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Student Information Plan Math 2318 Linear Algebra INSTRUCTOR: DAY(S): OFFICE: TIME: OFFICE HOURS: ROOM NUMBER: OFFICE PHONE NUMBER: INSTRUCTOR E-MAIL: TEXT: Linear Algebra and its Applications (2nd Edition) by David C. Lay Course Description: Topics included in this course are systems of linear equations and matrices, vector spaces and linear transformations, eigenvectors and eigenvalues, determinants, and orthogonality. Objectives: This course is designed to develop the understanding of linear algebra as it is used in science, engineering, economics and other subjects. In addition, it will prepare mathematics students for the study of the many subjects depending on it. The level of abstraction involved is an excellent preparation for more advanced courses. Course Outline: A. Linear Equations in Linear Algebra 1. Systems of Linear Equations 2. Row Reduction and Echelon Forms 3. Vector Equations 4. The Matrix Equations Ax=B 5. Solutions Sets of Linear Systems 6. Linear Independence 7. Introduction of Linear Transformations 8. The Matrix of a Linear Transformation 9. Linear Models in Business, Science and Engineering B. Matrix Algebra 1. Matrix Operations 2. The Inverse of a Matrix 3. Characterizations of Invertible Matrices 4. Partitioned Matrices 5. Matrix Factorizations 6. Iterative Solutions of Linear Systems 7. The Leontief Input-Output Model 8. Applications to Computer Graphics 9. Subspaces of |Rn C. Determinants 1. Introduction 2. Properties of Determinants 3. Cramer’s Rule, Volume, and Linear Transformations D. Vector Spaces 1. Vector Spaces and Subspaces 2. Null Spaces, Column Spaces, and Linear Transformations 3. Linearly Independent Sets; Bases 4. Coordinate Systems 5. The Dimension of a Vector Space 6. Rank 7. Change of Basis 8. Applications of Difference Equations 9. Applications of Markov Chains E. Eigenvalues and Eigenvectors 1. Eigenvalues and Eigenvectors 2. The Characteristic Equation 3. Diagonalization 4. Eigenvectors and Linear Transformations 5. Complex Eigenvalues 6. Discrete Dynamical Systems 7. Applications to Differential Equations 8. Iterative Estimates for Eigenvalues F. Orthogonality and Least Squares 1. Inner Product, Length and Orthogonality 2. Orthogonal Sets 3. Orthogonal Projections 4. 5. 6. 7. 8. The Gram-Schmidt Process Least-Squares Problems Applications of Linear Models Inner Product Spaces Applications of Inner Product Spaces G. Symmetric Matrices and Quadratic Forms 1. Diagonalization of Symmetric Matrices 2. Quadratic Forms 3. Constrained Optimization 4. The Singular Value Decomposition 5. Applications of Image Processing and Statistics Grading: A. Methods of Evaluation 1. 2. 3. 4. Homework Quizzes Exams Comprehensive Final Exam B. Grading System Course Average 90- 100 80- 89 70- 79 60-69 below 60 Grade A B C D W, I or F Attendance. Regular attendance in class is expected. If an absence is unavoidable, the student is responsible for completing all work missed during the absence. Any work missed and not subsequently completed will affect the grade of the student regardless of the reason for the absence. Your instructor may initiate administrative withdrawal procedures for a student who exceeds course absence standards. Withdrawal from class may affect enrollment in other courses, insurance eligibility, financial aid, and/or veteran’s benefits. It should be noted that ceasing to attend class does not terminate enrollment. Therefore, a student who ceases to attend class without officially withdrawing from that class, may receive a failing grade. Classroom Behavior. It is expected that students will behave in a mature and courteous manner. Disruptive behavior during class will not be tolerated. Students are expected to be attentive, take notes, ask pertinent questions, arrive on time, and not leave until the class is dismissed. Conflicts which arise between the scheduled class time and the student=s personal schedule must be resolved by the student. Academic Honesty is Assumed. A student found guilty of scholastic dishonesty is subject to disciplinary action. Violations such as plagiarism, cheating on tests, and collusion are described in the ACC Student Handbook. Consequences are at the discretion of the instructor and range from receiving a 0 on the assignment/test to failing the course to expulsion from the College. Camcorders and any other video recording devices are prohibited in the classroom. Audio recording may be allowed ONLY WITH THE PERMISSION OF THE INSTRUCTOR. Cellphones are not to be used and are not to ring during class. Cellphones are not to be out during tests. IF there are special circumstances, arrangements must be made with the instructor. ADA Compliance. This College will adhere to all applicable federal, state, and local laws, regulations, and guidelines with respect to providing reasonable accommodations as required to afford equal educational opportunity. It is the policy of Alvin Community College to provide reasonable accommodations for qualified individuals who are students with disabilities. It is the student’s responsibility to contact the Counseling Center in a timely manner to arrange for appropriate accommodations.