular form and evaluate them. 3. Solve system of linear equations using Cramer s rule. 4. Solve problems involving applications of determinants.

3 MAJOR COURSE LECTURE, TOPICS DESCRIPTION/REQUIRED/RECOMMENDED READINGS/ELECTRONIC RESOURCES TO VIEW: SUMMER 2011 Tentative Schedule (Subject to change by your instructor) Date CH./ SEC. Topic/Lecture/Event Assignments 5/09 Introduction, Policy Introduction to matrices and system of linear equations 3, 5, 9, 11, 17, 21, 27, 31, Echelon form and Gauss-Jordan elimination 23, 25, 29, 31, 33, Consistent systems of linear equation. 9, 11, 13, 17, 21, Applications 1, 3, Matrix operation 3, 5, 7, 9, 15, 41, 45, Algebraic properties of matrix operation. 3, 5, 7, 11, 13, 19, 25, 35, Linear independence and nonsingular matrices. 7, 11, 13, 19, 23, 31, Matrix inverses and their properties. 3, 7, 11, 19, 25, 29, 37, , 47 6/2 Review 4 Test # Vector space R n. 1, 5, 11, 17, 19, 21, 23, Vector space properties of R n 1, 3, 9, 13, 15, 17, 23, Example of subspaces. 1, 3, 5, 23, 25, 27, 31, Bases for subspaces. 1, 3, 7, 9 Review 16 Test # Dimension 13, 15, 17, 21, 23, 25, 26

4 Date CH./ SEC. Topic/Lecture/Event Assignments Orthogonal bases for subspaces. 1, 3, 5, 7, 9, 11, 13, 15, 17, Linear transformation from R n to R m 1, 3, 9, 11, 13, Least-Squares solutions to inconsistent systems 1, 3, 7, 9, Theory and practice of least squares 1, 3, 7, 9, 11 Review 28 Test #3 7/2 4.1 Eigen Value Problems for (2x2) Matrices 4.2 Determinants and eigenvalue problems Elementary operations and determinants Eigenvalues and the characteristic polynomials 3, 7, 11, 15 9, 15, 17, 19 5, 7, 9, 13, 17 7, 9, 11, Eigenvectors and Eigenspaces 19, 21, Review 14 Test # Applications of determinants, Inverse and Wronskains. 1, 3, 7, 13, 17, Matrix representations for quadratic forms 3, 5, 9, 13, 17, 19 8/1-3 Review Final 23 Final Exam August 5, 2011 REQUIRED TEXT AND MATERIALS: INTRODUCTION TO LINEAR ALGEBRA by Johnson/Reiss/ Arnold 5 th edition Scientific calculator.

5 GRADING CRITERIA GRADING SCALE At the end of the semester I will drop one of your chapter test. If you missed a test it will be your dropped test. A % Chapter Tests 80% B 80-89% Final Exam 20% C 70-79% D 60-69% F 0-59% ACCOMMODATION STATEMENT: If you have a documented disability which will make it difficult for you to carry out class work as outlined and/or if you need special accommodations due to a disability, please contact (956) or visit the Support Services Office in the Auxiliary Services Building as soon as possible to make appropriate arrangements. GENERAL EDUCATION PROGRAM ASSESSMENT: Assignments from this course are subject to being archived for general education assessment. Procedures will follow protocols as prescribed by the research guidelines of the Association for Institutional Research. Final exam will also be used for course assessment. CLASS POLICIES: Four tests will be given during the semester, and your lowest test grade will be dropped before averaging; provided you have an average of 70 or better on homework, quizzes, class work and projects during the semester. There will be NO makeup tests, if you miss a test that will be your dropped test. FINAL exam is mandatory. No late work will be accepted. The use of cell phones is prohibited. (You may put your phone on silent mode) Copyright Statement The materials used in the course [textbooks, handouts, media files (podcast, MP3, Videos, RSS (Feeds), and all instructional resources on the colleges Learning Management System (Moodle)] are intended for use only by students registered and enrolled in this course and are only to be used for instructional use, activities associated with, and for the duration of the course. All materials generated for this course, which includes but are not limited to syllabi, quizzes, exams, lab problems, in-class materials, review sheets, and any additional materials. These materials may not be retained in another medium or disseminated further. They are provided in compliance with the provisions of the Teach Act. These materials may not be reproduced, displayed, modified or distributed without the express prior written permission of the copyright holder or TSTC. For further information contact your instructor.

6 Communicating with your instructor (MyMail System) All official college to students is sent through MyMail, the official student system at TSTC Harlingen. When communicating with instructors and/or employees of the college, you are required to use your TSTC MyMail student address. If you choose to forward your e- mail to another account, please be advised that you must respond from the MyMail account. TSTC Harlingen faculty, staff, and students are asked to report all threats, perceived or real, immediately to College Police located in the Auxiliary Building. If the threat is imminent, the College Police emergency phone line at or should be called. College Police will then coordinate the proper response in accordance with State and federal laws and TSTC System/College rules and regulations. NOTE: Any changes to this syllabus will be provided in writing to the student and updated on all posted locations (HB 2504, course Moodle sites, building offices, etc.).