MATH 218 Syllabus, Spring 2012

American University of Beirut Department of Mathematics Spring 2012 Math 218 – Elementary Linear Algebra with Applications Syllabus for all sections Textbook: Introduction to Linear Algebra with Applications, J. DeFranza–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 Rn, 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 the Gram–Schmidt process to construct orthonormal bases. ➢ Perform orthogonal diagonalization of a symmetric matrix. Homework and Exams: There will be weekly sets of homework or drop quizzes, two exams and a final. For the homework assignments only the questions in bold are to be handed in. The grades allocated towards the final grade are: ➢ Exam I..........................................25% ➢ Exam II.........................................25% ➢ Homework/Drop Quizzes............10% ➢ Final Exam................................... 40% Exam Dates: ➢ Exam I, Saturday 17 March, 2012: time and place to be announced. ➢ Exam II, Saturday 21 April, 2012; time and place to be announced. Please make a note from now of the dates of Exam I and Exam II, as given above; make sure that you keep those times reserved for Math 218. Course Policy: ➢ The grade for an unexcused missed exam will be zero. ➢ The university policy regarding incomplete work and other issues will be followed. Check the AUB catalogue for details. ➢ Regular attendance is expected. Students are responsible for all the materials presented in class, including announcements about course procedure. ➢ Last day for withdrawal from courses: 27 April, 2012. Assignments 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, 28, 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. 6.6 2, 4, 6, 8, 10, 12, 14, 20, 22, 24.