Instructors:
Teaching Assistants:
Announcements:
| Classroom |
Student's Last Name (range) |
| TSH/120 |
ABBASI - LOBO |
| CNH/104 |
LOPEZ-NEGRETE - ZWEEP |
Outline of the Course:
The course provides an overview of ordinary differential equations and covers also some related topics, such as Laplace transforms and elements of linear algebra (eigenvalues and eigenvectors). A number of applications to actual problems will be discussed. Students will also acquire programming skills in MATLAB, and will use them to solve a range of problems introduced during lectures.Course Objectives:
By the end of the course students should be familiar with the basic theory concerning ordinary differential equations, and should be able to apply this theory to solve problems arising in applications. They should also be able to develop MATLAB programs for the solution and visualization of such problems.Tutorials:
An important element of the course are the tutorials during which the Teaching Assistants will introduce MATLAB programming techniques necessary for the solution of homework assignments. MATLAB files containing the material of the tutorials will be posted in advance on the course website, and should be downloaded and reviewed before attending the tutorial. Students are strongly encouraged to bring their own laptops, so that they can actively follow the presentation.Primary Reference:
Software:
All homework assignments will have to be completed using MATLAB. This software will also be used for presentations during tutorials. While MATLAB can be used in a number of computer labs on the campus, students are encouraged to purchase The Student Edition of MATLAB to be able to work with MATLAB at home.Prerequisites:
Engineering Mathematics I and II (MATH 1Z04 \& MATH 1ZZ5), or equivalentAssignments:
Six homework assignments will be posted on the course website on the dates indicated in the table below. The assignments will be due by midnight on the dates indicated in the table. Solutions of the assignments should be prepared using the template file available from the course website, and be submitted electronically to the suitable Email address. Please see here for detailed instructions concerning submission of homework assignments. Late submissions will not be accepted under any circumstances. The solutions will be posted on the course website after the due date.Homework Post & Due Dates (tentative):
| # |
Post Date |
Due Date |
| HW 1 |
Monday, September 21 |
Monday, September 28 |
| HW 2 |
Monday, October 5 |
Tuesday, October 13 |
| HW 3 |
Monday, October 19 |
Monday, October 26 |
| HW 4 |
Monday, November 2 |
Monday, November 9 |
| HW 5 |
Monday, November 16 |
Monday, November 23 |
| HW 6 |
Monday, November 30 |
Monday, December 7 |
Tests:
There will be two tests scheduled tentatively on October 6 and November 10 (in lieu of November 17 announced initially). They will last 75 minutes and will take place in the evening (i.e., at or after 7pm) at a location to be announced later. The tests will focus on analytical issues, although may also address elements of MATLAB programming. Only the McMaster standard calculator Casio fx-991 will be allowed during the tests.Final Exam:
The course will be 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:
The final mark will be the better one obtained with the following two marking schemes:
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Excused Absences:
Exemptions from the assignments or tests for valid reasons are possible, but must be requested through the office of the Associate Dean of the Faculty that you are registered with. In the event of an exemption, no make up test or assignment will be administered, but your course grade will be re-weighted by increasing the weight of the final examination to compensate for the missed test or the weight of the remaining assignments for the missed assignment.Academic Integrity:
You are expected to exhibit honesty and use ethical behaviour in all aspects of the learning process. Academic credentials you earn are rooted in principles of honesty and academic integrity.Important Notice:
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.Topics:
| # |
Topic |
Sections from Ref. 1 |
| Week 1 |
September 10-11 |
- |
| Lecture 1 |
Introduction to the Course |
- |
| Week 2 |
September 14-18 |
- |
| Lecture 2 |
Definitions and Terminology |
1.1 |
| Lecture 3 |
Definitions and Terminology |
1.1 |
| Lecture 4 |
Solution Curves Without a Solution |
2.1 |
| Week 3 |
September 21-25 |
- |
| Lecture 5 |
Separable Variables Cont'd |
2.2 |
| Lecture 6 |
Linear Equations |
2.3 |
| Lecture 7 |
Linear Models |
2.7 |
| Week 4 |
September 28-October 2 |
- |
| Lecture 8 |
Preliminary Theory: Linear Equations Cont'd (skip 3.1.3) |
3.1 |
| Lecture 9 |
Preliminary Theory: Linear Equations Cont'd (skip 3.1.3) |
3.1 |
| Lecture 10 |
Homogeneous Linear Equations with Constant Coefficients |
3.3 |
| Week 5 |
October 2-9 (Test #1 on Tuesday, October 6) |
- |
| Lecture 11 |
Homogeneous Linear Equations with Constant Coefficients Cont'd |
3.3 |
| Lecture 12 |
Undetermined Coefficients |
3.4 |
| Lecture 13 |
Undetermined Coefficients Cont'd |
3.4 |
| Week 6 |
October 12-16 (Holiday on Monday, October 12) |
- |
| Lecture 14 |
Sections that are not cancelled are to use this as review or catch up |
- |
| Lecture 15 |
Variation of Parameters |
3.5 |
| Lecture 16 |
Variation of Parameters Cont'd |
3.5 |
| Week 7 |
October 19-23 |
- |
| Lecture 17 |
Cauchy-Euler Equations Cont'd |
3.6 |
| Lecture 18 |
Linear Models: Initial-Value Problems |
3.8 |
| Lecture 19 |
Linear Models: Initial-Value Problems Cont'd |
3.8 |
| Week 8 |
October 26-30 |
- |
| Lecture 20 |
Linear Models: Boundary-Value Problems |
3.9 |
| Lecture 21 |
Linear Models: Boundary-Value Problems Cont'd |
3.9 |
| Lecture 22 |
Review of Linear Algebra |
- |
| Week 9 |
November 2-6 |
- |
| Lecture 23 |
The Eigenvalue Problem |
8.8 |
| Lecture 24 |
The Eigenvalue Problem Cont'd |
8.8 |
| Lecture 25 |
Orthogonal Matrices |
8.10 |
| Week 10 |
November 9-13 ([NEW!] Test #2 on Tuesday, November 10) |
- |
| Lecture 26 |
Diagonalization Cont'd |
8.12 |
| Lecture 27 |
Preliminary Theory (Systems of Linear Equations) |
10.1 |
| Lecture 28 |
Homogeneous Linear Systems |
10.2 |
| Week 11 |
November 16-20 |
- |
| Lecture 29 |
Definition of the Laplace Transform |
4.1 |
| Lecture 30 |
Definition of the Laplace Transform Cont'd |
4.1 |
| Lecture 31 |
The Inverse Transform and Transforms of Derivatives Cont'd |
4.2 |
| Week 12 |
November 23-27 |
- |
| Lecture 32 |
Additional Operational Properties |
4.4 |
| Lecture 33 |
The Dirac Delta Function |
4.5 |
| Lecture 34 |
Systems of Linear Differential Equations |
4.6 |
| Week 13 |
November 30-December 4 |
- |
| Lecture 35 |
Series solutions about Ordinary Points |
5.1 |
| Lecture 36 |
Series solutions about Singular Points |
5.2 |
| Lecture 37 |
Review for Exam |
- |