Exam (elaborations)
MAT3700 EXAM PACK 2022
- Course
- Institution
Latest exam pack questions and answers and summarized notes for exam preparation. for assistance. All the best on your exams!!
[Show more]
Seller
Follow
iStudy
Reviews received
Content preview
MAT3700EXAM PACK
,UNIVERSITY EXAMINATIONS
September-December 2021
MAT3700
Mathematics III (Engineering)
Duration: 3 hours Marks: 100
Examiners:
First: Ms LE Greyling
Second: Mr S Blose
External: Dr JN Mwambakana
Use of a non-programmable pocket calculator is permissible.
This is a closed book examination and will be IRIS invigilated.
This online paper is the property of UNISA and may not be distributed electronically.
This examination question paper consists of 3 pages including this cover page plus
Formulae sheets (pages 4 to 8) plus
A table of integrals (pages 9 and 10) plus
A table of Laplace transforms (page 11).
Examination rules:
1. Students must upload their answer scripts in a single PDF file (answer scripts must not be password
protected or uploaded as “read only” files).
2. NO emailed scripts will be accepted.
3. Students are advised to preview submissions (answer scripts) to ensure legibility and that the correct
answer script file has uploaded.
4. Students are permitted to resubmit their answer scripts should their initial submission be unsatisfactory.
5. Incorrect file format and uncollated answer scripts will not be considered.
6. Incorrect answer scripts and/or submissions made on unofficial examinations platforms will not be marked
and no opportunity will be granted for resubmission.
7. Mark awarded for incomplete submission will be the student’s final mark. No opportunity for resubmission
will be granted.
8. Mark awarded for illegible scanned submission will be the student’s final mark. No opportunity for
resubmission will be granted.
9. Submissions will only be accepted from registered student accounts.
10. Students who have not utilised invigilation or proctoring tools will be subjected to disciplinary processes.
11. Students suspected of dishonest conduct during the examinations will be subjected to disciplinary
processes. UNISA has a zero tolerance for plagiarism and/or any other forms of academic dishonesty.
12. Students are provided one hour to submit their answer scripts after the official examination time.
Submissions made after the official examination time will be rejected by the examination regulations and
will not be marked.
13. Students experiencing network or load shedding challenges are advised to apply together with supporting
evidence for an Aegrotat within 3 days of the examination session.
14. Students experiencing technical challenges, contact the SCSC 080 000 1870 or email
Examenquiries@unisa.ac.za or refer to Get-Help for the list of additional contact numbers. Communication
received from your myLife account will be considered. Include screenshots of your problem.
, -2- MAT3700
September-December 2020
QUESTION 1
Solve the following differential equations:
1.1 1 x dy
2
dx
1 y . 2
(4)
1.2 x 2
y 2 dx x 2 xy dy 0 Hint: Let y vx . (7)
dy
1.3 y cot x cos x. (7)
dx
[18]
QUESTION 2
Find the general solution of the following differential equation using the method of
d 2y dy
undetermined coefficients: 3 2 2 y 2x 3 . (10)
dx dx
[10]
QUESTION 3
Find the general solution of the following differential equations using D-operator methods:
3.1 D 2
3D 2 y sin3 x . (8)
3.2 D 2
6D 9 y e 2 x
cosh 2 x . (6)
[14]
QUESTION 4
Solve for x and y by using D-operator methods in the following set of simultaneous
equations:
D 1 y x 4et
. (10)
y D 3 x 1
[10]
QUESTION 5
Determine the following:
5.1
L et cos 2t . (2)
8se 2s
5.2 L1 2 . (4)
s 9
[6]
[TURN OVER]
, -3- MAT3700
September-December 2020
QUESTION 6
Given y " y sin t
Use Laplace transforms to solve the equation if the initial values for the equation are
y 0 1 and y ' 0 0 . (8)
[8]
QUESTION 7
The equation of motion of a system is
d 2x dx
2
5 4 x 3 t 2
dt dt
If x 0 2 and x ' 0 2 find an expression for the displacement x in terms of t.
(12)
[12]
QUESTION 8
2
The period, T, of natural vibrations of a building is given by T where is an
2 1
eigenvalue of matrix A . Find the period(s) if A . (5)
1 2
[5]
QUESTION 9
Find all the eigenvalues of matrix A and an eigenvector corresponding to .
2 0 0
A 4 1 0 . (7)
1 2 1
[7]
QUESTION 10
A function f(x) is defined by
2 x 0
f x .
0x2
Determine the Fourier series expansion of the periodic function f(x) with period 4.
(10)
[10]
Full marks = 100
©
UNISA 2021
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller iStudy. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $2.85. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
67474 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy study notes for 14 years now