Course Objectives: The course introduces various methods of solving of ordinary differential equations. The students will learn how to integrate the first-order and secord-order equations, how to construct a characteristic equation for linear differential equations, and how to use the Laplace transform, the power series and the Fourier series in the context of differential equations. Lectures cover both the formalism and relevant proofs with an excessive number of examples. Tutorials, assignments, and tests are based on analytical problems of different levels which originate from various engineering applications. Projects include computational problems for differential equations.
Topics: First-order and second-order differential equations. Laplace transform. Series solutions. Fourier series.
Instructors and hours:
Section 1:
Dmitry Pelinovsky, HH-422, ext. 23424,
e-mail: dmpeli@math.mcmaster.ca
Lectures: Monday, Wednesday, Thursday (13:30-14:20); HSC/1A1
Office hours: Monday, Thursday (14:30-15:20)
Section 2:
Zdislav V. Kovarik, HH-425, ext. 23408, e-mail: kovarik@mcmaster.ca
Lectures: Tuesday, Wednesday, Friday (09:30-10:20); ITB/137
Office hours: Tuesday, Friday (14:00-15:00)
Teaching Assistant:
Marina Chugunova, HH-403, ext. 24411, e-mail: chugunom@math.mcmaster.ca
Tutorial 1: Thursday (16:30-17:20), TSH/B128
Tutorial 2: Friday (10:30-11:20), ITB/137
Math Help Center Hours for Math2M03 (M.Chugunova): Thursday 13:30-15:30, HH, second floor
Math Help Center Hours for Math2P04 (A.Morgante): Tuesday 13:30-15:30, HH, second floor
Textbooks:
"Advanced Engineering Mathematics", 3rd edition
by D. Zill and M. Cullen (Jones and Bartlett, 2006), ISBN 9780763745912
"Numerical Mathematics"
by M. Grasselli and D. Pelinovsky (Jones and Bartlett, 2008), ISBN 9780763737672
Lectures and Tutorials: There will be three lectures and one tutorial per week in each section. The list of required and optional problems for tutorial sections will be posted on the course webpage. The importance of doing all suggested problems cannot be overemphasised. You will not learn the material without working on problems by yourselves, with the help of your TA and instructor. Students who can do the homework problems should be able to do tests and exams.
Assignments: Five home assignments will be posted on the course webpage with specific deadlines. Each assignment corresponds to each chapter of the text. Assignments must be dropped at the course locker in Hamilton Hall. One problem of each assignment at the instructor's discretion will be graded.
Projects: Two projects will be posted on the course webpage with specific deadlines. Projects discuss applications of differential equations and numerical computation of various solutions. The completed projects must be dropped at the course locker in Hamilton Hall. Solutions to projects and results will be posted on the course webpage. You may discuss problems of the projects with each other, but we expect you to write up the answers by yourself.
Mid-Term Tests: There will be two mid-term tests on Mondays October 15 and November 5 for Section 1 and Tuesdays October 16 and November 6 for Section 2 during the regular lecture hours. Only the McMaster standard calculator Casio fx-991 is allowed on the tests. You must bring your student ID to the test room. Solutions to tests will not be posted on the course webpage.
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 before the end of term.
Alternative marking schemes:
| Final exam | 40% | 50% |
| Mid-term tests | 40% | 50% |
| Projects | 10% | 0% |
| Assignments | 10% | 0% |
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 and projects will not be graded. No make-up tests will be scheduled. Exemptions from the tests and 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.