MATH 218 Syllabus, Spring 2015

American University of Beirut Department of Mathematics Spring 2014-2015 Math 218 - Elementary Linear Algebra with Applications Textbook: Introduction to Linear Algebra with Applications, by J. DeFranza and D.Gagliardi Course Description: An introduction to linear algebra at a less theoretical level than Math 219. Systems of linear equations and Gaussian elimination, vectors in ℝ𝑛𝑛, matrices, determinants, vector spaces, subspaces and dimension, orthogonal projection and least-squares approximation, eigenvalues, eigenvectors and selected applications. Students cannot receive credit for both Math 219 and Math 218. Prerequisites: Mathematical maturity at a level equivalent to having taken Math 211. In particular, facility with sets, logic, mathematical induction and some background in basic mathematical proof. Course Learning Outcomes: Define systems of linear equations and use Gaussian elimination to solve linear systems. Find the transpose and inverse of a matrix using elementary row operations. Evaluate determinants using several techniques and use the properties of determinants to determine if a matrix is non singular. Determine subspaces, spanning sets and bases of vector spaces and demonstrate linear independence or dependence of a set of vectors. Relate linear transformations to matrices and compute their rank. Compute the eigenvalues and eigenvectors of a matrix and learn the diagonalization of matrices. Define inner product spaces, angles and orthogonality, orthonormal bases. Apply Gram-Schmidt process to construct orthonormal bases. Perform orthogonal diagonalization of a symmetric matrix. Exams: The grades allocated towards the final grade are: Exam I ……………….………………….25% Exam II………………….……………….25% Final Exam…………………………...….50% Exam Dates: Exam I: Tuesday, February 24, 2015 at 6:00 pm (location to be announced). Exam II: Monday, March 23, 2015 at 6:00 pm (location to be announced). Course Policy: -The grade for an unexcused missed Exam will be a zero. Students who miss an exam for a valid medical reason must provide a medical excuse from AUBMC within one week from the date of the exam. -The university policy regarding incomplete work and other issues will be followed. Check the AUB catalogue for details. -Students are expected to read and follow the code of conduct in the AUB Student Handbook. -Regular attendance is expected. Students are responsible for all the material presented in class, including announcements about course procedure. -Last day for withdrawal from courses: Thursday, April 2, 2015. ASSIGNMENT SHEET Section Suggested Problems 1.1 3, 10, 12, 18, 21, 25, 28, 29, 32, 34, 38, 40, 43, 44. 1.2 8, 20, 22, 24, 26, 28, 32, 34, 36, 40, 42, 46, 48, 50, 51. 1.3 12, 16, 18, 20, 22, 24, 27, 28, 29, 30, 32, 35, 36, 38, 40, 42, 43, 44. 1.4 6, 11, 12, 13, 16, 18, 19, 20, 24, 26, 27, 28, 30, 32, 34, 37, 38, 40. 1.5 6, 12, 16, 22, 26, 28, 32. 1.6 2, 3, 4, 18, 20, 23, 25, 28, 30, 32, 36, 40, 43, 52, 53, 54. 2.1 16, 21, 22, 28, 30, 34, 36, 38. 2.2 9, 10, 12, 15, 16, 19, 20, 22, 24, 27, 28, 33, 37, 38, 39. 2.3 7, 8, 9, 10, 13, 14, 20, 21, 24, 27, 28, 31, 32, 37, 38, 42. 3.1 3, 4, 7, 8, 9, 10, 12, 14, 15, 16, 17, 25, 31. 3.2 2, 4, 7, 8, 9, 11, 13, 14, 16, 18, 20, 23, 24, 26, 30, 32, 36, 38, 40, 43, 50. 3.3 3, 4, 6, 10, 11, 12, 16, 19, 20, 22, 24, 28, 36, 41, 42, 44. 3.4 3, 4, 8, 11, 16, 22, 24. 4.1 2, 3, 4, 5, 10, 11, 12, 14, 16, 18, 22, 26, 28, 30, 32, 34, 36, 38, 42. 4.2 4, 6, 7, 10, 12, 14, 16, 18, 20, 26, 28, 29, 30, 32, 34, 40, 43. 4.3 2, 8, 10, 12, 16, 19, 20, 22, 26, 27, 29, 30, 31, 32. 4.4 2, 6, 10, 14, 16, 17, 20, 24, 32. 4.5 2, 4, 6, 8, 10, 12, 16, 17, 18. 5.1 2, 4, 8, 12, 14, 17, 18, 19, 20, 21, 23, 24, 28, 29, 32, 35. 5.2 2, 4, 6, 8, 12, 16, 20, 22, 24, 27, 28, 30, 31, 32, 33, 34, 35, 38. 6.1 2, 3, 4, 11, 12, 13, 14, 15, 16, 18, 24, 30. 6.2 2, 6, 8, 10, 12, 18, 20, 22, 28, 30. 6.3 4, 8, 12, 14, 16, 18, 20, 24, 31, 34, 36, 37. 6.4 4, 6, 10, 14, 16, 18, 22, 27, 29. 6.5 2, 4, 6, 8.