ENGR 311
Transform Calculus and Partial Differential Equations
Winter 2024
Course Instructor: Prof. Alexandre Paradis, ing Ph.D.
E-mail : alexandre.paradis@concordia.ca
Office Hours: Monday, 14:00 – 15:00, Tuesday, 11:00-12:00, Thursday, 11:00-12:00 in EV 4.219
Section W
Lecture Hours: M-W 8h45 – 10h00
H 920
Tutorials: Please see your class schedule for details
Tutorial WA Thursday 8h20-10h00
- H 1011
Tutorial WB Thursday 16h15-17h55
- LS 208
Labs: N/A
Course Calendar Description:
The Laplace transform: Laplace transforms and their properties, solution of linear differential equations with constant
coefficients; further theorems and their applications. The Fourier transform: orthogonal functions, expansion of a
function in orthogonal functions, Fourier series. Partial differential equations: physical foundations of partial differential
equations, introduction to boundary value problems, introduction to non-homogeneous PDE
Prerequisites: ENGR 233
Co-requisites: N/A
Specific Knowledge and Skills Needed for this Course:
Students taking this course are expected to have sufficient knowledge of the following topics. Should
you have difficulties in any of these topics, you are strongly encouraged to review them before the
DNE deadline.
o Knowledge of Ordinary Differential Equations
o Good Integration techniques
Course materials
• Required Textbook: Required textbook(s): Advanced Engineering Mathematics, by Dennis G. Zill and
Warren S. Wright, 7th Edition1, Published by Jones and Bartlett.
•
•
1
Instructor’s lecture notes: will be posted in Moodle course management site
OtherTextbook: Not required: Advanced Engineering Mathematics, by Kreyszig, 10th Edition, Published by
Wiley.
Please note that 5th and 6th editions have very minimal difference with the 7th section. Some exercises at the end of
each section might have been re-ordered.
Grading
•
•
•
Assessment Tool
Weight
Midterm during tutorial
35%
Final
65%
Total
100%
A score of zero will be given to a missed midterm. Case by case arrangement will be made for students
who submit proper justification (medical certificate for example) no later than 5 days after the original
midterm.
GCS Faculty approved calculator only. Electronic communication devices (including cell phones) will
not be allowed in examination rooms.
In order to pass the class, at least 50% of the marks are required.
NOTE: Electronic communication devices (including cellphones and smartwatches) will not be allowed during examinations and are prohibited
in the examination rooms. Only “Faculty Approved Calculators" will be allowed for midterm and final exams [SHARP EL-531 or CASIO FX300MS]. See Moodle site for an extensive list of the calculators.
Tentative Course Schedule; suggested problems are from the 7ed of the book
Topics
Review and Definition of the Laplace Transform, (Textbook 4.1)
4.1: 3, 6, 10, 14
Inverse and Derivatives of the Laplace Transform Translation Theorems of the
Laplace Transform (Textbook 4.2-4.3)
4.2: 5,6,13,16,36 and 4.3: 5,12,22,24,41,45
Additional Operational Properties of the Laplace Transform (Textbook 4.4)
4.4: 4,7,10,45, 46,52
The Dirac Delta Function and Systems of Linear Differential Equations (Textbook
4.5, 4.6)
4.5: 3,9,12 and 4.6: 4,10,14
Orthogonal Functions and Fourier Series (Textbook 12.1 and 12.2))
12.1: 3,10,18,21 and 12.2: 10,12,16
Fourier Cosine and Sine Series (Textbook 12.3)
12.3: 4,6,12,30,33
Separable Partial Differential Equations (Textbook 13.1)
Week
1
2
3
4
5
6
7
13.1: 3, 8, 24
Classical PDEs and Boundary-Value Problems (Textbook 13.2)
13.2: 3,10,12
Heat Equation (Textbook 13.3)
13.3: 2, 5, 9
Wave Equation (Textbook 13.4)
13.4: 3, 5, 10
Laplace’s Equation (Textbook 13.5)
8
9
10
11
13.5: 4, 10, 13
Nonhomogeneous BVPs (Textbook 13.6)
13.6: 1, 6
12
Lab Details
N/A
Engineering Tools
N/A
Details on Assessment Tools:
N/A
Other relevant information
N/A
Graduate Attributes:
The following is the list of graduate attributes (skills) that students use, learn and/or apply throughout the
term.
Graduate Attribute
Indicators
Assessment
Level of
Results
Coverage
Reported
Knowledge base for engineering KB1: Knowledge base of
Intermediate
Yes
mathematics
Knowledge base for engineering KB3: Knowledgebase in a specific
Problem Analysis
domain
PA3: Problem Solving
Intermediate
Yes
Intermediate
Yes
Course Learning Outcomes (CLOs):
By the end of this semester, students are expected to master the following concepts.
Course Learning Outcome
Related Graduate Attributes
Knowledge base for engineering/
Select, apply, and adapt a wide array of
Knowledge base for specific engineering field
mathematical techniques aiming to solve
specific engineering problems
Knowledge base for engineering/ Knowledge base
Understand and apply mathematics knowledge
for mathematics
base of engineering fundamentals
Problem Analysis/
Develop the ability to use this base knowledge
Knowledge base for mathematics
in analysis of engineering problems
Problem Analysis/
Formulate, solve problems and to reach
Knowledge base for mathematics
satisfactory engineering conclusions
Health and Safety Guidelines
All health and safety rules specific to this course can be found in the lab manual. General health and
safety instructions and available health and safety trainings are discussed at:
Safety Programs - Concordia University
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and resources available for students.
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