Mathematics 3Q03: Numerical Explorations (Fall, 2014)

Course Objectives: Numerical computations are the only realistic way to obtain solutions of many problems involving inversion of a large system of linear equations, eigenvalues of a boundary-value problem, or evolutions of a partial differential equation. This course focuses on numerical algorithms for polynomial interpolation, function approximations, differentiation and integrating, initial-value and boundary-value problems for differential equations. Theoretical aspects of mathematical algorithms will be discussed together with practical aspects of robustness and visualizations of numerical computations. Numerical examples and computer assignments are based on computer programs with Matlab. Tests and exams are based on the theoretical material of the course.

Topics: Scientific computations using MATLAB; spline interpolations; approximations of functions; orthogonal polynomials; numerical differentiation and integration; and numerical methods for differential equations.

Dr. Dmitry Pelinovsky, HH-422, ext.23424, e-mail:

Alexandra Teslya, e-mail:

Lectures: Mondays, Wednesdays, and Thursdays (10:30-11:20); HH-217
Office hours: Monday, Thursdays (12:30-13:20) or by appointment.

Courseware "Numerical Explorations" by D.E. Pelinovsky (McMaster University, 2014)

Assignments: Five 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 Results of the four best assignments will be counted towards the final mark.

Class Tests: There will be two class tests on Thursdays October 9 and November 20 during the regular lecture hour. Lecture notes and McMaster calculators are allowed on the tests.

Final Exam: The course is completed by a three-hour final examination. Textbooks, lecture notes, and McMaster calculators are allowed on the final exam. 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%

Important message: The instructor and university reserve the right to modify elements of the course during the term. The university may change the dates and deadlines for any or all courses in extreme circumstances. If either type of modification becomes necessary, reasonable notice and communication with the students will be given with explanation and the opportunity to comment on changes. It is the responsibility of the student to check their McMaster email and course websites weekly during the term and to note any changes.

Academic Dishonesty: Any student who infringes academic dishonesty will be treated according to the policy of the McMaster University. 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.

Requests for Relief for Missed Academic Term Work: Using the McMaster student absence form (MSAF) on-line, self-reporting tool, undergraduate students may report absences lasting up to 5 days and may also request relief for missed academic work, which is less than 30% of the final mark. The submission of medical or other types of supporting documentation is normally not required. Students may use this tool only once per term. Students who are absent more than five days cannot use the on-line, self-reporting tool to request relief. They MUST report to their Faculty Office to discuss their situation and may be required to provide appropriate supporting documentation.

Additional information: Late assignments will not be graded. No make-up tests will be scheduled. In the event of an exemption from the test or more than one assignment, your course grade will be re-weighted by increasing the weight of the final examination to compensate for the missed test or assignment.