Instructors:
Teaching Assistants:
Announcements:
Classroom 
Student's Last Name (range) 
TSH/120 
ABBASI  LOBO 
CNH/104 
LOPEZNEGRETE  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 fx991 will be allowed during the tests.Final Exam:
The course will be completed by a threehour final examination. The date and location of the final exam will be announced by the Registrar's office in midterm.Marking Scheme:
The final mark will be the better one obtained with the following two marking schemes:


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 reweighted 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 1011 
 
Lecture 1 
Introduction to the Course 
 
Week 2 
September 1418 
 
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 2125 
 
Lecture 5 
Separable Variables Cont'd 
2.2 
Lecture 6 
Linear Equations 
2.3 
Lecture 7 
Linear Models 
2.7 
Week 4 
September 28October 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 29 (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 1216 (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 1923 
 
Lecture 17 
CauchyEuler Equations Cont'd 
3.6 
Lecture 18 
Linear Models: InitialValue Problems 
3.8 
Lecture 19 
Linear Models: InitialValue Problems Cont'd 
3.8 
Week 8 
October 2630 
 
Lecture 20 
Linear Models: BoundaryValue Problems 
3.9 
Lecture 21 
Linear Models: BoundaryValue Problems Cont'd 
3.9 
Lecture 22 
Review of Linear Algebra 
 
Week 9 
November 26 
 
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 913 ([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 1620 
 
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 2327 
 
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 30December 4 
 
Lecture 35 
Series solutions about Ordinary Points 
5.1 
Lecture 36 
Series solutions about Singular Points 
5.2 
Lecture 37 
Review for Exam 
 