Course Objectives: Numerical computations are the only realistic way to obtain solutions of many problems involving large systems of linear equations, eigenvalues of large matrices, and other problems of linear algebra. This course focuses on numerical methods and algorithms for direct and iterative solutions of linear systems, computations of eigenvalues and eigenvectors, as well as for decompositions, projections, and factorizations in finite-dimensional vector spaces. Examples and problems will be implemented in the numerical solution using MATLAB. Theoretical aspects of matrix norms, condition numbers, computational complexity, stability and convergence of iterations will be discussed together with practical aspects of robustness, compactness, and visualizations of the numerical codes.
Topics: Lectures cover introduction to MATLAB, matrix norms and convergence of algorithms, solutions of linear systems, least square approximations and orthogonal projections, and computations of eigenvalues and eigenvectors. Numerical examples and computer assignments are based on computer programs with Matlab.
Instructor:
Dr. Dmitry Pelinovsky, HH-422, ext.23424, e-mail: dmpeli@math.mcmaster.ca
Teaching Assistant:
Azzam Hazim, e-mail: hazima@mcmaster.ca
Hours:
Lectures: Tuesday, Thursday, Friday (11:30-12:20); BSB-108
Computer Labs: Wednesday (10:30-11:20); KTH-B121
Office hours of D.Pelinovsky: Tuesday, Thursday (10:30-11:20)
Office hours of A.Hazim: Thursday (13:30-15:20) in MATHCafe.
Textbook:
"Numerical Mathematics" by M. Grasselli and D. Pelinovsky
(Jones and Bartlett, 2008), ISBN 9780763737672
Labs: MATLAB 7 is installed in computer lab of KTH. Lab hours are reserved for the work of students with computer-based problems. Unless the labs are reserved for large-class tutorials, students might be able to work in the computer labs beyond the scheduled time. Students are also encouraged to purchase "The Student Edition of MATLAB" to be able to work with Matlab at home.
Assignments: Four home assignments will be posted on the course webpage with specific deadlines. Solutions of the assignments should only include working MATLAB codes and should be submitted by e-mail to math2t03@math.mcmaster.ca. Results of the three best assignments will be counted towards the final mark.
Class Test: There will be two class tests on Fridays February 06 and March 20 during the regular lecture hour. The test will cover analytical questions of the course. Laptops and calculators of all kinds are allowed on the test.
Final Exam: The course is completed by a two-hour final examination. The date and location of the final exam will be announced by the registrar's office in mid-term.
Marking scheme:
| Final exam | 40% |
| Mid-term tests | 40% |
| Assignments | 20% |
Senate Policy Statement: The course is regulated under the following documents: Statement on Academic Ethics and Senate Resolutions on Academic Dishonesty. Any student who infringes one of these resolutions will be treated according to the published policy. In particular, academic dishonesty includes (1) plagiarism, e.g. the submission of work that is not one's own, (2) improper collaboration in group work on home assignments, (3) copying or using unauthorized aids tests and examinations. It is your responsibility to understand what constitutes academic dishonesty, refering to Academic Integrity Policy.
Additional information: Late assignments will not be graded. No make-up tests will be scheduled. No exemption from one assignment for medical or other reasons is granted. Exemptions from the test and several assignments for valid reasons are possible, but must be requested through the office of the Associate Dean of the Faculty you are registered with. In the event of an exemption, your course grade will be re-weighted by increasing the weight of the final examination to compensate for the missed test or assignment.