| University | Auckland University of Technology (AUT) |
| Subject | ENGE601 Engineering Mathematics 2 and MATH605 Algebra and Calculus 2 |
ENGE601 Engineering Mathematics 2 MATH605 Algebra and Calculus 2 Assignment-1 Semester 2, 2025
Instructions
Use a pen, not a pencil to write your solutions.
You need to scan your solutions into a single pdf file and upload on Canvas in the assignment-1 section.
Only one pdf file should be uploaded.
One of the questions is on creating a MATLAB graph. You will need to provide the printouts from MATLAB (code and graph) and include them into your pdf file.
Write your full name and ID on the top right corner of the front page of your solutions.
Comply with the AUT Academic Integrity Declaration below.
AUT Academic Integrity Declaration
In submitting this work, I agree that:
- The assessment has been produced by me and is solely my work, UNLESS the work is for a designated collaborative (group) task.
- I have not sought or received unpermitted assistance from any other person, or other source (e.g. a website, tutorial or answer service).
- I have properly acknowledged all sources used in my work.
- I have not unfairly represented content created by artificial intelligence or generative artificial intelligence tools as my work (the use of Al tools in assessed work must be expressly permitted by Course Leads and its use acknowledged).
- This work has not previously been submitted by me for any assessment task, OR I have received approval to resubmit this work.
- I did not use any other unfair means to complete this work.
- I am aware that AUT may use text-matching software to check for plagiarism in assessments.
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Question 1
i) What does the equation 4x² + 4y² = 16 represent in 2D?
ii) What does the same equation represent in 3D?
iii) Use polar/cylindrical coordinates and MATLAB to produce a graph of this equation in 3D. Provide both the MATLAB code and graph.
12 marks
Question 2
Find the velocity and position of an object at any time t, given that its acceleration is a(t) = 6t, 12t + 2, et, its initial velocity is v(0) = < 2, 0, 1 > and its initial position is r(0) = < 0, 2, 8 >.
Question 3
Question 4
Question 5
Question 6
Question 7
Question 8
Question 9.
Question 10.
f(x, y, z) = 2x + 6y + 10z; x² + y² + z² = 35
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