FACULTY OF APPLIED SCIENCE
DEPARTMENT OF MATHEMATICS
B.ENG TECH: ELECTRICAL, POWER,
MECHANICAL,INDUSTRIAL, CIVIL,
GEOMATICS, CHEMICAL
BICT: Internet of Things
PROGRAMME CODES:
Engineering: BNELC1, BNPWE1, BNMCH1,
BIND1, BNCVL1, BBGMT1, BNCME1
Information Systems: BICT IoT
Study Guide
Semester 1 2025
ENGINEERING MATHEMATICS 1A
MODULE CODE: EMTA101
SAQA CREDITS: 12
This module was revised in January 2025
Revised by: Prof M.Govender/Dr.N.Ally
1
Contents
Lecturer/Department Details ........................................................................................................... 3
1.
Welcome .................................................................................................................................. 4
2.
Using your onlineThinkLearnZone (Moodle) classroom .................................................. 4
3.
Introduction to the module .................................................................................................... 5
Table 1: Pre-Requisites ............................................................................................................... 5
4.
Learning outcomes ................................................................................................................ 6
Table 2: Learning Outcome ......................................................................................................... 6
5.
Learning, teaching and assessment strategies ................................................................. 7
Mark Breakdown ........................................................................................................................... 8
Test results ................................................................................................................................... 9
Scanning of scripts - appeals process ..................................................................................... 10
Absenteeism ................................................................................................................................ 10
Tutorial Programme: ................................................................................................................... 10
Study tips...................................................................................................................................... 11
6.
Scheme of work .................................................................................................................... 12
7.
Copyright and plagiarism .................................................................................................... 13
8.
Student support .................................................................................................................... 13
9.
Work Integrated Learning (WIL), industry, community, and occupation-related
information. ...................................................................................................................................... 14
10.
Quality assurance and enhancement ............................................................................... 14
Medical Form ................................................................................................................................... 15
Declaration Form............................................................................................................................. 16
2
Lecturer/Department Details
Name of Lecturer/s
:Prof M Govender, Dr.N.Ally, Dr.M.Nene, Dr.G.Mazibuko, Dr.V.Zitha
Office
: Mathematics
Campus location
: Steve Biko Campus: Block S3 - level 1
Telephone
: 031-3732075
Fax No
: 031-3732723
E-Mail
: NoorA@dut.ac.za.
Consultation times with Lecturer: Lecturers to inform their respective classes.
Module coordinator
: Prof M Govender
Head of Department
: Prof D B Lortan
Campus location
: Steve Biko Campus: Block S3 - level 1
Telephone
: 031-3732297
Departmental Secretary : Mrs D.F.Day
Contact details
Lectures
: 031-3732075
DianaD@dut.ac.za.
: 4 per week as per timetable
Tutorials
: 1 per week as per timetable
Lecture Venue
: As per timetable
Tutorial Venue
: As per timetable
Duration
: 1 Semester (14 weeks)
Relevant Policies and rules:
DUT and departmental Policies and Rules will be adhered to. Students are referred to the
relevant Programme Handbooks and the DUT website.
3
1. Welcome
Welcome to Mathematics IA. Successful Engineering and Science students at DUT should
have a competent grasp of two languages, that is, English and Mathematics. In this subject
students will be exposed to the universal “language” of Mathematics and will be provided with
a “tool kit” of Mathematical techniques which can be applied to problems they will encounter
in their Engineering and Science subjects.
In this course the emphasis will be on problem solving and lectures will be based on the
assumption that all students will access the recommended textbooks and that all assigned
reading and tutorial work has been completed before the next lecture takes place.
2. Using your online ThinkLearnZone (Moodle) classroom
All taught subjects/modules have their own online classroom on the ThinkLearnZone. You
can access your classroom at https://tlzprod.dut.ac.za
Click on (Log in) on top right hand corner
On the next screen click on “OpenID Connect”
Use your dut4life email address to sign (yourstudentnumber@dut4life.ac.za) and your
email password as your password (Dut + first six digits of your ID no., e.g. Dut980610.
For first-time 2020 students - use $$Dut + first six digits of your ID no., e.g.
$$Dut980610)
4
Ask your lecturer for guidance or check out “how to log in” on the DUT e-learning
website https://elearning.dut.ac.za/faq/faq_students/
The e-learning website also has contact information for help and technical assistance
http://elearning.dut.ac.za/contacts/
You can call the e-learning helpdesk on 031 373 6758 or email them on
tlzsupport@dut.ac.za
N.B. Your Mathematics1A online classroom in Moodle is:
EMTA101ALL: ENGINEERING MATHEMATICS IA: [SEM1]: 2025
N.B. Any change to the above Moodle classroom name will be communicated by your lecturer.
3. Introduction to the module
It is important to realize that Mathematics is a life-long learning experience. From birth we
come across the concept of size, shape and form. Initially numbers are learned by observation
and during formal schooling these concepts are formalized into structures - arithmetic, algebra,
geometry, calculus etc. At tertiary level we continue to build on prior knowledge, introducing
and using additional techniques that are useful in solving real life engineering and science
problems.
In order to register for Mathematics IA you need to have satisfied the admission requirements
for Mathematics at the level required by your programme department. Your admission to this
module will indicate that you have shown competences in the following outcomes:Table 1: Pre-Requisites
Assessment Criteria
Specific Outcome
Factorize algebraic expressions
Difference of two squares
Trinomial factorization
Grouping
Sum and difference of two cubes
Operate with fractions
Numeric and algebraic fractions, added
and /or subtracted, multiplied and/or
divided.
Fractional equations solved
Powers with the same base can be
multiplied/divided/ roots found & raised to
powers.
Equations solved using factorization,
formula and elimination of variables
Manipulate powers
Solve simultaneous equations
Manipulate formulae
Formulae can be operated on by:
substitution and changing the subject
5
Define and use algebraic and
trigonometric functions
Differentiate simple algebraic functions.
Perform co-ordinate geometry operations
Algebraic functions (polynomial,
exponential) and trigonometric functions
can be defined and used to solve
problems. Inverse functions can be found
where applicable
Algebraic polynomials can be
differentiated using the standard form axn.
Co-ordinate geometry problems including:
Distance and gradient between points,
finding equation of straight lines, parallel
and perpendicular relationships, locus
situations can be solved.
If you have passed a Mathematics module from another programme or institution and you
intend to apply for exemption from Mathematics 1A, please follow the procedure detailed
below.
 Recognition of prior learning (exemptions)
Bring your original certificate together with the DUT form requesting exemption/credit
(obtained from the Engineering Faculty Office) to the Mathematics Department. In addition,
you will be required to bring a syllabus outline. The Head of Department (or any other
designated member of staff) will then decide whether you can be exempted from doing
Mathematics IA.
4. Learning outcomes
The course is designed to provide the following learning outcomes:
Table 2: Learning Outcome
LEARNING OUTCOME
Demonstrate knowledge of numbers and the number
system
Perform, analyse and apply operations in basic
algebra
Identify and calculate surface areas and volumes of
common solids
Demonstrate the ability to use and apply properties
and laws pertaining to logarithms, exponents and
hyperbolic functions.
ASSESSMENT CRITERIA
Numbers can be represented in different ways
Basic algebra can be used to simplify expressions,
solve equations and manipulate formulae,
Properties of circles are found and surface area and
volumes of common solids calculated.
Utilize the log rules [log of a product, log of a
quotient, log of a power, change of base]
Natural log and exponential functions can be
manipulated.
Apply, solve, manipulate and explore relationships in
trigonometry in both Cartesian and polar form.
Trig identities can be simplified.
Trig equations can be solved.
Interchange Cartesian and polar co-ordinates
Algebraic and trigonometric curves can be sketched
and interpreted.
Operations with different representations of complex
numbers can be performed
Derivatives can be computed and applied using
Graph and interpret curves of functions.
Identify, manipulate and use complex numbers.
Use different methods to compute and apply
6
derivatives of algebraic, trigonometric and hyperbolic
functions.
Evaluate and apply standard integrals.
different techniques including the chain rule,
logarithmic and implicit differentiation.
Indefinite and definite integrals can be found.
After completing this subject the student should be competent to use Mathematical tools to:identify, analyze, describe and solve discipline-related problems. Table 3 lists some
overlapping examples.
Table 3: Discipline-related Examples
EXAMPLE
DISCIPLINE
Electrical and Electronic Engineering
Mechanical and Industrial Engineering
Civil Engineering and Surveying
Chemical Engineering, Chemistry and
Pulp and Paper
Solve trigonometric equations and give
the amplitude and phase angle for
compound sine and cosine functions.
Substitute into a mechanical formula
and/or change the subject of a formula.
Substitute into a civil and survey formula
and/or change the subject of a formula.
Differentiate and integrate standard
Mathematical equations using the rules,
techniques and standard forms used in
elementary calculus.
5. Learning, teaching and assessment strategies
a) Learning activities
1. Credit value - 12.
2. Notional hours – 120
3. Number of lectures per week – 4
4. Number of tutorials per week – 1
These periods are used for lectures, tutorial work and classroom assessments. All lectures
and tutorials are compulsory. During lecture periods students will be expected to take their
own notes. References to textbooks will be made where applicable. Problems/tutorial
questions will be given relating to the work covered in the lectures. It is essential that tutorial
work is completed by the end of each week as new work is built on what has gone before.
Lecturers are available to provide assistance and feedback to students during contact periods
and by appointment outside of formal contact time.
Students are expected to work, on average, four hours per week outside of formal lecture time
in Mathematics. Self-discipline plays an important part in your success. Therefore, it is
important to recognize at the start of the course that you are going to have to work hard and
consistently in order to pass.
7
Online teaching and Learning: Teaching and Learning material including detailed notes,
Tutorials, Revision Exercises, Selected Solutions and Diagnostic quizzes will appear
sequentially on the following Moodle site:
EMTA101ALL: ENGINEERING MATHEMATICS IA: [SEM1]: 2025
N.B. Any change to the above Moodle classroom name will be communicated by your
lecturer.
‘This course is only one semester, it is not a life sentence so keep up to date and to
maximize your chances of success’.
b) Graduate attributes
Table 4: Graduate Attributes
Graduate Attribute
Critical and creative
thinkers who work
independently and
collaboratively
Active and reflective
learners
Nascent Employability
Skills
Problem solving
Flexibility in working
creatively within a team as
well as independently
Lifelong learning
Activity
Group assignment on
differentiation and
integration
Self-study project on the
use of functions in the
various disciplines
c) Assessment
Mark Breakdown
There is no examination at the end of this course. The final mark is calculated from tests
written during the semester as follows:-
TYPE OF
ASSESSMENT
MAJOR TEST 1
PROVISIONAL
DATE
28 March 2025
WORK TO BE TESTED
% OF FINAL
MARK
Number and Algebra
Logarithms
Exponents
Trigonometry
Graphs
40
8
MAJOR TEST 2
CLASS MARK :
30 May 2025
Minor Test 1 –
3 Minor Test marks: 7 March 2025
Minor Test 2 –
*The best TWO of
11 April 2025
THREE Online
Minor Tests will be Minor Test 3 –
2 or 23 May 2025
used for the ‘Final
Mark calculation’.
Calculus Differentiation
Calculus - Integration
40
This will be given to you
by your lecturer
20
NO MAKE UP
TESTS FOR
MINOR TESTS
TO BE
WHOLE SYLLABUS
CONFIRMED
*N.B. – All THREE MINOR TESTS will be conducted via the online Moodle class –
To be Confirmed
SPECIAL TEST
THE ONUS IS ON THE STUDENT TO ENSURE THAT HE/SHE IS AWARE OF THE WORK
TO BE TESTED, THE CONFIRMED TEST DATE, TIME AND VENUE. ALL SUCH
INFORMATION WILL BE DISPLAYED ON THE MATHS NOTICE BOARDS SITUATED AT
S3 LEVEL 1.
FINAL MARK = (Major Test 1 x 0.4) + (Major Test 2 x 0.4) + (Minor Test A x 0.1) +(Minor Test
B X 0.1). N.B. Minor tests A & B are the best two marks taken from Minor Test 1, 2 and 3.
The pass mark is 50%.
NOTE:
If a student obtains a final result from 45% to 49% inclusive for Maths IA he/she will be
eligible to write a 3-hour SPECIAL test covering the whole syllabus. The date for the
special test will be displayed on the Department notice board (S3 Level 1) and posted
on the Maths 1A Moodle site. If a student passes this he/she will be allocated a final
result of 50%. However, if the student fails this special test, the original results will
stand. If a student who is eligible for the test does not write it for any reason he/she
will NOT be eligible for any further test and will have to re-register for the subject.
Test results
The results of each Major Test will be displayed on the ITS Student Portal. Kindly check the
portals for your results at least two weeks after the test has been written. Please report any
errors to your lecturer timeously.
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Scanning of scripts - appeals process
Learners have 1 week after the results of each test have been released to scan their Major
Test scripts. Each lecturer will inform their learners during which periods they may scan their
scripts. Thereafter the scripts will be collected back and stored in the archives and will not be
available for scanning. The purpose of the scanning is to provide the learner with feedback
and to give the learner the opportunity to check that all questions they have answered have
been marked and that the addition is accurate.
In the case of the online minor test, the results will be released after the moderation of the
test.. In the case of assignments and projects the results will be released on or before 3 weeks
prior to the commencement of examinations.
N.B. STUDENTS WILL BE INFORMED OF CHANGES TO THE RELEASE OF TEST AND
ASSIGNMENT RESULTS AND MEMORANDA WHERE A FULLY ONLINE LEARNING AND
TEACHING APPROACH IS IMPLEMENTED.
Absenteeism
If a student misses a Major Test 1 or Major Test 2, satisfactory evidence, eg: DUT Medical
Certificate attached at the end of this guide, must be submitted to the Secretary, WITHIN
SEVEN CALENDAR DAYS of the test being written. If this is not forthcoming a student will
be given 0 % for the test. If a student has produced satisfactory evidence for his/her absence
he/she will be required to write an Aegrotat Test.
Note: Aegrotat tests apply only to major test 1 and major test 2. There will be no Aegrotat
tests for the multi choice tests.
Both Major 1 and Major 2 Aegrotat Tests will be written on the same day and at the same time
as the Special Test mentioned above. Furthermore, results from the Aegrotat Test will be
used to obtain the final mark and no further tests will be conducted thereafter irrespective of
the final result. If a student misses the Aegrotat tests Rule G13(3)(b)(iii) will apply.
NB: In terms of DUT general rule G13 3(a)(i) a doctor’s Certificate will only be accepted
if you are examined on or immediately before the date of the Major test you have
missed. (No retrospective Doctor’s certificates will be accepted).
d) Activities to promote learning
Tutorial Programme:
Your lecturer will acquaint you with the procedure in which tutorials are conducted. Tutorials
are conducted on a weekly basis and assigned problems must be attempted before the
tutorials. Attendance of tutorials are compulsory.
e-Learning Assessments: The course requires students to complete online assessments
using the University’s Learner Management System, Moodle. The onus is on the student to
ensure the following are readily accessible during the time that such assessments remain
open:
1. Login requirements – Username and password
2. Suitable devices with the necessary specifications to access Moodle.
10
Questionnaires:
Students are expected to complete both the ‘Subject Evaluation Questionnaire’ (SEQ) as well
as the ‘Lecturer Evaluation Questionnaire’ (LEQ) before week 6 of the semester. Your
respective lecturer will provide further information.
Study tips
a. Theory: Read the theory pages carefully, making sure you understand the work. Work
through the worked examples on your own after going through them in the book and check
your answer carefully. Do the revision exercises at the end of the chapter.
b. Time: Use time efficiently. When tackling problems on your own don’t spend more than 15
minutes on any one problem. If by this stage you are not getting anywhere, leave the problem
and move on to the next one. The next lecture/tut you have you can ask your lecturer for help.
c. Recap: At the end of each week take a quick look back at the weeks work. If you don’t feel
confident about any part of it speak to your lecturer as soon as possible.
d. Co-operative learning: Try to assist your fellow students with problems they are
experiencing - you will find by explaining to others you understand the work much better
yourself. You will also find that other views sometimes clarifies aspects of the work you may
be struggling with.
e) Library orientation – Dependent on the covid-19 lockdown levels
Library orientation will be held during the first semester. Should you require assistance in
respect of the library, you may contact the subject librarian for the Faculty of Applied Sciences,
Mrs N Sogoni. She is based at the Alan Pittendrigh Library on Steve Biko campus.
Library hours are indicated in the table below:
Day
Mon - Thur
Fri
Sat
Sun (exam time)
Term Time
07h30 – 22h30
07h30 – 18h00
09h00 – 17h00
10h00 – 14h00
11
Vacation Time
07h30 – 18h00
07h30 – 16h30
10h00 – 14h00
6. Scheme of work
Recommended books:
Modern Eng Maths 5th Ed :Glyn James
Higher Engineering Mathematics, Bird.J, 6th edition.
Calculus. A complete course: Adams, R.A., Essex, C. 7th edition
Calculus. Early Transcendentals: Bivens, I.R.A., Anton, A., Davis, S. 10 th edition
Additional Lecture notes will also be made available by lecturers.
Table 5: Scheme of Work
Topic
Number and Algebra
Content
Week
Basic operations with algebraic expressions.
1
Absolute values
Logarithms and Exponents
Exponents: Revision
Exponential functions
Logarithms: laws and equations.
Natural logarithms
Logarithmic Functions
2
Trigonometry:
Radian measure
3&4
Six trig ratios
Trig identities.
Trig equations
Functions and Graphs:
Functions and inverse functions
5&6
Curves of functions
Hyperbolic functions
Complex Numbers:
Calculus
Rectangular, polar and exponential format.
Addition, subtraction, multiplication and division
of complex numbers
De Moivre’s Theorem
Roots of complex numbers
Limit Concept and calculations
12
7
8
Calculus - Differentiation
Concepts (derivative, slope, velocity, rate of
change )
9 & 10
Differentiation of Algebraic, trig and hyperbolic
functions using the following:- standard rules
- the chain (function of a function) rule
- the product rule
- the quotient rule
- the log technique
- implicit functions
- parametric functions
The differentiation techniques above can be
applied to :- the equations of tangents and normals to a
curve.
Calculus – Differentiation
Applications
Calculus - Integration
Related rates; tangents and normals
11
Anti- differentiation
12 &
13
Introduction of a Riemann sum
Integration of Algebraic, trig and hyperbolic
functions using the following:- standard forms
- constant rule
- sum and/or difference rule
- algebraic substitution
Using Integration to find areas.
Calculus - Integration
Application - Areas
14
7. Copyright and plagiarism
Students are expected to read and take note of the institution’s plagiarism policy found in the
general handbook for students which is available at www.dut.ac.za. under the Library link. In
the event of assignments being submitted for part of the DP mark the student is reminded of
the DUT policy on plagiarism (Refer to Rule G13 (1)(o)).
8. Student support
a) Tutors are appointed to assist students individually. They are stationed in the Mathematics
room and are available from Monday to Friday (To be confirmed).
b) Lecturer consultation with students – depends on lecturer availability
c) Library: Students are encouraged to utilize the resources available in the library on a regular
basis. Recommend textbooks and websites appear in section 7 below.
13
N.B. Students requiring assistance regarding other issues such as clinic, library, fees, etc.
should contact their respective departments to direct them to the appropriate centres.
9. Work Integrated Learning (WIL), industry, community, and occupation-related
information.
Not applicable to the Mathematics Department.
10. Quality assurance and enhancement
You, the student, are the best source of assistance to the department of Mathematics in
maintaining and improving our standards. Hence we request that you evaluate this study guide
and make your contribution to your lecturer in this regard. We request that you participate in
the subject evaluation (SEQ) and lecturer evaluation (LEQ) which are conducted in the sixth
week of the semester. Areas of concern will be addressed during the student/staff committee
meeting which is held at least once per term.
14
Medical Form
TO BE COMPLETED BY A MEDICAL PRACTITIONER (registered with the South African Medical and Dental
Council), Sister or Psychologist from the University’s Student Health Clinic (registered with the South African
Medical and Dental Council), Homoeopath or Chiropractor (registered with the Chiropractors, Homoeopaths and
Allied Health Service Professions Council of South Africa).
It is hereby certified that Mr
Ms
student: .............................................................................................................................
of (address) ................................................................................................................ ...............................
who states that he/she is a registered student of Durban University of Technology, was attended by me on
(please give precise date(s))................................................................................................
on which day(s) I found him/her to be suffering from (please print as precise a diagnosis as possible)
....................................................................................................................................................................
I,...........................................................................................................................
.......................................
(please print your full name)
hereby certify that this illness rendered the student in question unfit to be examined by the University on the
following day(s)
..........................................................................to ............................................................(Inclusive).
(please state these dates precisely)
SIGNATURE: .........................................................
DATE: .................................................
DESIGNATION: ......................................................
TEL NO: ............................................... ADDRESS:
......................................................................................................................................................
....................................................................................................................................................................
PLEASE ENDORSE WITH YOUR OFFICIAL STAMP
Receipt of medical certificate (For proof of application of special/make-up test)
Student Name_
Math 2B
Student Number_
(tick appropriate box)
Date received :
Received by:
Math 1
15
Math IB
Math2A
Declaration Form
This sheet must be completed and returned to your lecturer immediately
I, (Print SURNAME, INITIALS in Block letters)
(Print STUDENT NUMBER)
(Print QUALIFICATION Registered for)
(Print LECTURER’S Name)
DECLARE THAT I:
1. Am a registered student for the Mathematics module .
2. Agree to abide by the Rules of the University.
3. Have familiarized myself with the Mathematics Learner Guide which appears on Moodle.
4. Have understood the rules pertaining to tests and assessments.
5. Accept that I am responsible for my Moodle username, password and device, especially in respect of
the online tests.
6. Will work from the very beginning and not wait until the day before a test to consult my lecturer on
problems I may have encountered with the syllabus.
SIGNATURE
DATE
N.B. Students will be advised by their lecturers how to submit the form electronically.
This module was revised on: January 2024
Revised by: Dr.N.Ally