Course Objectives: Numerical computations give the only way for solving almost all applied mathematical problems that occur in science and engineering. With the aid of high-level programming languages and customized software libraries, realistic analysis and design problems can be solved quickly, with a minimum of effort. This course focuses on numerical methods and algorithms for solutions of ordinary and partial differential equations.
Topics: Lectures cover problems of polynomial interpolation and approximation, numerical differentiation and integration, ODE solvers, finite-difference and finite-element solutions for PDEs, and spectral methods. 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:
Jonathan Gustafsson, HH-403, ext.24411,
e-mail: Jonathan.Gustafsson@math.mcmaster.ca
Hours:
Lectures: Tuesday, Thursday, Friday (11:30-12:20); CNH-106
Computer Labs: Wednesday (12:30-13:20); BSB-248
Office hours of D.Pelinovsky: Tuesday, Thursday (12:30-13:20)
Office hours of J.Gustafsson: Wednesday (13:30-14:20)
Textbook:
"Numerical Mathematics" by M. Grasselli and D. Pelinovsky
(Jones and Bartlett, 2008), ISBN 9780763737672
Labs: MATLAB 7 is installed in computer lab of BSB-248. 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 of BSB 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: Six home assignments will be posted on the course webpage with specific deadlines. Each assignment corresponds to each chapter of the text. Solutions of the assignments should only include working MATLAB codes and should be submitted by e-mail to math4q03@math.mcmaster.ca. Results of the five best assignments will be counted towards the final mark.
Class Test: There will be one class test on Thursday February 14 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 three-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 | 60% |
| Mid-term test | 20% |
| 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.