ENGR 311 Transform Calculus and Partial Differential Equations Final Exam prep 2026 Concordia University

ENGR 311 Transform Calculus and Partial
Differential Equations Final Exam prep 2026
Concordia University

, Transform Calculus and Partial Differential Equations (ENGR 311) Name:

Final Exam – Winter 2026 Student #:
Date: April 21, 2023 Time: 3 hours
Grading: 100 pts.
Weight: 40% of the total course grade
INSTRUCTIONS
• Do not start until instructed by the invigilator.
• If you believe there is an error in a question, make an assumption and continue based on that assumption. Be sure to
argue your assumption clearly in writing to have a chance at partial credit.
• This exam is closed book.
• ENCS Faculty-approved calculator may be used.
• The invigilators will not attempt to interpret or clarify a question, only handle administrative issues.
• The exam has 4 questions (25 pts for each question).
• GOOD LUCK!


1. Use the Laplace transform to solve the following ODE problem (y=y(t)).
3𝑦′ − 6𝑦 = 1 + 2 exp(−3𝑡) , 𝑦(0) = 0

2. Expand the following function (with a period of 0<x<2π) in a Fourier Series.
F(x)=e-x

3. Use the Laplace transform to solve the following PDE problem.
𝛛2 𝑢 𝛛2𝑢
= 𝑐2
𝛛𝑡2 𝛛𝑥2

𝛛𝑢
Initial Conditions: 𝑢(𝑥, 0) = (𝑥, 0) = 0
𝛛𝑡

𝑢(∞, 𝑡) = 0
Boundary Conditions: {
𝑢(0, 𝑡) = 𝑡

4. Solve the following PDE using the separation approach.
𝛛2 𝑢 𝛛2𝑢
=
𝛛𝑡2 𝛛𝑥2

𝛛𝑢 (𝑥, 0) =0
Initial Conditions: { 𝛛𝑡
𝜋
𝑢(𝑥, 0) = (𝑥 + 1) + sin ( 𝑥)
4

𝑢(4, 𝑡) = 5
Boundary Conditions: {
𝑢(0, 𝑡) = 1


[END OF EXAM]. ENJOY YOUR SUMMER!