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Course Outline

Lectures

See the Undergraduate Schedule of Classes.

Purpose

This course will introduce students to ordinary differential equations, initial-value problems, their solutions through the use of Laplace transforms, the Fourier series representation of periodic functions and how Fourier series naturally interact with the Laplace transform, and an introduction to partial differential equations.

Recommended Texts

Glyn James, Modern Engineering Mathematics. Fourth Edition, Prentice Hall, 2011. Volume I (MEM).
Glyn James, Advanced Modern Engineering Mathematics. Fourth Edition, Prentice Hall, 2011. Volume II (AMEM).

Prerequisites

MATH 119 Calculus 2 for Engineering, ECE 140 Linear Circuits, and ECE 150 Fundamentals of Programming.

Co-requisite

MATH 115 Linear Algebra.

Post-requisites

MATH 212, ECE 207, ECE 316, ECE 318, ECE 380, ECE 413, ECE 414, ECE 418, ECE 443.

Math 211 website

https://ece.uwaterloo.ca/~math211/

Grading Scheme

If the grade on the final examination is 40 % or above,

  Final Grade 100 % =
  Final Exam 50 % +
  Assignments 10 % +
  Lab 10 % +
  Lab Final Exam 10 % +
  Midterm Exam 20 % (See the midterm schedule).

If the exam grade less than 40 %, the final examination grade will be the final grade.

Assignments

There will be an assignment nearly every week. Be sure to check the Homepage or with the instructor afterwards for the solutions, since not all of the submitted problems will be marked each week. Assignments will be due Thursday in class no later than 11:25. Late assignments will NOT be accepted and will receive a grade of 0.

Getting your marked assignments back

We will normally need one week to get all of the assignments graded. After that, they will be distributed by the course professor at the end of the lecture (if you fail to collect an assignment you will need to see your instructor during office hours to retrieve it). To facilitate this process, a class serial number is assigned to every student. The student's name and serial number should be written in large font at the left corner of the first page.

In order to comply with the provincial Freedom of Information and Protection of Privacy Act, we also give you the option of having your assignments returned to you by mail. If this is what you would prefer, then inform your instructor by e-mail by September 23rd. It would be your responsibility to provide a sufficiently large, stamped, self-addressed envelope for each assignment.

Laboratories

There are eleven laboratories and one Final laboratory examination. Laboratories will be due as specified in the laboratory sections. There will be a late box where a student will receive a maximum grade of 80. Laboratories submitted after the drop box closes will receive a grade of 0.

Tutorials

There are twelve tutorials, the first of which is a review of relevant material from MATH 119. The one-hour weekly tutorials will be used primarily to assist you with the assignments. You will get some hints and tips, and see some similar problems worked through. You may also see some extra examples of problems related to the topics discussed in recent classes.

Academic Discipline

You are expected to know what constitutes an academic offense (see Policy #17 Student AcademicDiscipline,http://www.adm.uwaterloo.ca/infosec/Policies/policy71.html. We remind you that although you are encouraged to discuss assignment problems with each other, you are expected to write up your solutions independently. Direct copying (from any source) is plagiarism, and will be treated as an academic offense if detected. Students who are unsure whether an action constitutes an offense, or who need help in learning how to avoid offenses (e.g., plagiarism, cheating) or about "rules" for group work / collaboration should seek guidance from the course professor, TA, academic advisor, or the Undergraduate Associate Dean.

Illness during exams

If you miss the midterm exam due to a documented illness, the weight will be transferred to the final exam. Be aware that we do NOT automatically grant requests for deferrals of final exams. These requests will be granted only to students who are severely ill or otherwise physically incapable of attending the examination, and whose performance in the course suggests a reasonable chance of success. Be aware that appropriate documentation (as decided by the course professor) must be provided.

Grievances

A student who believes that a decision affecting some aspect of his/her university life has been unfair or unreasonable may initiate a grievance. Read Policy 70, Student Petitions and Grievances, Section 4: http://www.adm.uwaterloo.ca/infosec/Policies/policy70.htm.

Note for students with Disabilities

The Office for Persons with Disabilities (OPD), located in Needles Hall, Room 1132, collaborates with all academic departments to arrange appropriate accommodations for students with disabilities without compromising the academic integrity of the curriculum. If you require academic accommodations to lessen the impact of your disability, please register with the OPD at the beginning of each academic term.

Tentative Schedule

WeekDaysTopic Notes SetText Sections
1Sept 12-
Sept 16
Introduction, 1st-order DE's, separable, exact.1I: 10.3 - 10.5.5
2Sept 19-
Sept 23
General 1st -order linear DE; the superposition principle. Second Order DE: introduction.1,2I: 10.5.7,9, 10.8
3Sept 26-
Sept 30
2nd -order DE: linear, homogeneous. Particular solution of inhomogeneous eq.: Method of judicious guessing; the initial-value problem.2, 3I: 10.9.1,3
4Oct 3-
Oct 7
Engineering applications, quantitative Analysis, boundary value problems.3,4,5I: 10.10, 10.12
5Oct 10-
Oct 14
Introduction to the Laplace transform; definition; simple transforms; applications to ODE's.6II: 5.1, 2, 3, 5.5.5
6Oct 17-
Oct 21
L -transform of step functions and periodic functions; impulse function and Dirac delta.7II: 5.5.2 - 4; 5.5.6, 8, 10
7Oct 24-
Oct 28
MIDTERM WEEK
8Oct 31-
Nov 4
Convolution and its uses; transfer function and impulse response; block diagram representation.7,8II : 5.6.6, 5.6.1, 5.6.3
9Nov 7-
Nov 11
System stability; the origin of Fourier series; Fourier theorem; even and odd functions.8,9II: 5.6.2, 7.1, 7.2.2 - 7.2.5
10Nov 14-
Nov 18
Half-range expansions; convergence of Fourier series; the Gibbs phenomenon.9,10II: 7.2.7, 7.3
11Nov 21-
Nov 25
Integration and differentiation of Fourier series; complex form; Parseval's theorem.Introduction to Partial-differential Equations: introduction, definitions, and classifications.10,11II: 7.4.1,2, 7.6.1 - 2, 9.1
12Nov 28-
Dec 3
Separation of variables. The heat and wave equations, D'Alembert Solution.11II: 9.2.2,3, 9.3.1,2, 9.4.1, 9.5.1
13Dec 5Application to the solution of PDE's.11II: 9