Exam (elaborations)
MAT3700 EXAM PACK 2022
- Institution
- University Of South Africa (Unisa)
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MAT3700EXAM PACK
+27 81 278 3372
,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
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