Instructors:
Teaching Assistants:
Announcements:
Outline of the Course:
The course provides an overview of Fourier series, vector calculus, line and surface integrals together with integral theorems. It also provides an introduction to some elementary partial differential equations. A number of applications to actual problems will be discussed. Students will also further develop their 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 Fourier series, vector calculus, line and surface integrals, as well as partial 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, II and III (MATH 1Z04, MATH 1ZZ5, & MATH 2Z03), or equivalentAssignments:
Five homework assignments will be posted on the course website on the dates indicated in the table below. The assignments will be due one minute past 11:59pm on the dates indicated in the table. Note that while assignments #1, #2, #3 and #4 will be due on Mondays, assignment #5 will be due on Thursday. Solutions of the assignments should be prepared using the current 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, January 25 |
Monday, February 1 |
HW 2 |
Monday, February 8 |
Tuesday, February 16 |
HW 3 |
Monday, February 22 |
Monday, March 1 |
HW 4 |
Monday, March 8 |
Monday, March 15 |
HW 5 |
Thursday, March 25 |
Thursday, April 1 |
Tests:
There will be two tests scheduled tentatively on February 4 (Thursday) and March 16 (Tuesday). 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.Course Schedule:
# |
Topic |
Sections from Ref. 1 |
Week 1 |
January 4-8 |
- |
Lecture 1 |
Introduction to the Course |
- |
Lecture 2 |
Orthogonal Functions |
12.1 |
Lecture 3 |
Fourier Series |
12.2 |
Week 2 |
January 11-15 |
- |
Lecture 4 |
Fourier Series (cont'd) |
12.2 |
Lecture 5 |
Fourier Cosine and Sine Series (cont'd) |
12.3 |
Lecture 6 |
Complex Fourier Series (cont'd) |
12.4 |
Week 3 |
January 18-22 |
- |
Lecture 7 |
Vector Functions |
9.1 |
Lecture 8 |
Motion on a Curve |
9.2 |
Lecture 9 |
Curvature and Components of Acceleration |
9.3 |
Week 4 |
January 25-29 |
- |
Lecture 10 |
Curvature and Components of Acceleration (cont'd) |
9.3 |
Lecture 11 |
Partial Derivatives (cont'd) |
9.4 |
Lecture 12 |
Directional Derivatives (cont'd) |
9.5 |
Week 5 |
February 1-5 (Test #1 on Thursday, February 4) |
- |
Lecture 13 |
Tangent Planes and Normal Lines |
9.6 |
Lecture 14 |
Divergence and Curl |
9.7 |
Lecture 15 |
Divergence and Curl (cont'd) |
9.7 |
Week 6 |
February 8-12 |
- |
Lecture 16 |
Lines Integrals (cont'd) |
9.8 |
Lecture 17 |
Independence of Path (cont'd) |
9.9 |
Lecture 18 |
Double Integrals (cont'd) |
9.10 |
Week 7 |
February 15-19 (Reading Week) |
- |
Week 8 |
February 22-26 |
- |
Lecture 19 |
Double Integrals in Polar Coordinates |
9.11 |
Lecture 20 |
Double Integrals in Polar Coordinates (cont'd) |
9.11 |
Lecture 21 |
Green's Theorem (cont'd) |
9.12 |
Week 9 |
March 1-5 |
- |
Lecture 22 |
Surface Integrals (cont'd) |
9.13 |
Lecture 23 |
Stokes' Theorem |
9.14 |
Lecture 24 |
Triple Integrals (cont'd) |
9.15 |
Week 10 |
March 8-12 |
- |
Lecture 25 |
Divergence Theorem (cont'd) |
9.16 |
Lecture 26 |
Change of Variables in Multiple Integrals (cont'd) |
9.17 |
Lecture 27 |
Separable Partial Differential Equations |
13.1 |
Week 11 |
March 15-19 (Test #2 on Tuesday, March 16) |
- |
Lecture 28 |
Classical Equations and Boundary-Value Problems |
13.2 |
Lecture 29 |
Classical Equations and Boundary-Value Problems (cont'd) |
13.2 |
Lecture 30 |
Heat Equation |
13.3 |
Week 12 |
March 22-26 |
- |
Lecture 31 |
Wave Equation |
13.4 |
Lecture 32 |
Laplace's Equation |
13.5 |
Lecture 33 |
Heat, Wave, Laplace's Equation (cont'd) |
13.3-13.5 |
Week 13 |
March 29 - April 2 (Holiday on Friday, April 2) |
- |
Lecture 34 |
Nonhomogeneous Boundary-Value Problems |
13.6 |
Lecture 35 |
Orthogonal Series Expansion |
13.7 |
Lecture 36 |
Section that are not cancelled are to use this for review or catch up |
- |
Week 14 |
April 5-8 |
- |
Lecture 37 |
Fourier Series in Two Variables |
13.8 |
Lecture 38 |
Review for Exam |
- |
Lecture 39 |
Review for Exam |
- |