FACULTY OF SCIENCE
DEPARTMENT OF MATHEMATICS AND APPLIED
MATHEMATICS
APPLIED MATHEMATICS EXTENDED PROGRAMME
APPLIED MATHEMATICS 1A2E
INTRODUCTION TO STATICS - EXTENDED
MODULE CODE: APM2EA1
DEPARTMENT: MATHEMATICS AND APPLIED MATHEMATICS
(APK CAMPUS)
ASSESOR: MR M. ZHANGAZHA
HEAD OF DEPARTMENT: PROF F. NYABADZA
DATE: FEBRUARY 2023
Prerequisite module(s) for this course: APM1EB1 and MAT1EA1.
Lectures
Offering
Lecture
Day
Monday
Tutorial
Wednesday
Lecture
Friday
Time
14H4016H15
13H0014H35
10H3012H05
Venue
D1 Lab K11
C Les 201
D1 Lab K11
Students must make use of the timetable provided on uLink
Lecturer:
Office:
Telephone:
Email:
Mr. M Zhangazha
C Ring 513
+27643088933
mosterz@uj.ac.za
For emailing instructions, see Communication (take note of this as emails which do not
adhere to the specified format will be ignored). For information on the purpose of
consultation, see Consultation.
Secretary:
Office:
Telephone:
Email:
Nicolene Jonker
B Ring 534A
011 559 2661
najonker@uj.ac.za
The scope of this course
The course follows a textbook (see Module Resources for specification), provided digitally to
students, but students are required to make use of the lecture notes as the text to follow.
Students are instructed to make use of the notation and terminology specified in
the lecture notes (and not of any other reference material, including the textbook
which this course follows). It is, however, wise for students to expose themselves to
other reference material to encounter other notations and terminologies. Finally,
with reference to the reference textbook, the scope of this course is Chapter 2. The
particular topics of this course are presented.
1. Mechanics
i
Basic concepts
ii Fields of Application of Mechanics
iii Limitation of classical Mechanics
2. NEWTON’S LAWS
3. UNITS
4. FORCES
i
Point of Application
ii Classification of Forces
5. AXIOMS
6. EQUILIBRIUM OF A PARTICLE
i
Condition of equilibrium
ii Coupled particles.
7. TWO DIMENSIONAL SYSTEMS OF FORCES
i
Resultant of Non-parallel forces
ii Resultant of Parallel forces
iii The couple
iv Reduction of two-dimensional system of forces
8. MOMENTS
i
Definition and dimensions
ii Moment of equivalent forces
iii The vector nature of moment
9. COUPLES
i
Moment of couples
ii Equivalence of couples
iii Summation of couples
10. RESULTANT OF SYSTEM OF FORCES
i
Reduction Theorem
ii Special case
11. EQUILIBRIUM OF RIGID BODY
i
General condition of equilibrium
ii Equilibrium of two dimensions
iii Equilibrium of three dimensions
Note. Unless specified otherwise, when a section is mentioned as part of the scope
(of the course, test, or exam), then all content contained in the section must be
known - whether or not discussed during a lecture or covered in a tutorial. For
example, if the scope is Section 2.1, then everything contained in Section 2.1 must be
read and known by the student, even if Section 2.1 is skipped during the lectures.
Students are expected to be prepared for lectures. This means that students
need to read through the sections of the book which will be covered in a particular
lecture, before the lecture takes place.
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Consultation and Communication
Communication
Emails are monitored strictly during office hours and outside of other duties the
lecturer must perform for the UJ. If no response is received after 48 hours of the
email sent during office time (excluding Fridays; in this case, by the end of
Monday), then ensure that the email address is correct, the required email
structure and format is met and the email does, in fact, warrant a response. If
these conditions are true, then a follow-up email may be sent. If at least one
condition is not met, then the email is invalid, and it will never receive a response.
When sending an email, the subject line of the email must begin with “APM2EA1
2023:” and then the intended subject (not excessively long - a guideline would be
approximately 4 words).
The email must be concluded with the student’s surname, initials, student number
and title in the following format:
Surname, Initials (Student Number, Title).
For example, a student with student number xxxxxxxx, surname Bobo, first names Joe
and title Mr would send an email which looks as follows:
From: xxxxxxxx@student.uj.ac.za
To: mosterz@uj.ac.za
Subject: APM2EA1 2023: Consultation appointment request
Dear Mr Zhangazha
I would like to request an appointment for consultation on "DAY",
"DATE", at "TIME".
I am having trouble with the proof of Theorem 1.4.2 of Section 2.4.2 of
the textbook.
Regards
Bobo, J (xxxxxxxx, Mr)
Any email that does not adhere to the required structure will be ignored by the
lecturer.
Replace “DAY” with the proposed day, replace “DATE” with the proposed date and
replace “TIME” with the proposed time.
Due to the excessively high volume of emails, responses may take up to a week.
Consultation
After consultation with a tutor, if a student still has a problem, the student may
email their specific query to the lecturer with the subject: “APM2EA1 Consultation
DATE”, where DATE is the intended date for consultation.
Take note that consultation is not a private lecture; it is time to assist a student on
a very particular problem (such as, how to tackle a given problem). Consultation
sessions are quick. Once the aid is given, the session is over.
Consultation sessions are Mondays, 13:00-14:00 and Fridays, 09:00-10:00.
Consultation takes place by appointment only. Appointment requests must be
made via email only. Appointments are to be confirmed, via email, by the lecturer;
no confirmation of an appointment results in no consultation. The lecturer will
not remain in the office during consultation time when no appointments are
confirmed.
Tutorials
The attendance of tutorials is compulsory!
As per the UJ’s regulations, a minimum attendance of 80% of the tutorials is
required and a student may be excluded from the exam if the student fails to
attend at least 80% of the tutorials. Attendance per group will alternate per week.
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During the tutorial session, the tutor will provide assistance to only the students
who have prepared for the tutorial and need assistance.
Tutors are available at the Mathematics Learning Centre (MLC), located in Passage
2 of Mathematics, C Ring 5.
Assessment
All results are published on Blackboard and, or uLink.
Tutorial tests, Class Tests and Assignments
Tutorial tests, class tests and assignments will be communicated either in class or
on Blackboard. The availability will be announced along with the announcement.,
Semester Tests and Exam
Assessments will commence promptly - at the scheduled start time. The UJ
recommends arriving on campus at least an hour before the scheduled start
time. No bags will be allowed in the venue or just outside of the venue.
Assessment
Semester Test 1 (ST1)
Semester Test 2 (ST2)
Final Exam
Date
12 APRIL 2023
17 MAY 2023
20 JUNE 2023
Time Session
TBA
TBA
16:40-18:40
Venue
TBA
TBA
TBA
Pocket calculators are permitted for each assessment.
No notes are permitted - the assessments are closed book.
A Final Period Mark (FPM) will be calculated at the end of the semester for each
student and it will be determined by the student’s performance in both the
semester tests and assignments. The mark is calculated as (subject to change with
immediate implementation):
FPM = 45% × (ST1 + ST2) + 10% × A,
where ST1 is the mark of Semester Test 1 (or SSA Semester Test 1 where
applicable), ST2 is the mark of Semester Test 2 (or SSA Semester Test 2, where
applicable) and A is the (Assignments, Class tests and Tutorial mark).
The formula may be adjusted without prior notice.
The student needs an FPM of 40% or greater in order to obtain entrance to the
final examination (by obtaining an FPM strictly less than 40%, the student fails
the module). The student will obtain an exam mark (EM) upon attending and
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writing the final exam (if exam entrance has been granted), and the student
requires an EM of 40% or greater in order to pass the final exam. The final mark
(FM) for the student is calculated as:
FM = 50% × EM + 50% × FPM.
Importantly note the following:
1. To obtain exam entrance, the FPM ≥ 40%.
2. To pass the course, the EM ≥ 40% and the FM ≥ 50%.
3. If a student obtains an FPM < 40%, the students fail the course.
4. A student who obtained exam entrance and obtained an FM < 40% fails the
course.
5. A student who obtained exam entrance and obtained an FM satisfying.
40% ≤ FM < 50%
fails the course but will be given a second chance by means of the SSA Exam.
6. A student who obtained exam entrance and an FM ≥ 50% but has that the EM
< 40% fails the course, but will be given a second chance by means of the
SSA Exam.
Note on the SSA Exam as a second chance:
The pass requirements remain the same, except by substituting EM with the SSA
Exam’s result. There is no third chance, so after the second chance, an FM < 50%
means that the student fails the course. Furthermore, the FM will be capped to
50% (i.e., if FM ≥ 50%, then an FM = 50% will be recorded on the student’s
academic record). The pass requirements are summarised:
Pass Requirements: Credit for this module requires both a
minimum final mark of 50% and a minimum exam mark of 40%. A
student is admitted to the final exam by obtaining a minimum final
period mark of 40%.
Missed Assessment Opportunity
In the event of illness or due to a contingency such as the sudden death of a family
member, the student will be exempted from the scheduled assessment
opportunity and may apply for a substitute assessment opportunity. A student
may not apply for the substitute assessment opportunity due to a poor result in, or
failure of, the scheduled assessment opportunity.
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In the case of illness, a doctor’s certificate is required as well as a completed sick
form (to be obtained from BBor Ulink) which must be filled in by the doctor - both
the form and the note are required.
For other contingencies, the required documentation will be specified upon the
student asking the lecturer. The query of the required documentation and the
presentation of the documentation must be made and done before the start of the
substitute assessment.
No substitute assessment exists for tutorial tests/ class tests and assignments.
No substitute assessment will be granted for reasons of technological ignorance,
load shedding occurrence or internet connectivity issues.
Module Resources
Online
This module can be found on Blackboard. To access it, students should sign into
uLink by going to the site: ulink.uj.ac.za and then clicking on the Blackboard link.
Notes
This module follows the book (notes/textbook) “Introduction to Mechanics” by
CM Villet (the 2011 version). It is a set of bilingual notes. The book is available as
a PDF for download on Blackboard.
Assessment Mark Querying
Tutorial Tests, Class Tests and Assignments
No mark querying will be accepted.
Semester Tests
Queries must be made within three days from the release of the marked semester
test (including the day on which the test is released).
Exam
The exam does not have a mark querying process. However, students are allowed
to view their exams. The viewing must be done by making an arrangement with
the lecturer and within three days of the release of the results the exam may be
viewed (including the day of release).
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Take note that no copy of the exam may be made in anyway. There will be no
discussion.
For details on the reason for three days being permitted, refer to the UJ’s
regulations.
Information Dissemination
General information and information pertaining to this module at the Department
will be conveyed to students either verbally, in print or electronically. Verbal
dissemination occurs during lectures. Information released in print will be
available on the notice boards outside the entrance of the Applied Mathematics
Passage (at C Ring 5). Electronic release of information will be achieved via the
Blackboard page.
It will be the responsibility of the student, and not the lecturer, to make sure that
the student knows where information pertaining to this module will be released
and to read it on the student’s own.
In any matter of dispute, ignorance, whether negligent or wilful, of information
verbally given in lecture or tutorials, or published on the Blackboard page, will not
be used as an excuse for work not being completed or an assessment opportunity not
being attended and will carry no weight in substantiating why the work had not
been completed or why the assessment opportunity was not attended.
Grievance Procedure
If a student has any concerns regarding this module, or the teaching of this
module, please direct your concerns to the Course Coordinator:
1. Mr Zhangazha (mosterz@uj.ac.za)
If you are still dissatisfied, please direct your concerns to the following Deputy
Head of the Department:
2. Dr Visaya (mvvisaya@uj.ac.za)
If you are still dissatisfied, please direct your concerns to the Head of
Department:
3. Prof Nyabadza (fnyabadza@uj.ac.za)
If you are still dissatisfied, please direct your concerns to the Vice-Dean of
Teaching and Learning:
4. Prof Leung (wsleung@uj.ac.za)
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It is very important that you follow this order (1. through to 4.), when directing
your concerns. If you direct your concerns outside of this order (or to any
other person), your email will be redirected to follow this hierarchy (which
will only delay your concerns being addressed).
The subject line of your written (via email) concern should be: Complaint:
Module Code
Your email should include full detail regarding your concerns, or it will be sent
back to you to request clear and precise information.
Assessment Regulations
The remainder of this document contains the University’s assessment regulations.
A violation of a regulation cannot be defended by ignorance of the regulation.
The regulations are contained on the following page. Any update to the
regulations will be verbalised before starting an assessment opportunity. Take
note that this is not a complete list of the UJ’s assessment regulations. The
University’s website (http://www.uj.ac.za) contains all of its regulations (beyond
that of only assessment regulations). In order for a student to register, the student
must agree to the UJ’s regulations, making ignorance of any of its regulations no
excuse.
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ANNEXURE 1
UNIVERSITY OF JOHANNESBURG
ASSESSMENT REGULATIONS
1.
No candidate will be allowed to enter the assessment venue half an hour after the official starting time.
2.
No candidate may leave the assessment venue in the first 30 minutes of the official commencement of an
assessment opportunity.
3.
A candidate may leave the assessment venue temporarily, but only with the permission of the Chief Invigilator and
under supervision.
4.
During the assessment opportunity, no smoking or eating will be permitted and no candidate may leave the
assessment venue to smoke or eat.
5.
As soon as the assessment papers are handed out, silence must prevail. If candidates require any information,
they must raise their hands to attract the attention of the invigilator.
6.
(a)
article.
Students may write only in the assessment book/test paper and not on the question paper or any other
(b)
Any rough work done in the assessment book or on the test paper must be crossed out and marked as
such.
(c)
No part of the assessment book/test paper may be torn out.
(d)
No rough copy, assessment book, test paper or part thereof may be removed from the assessment venue,
but must be handed to the invigilator before leaving the assessment venue.
7.
Tests are written on the official test paper of the University and regulation 6 above is applicable.
8.
Noiseless pocket calculators may be used only if permission for the use thereof is explicitly stated on the
assessment paper.
9.
A candidate commits a contravention:
(a)
if he/she is in possession of any book, memorandum, notes, paper or document other than the answer
books or other books, paper or documents provided by the invigilator and if required by the particular
Assessment, students may be in possession of all aids as stated by the examiner for that particular
assessment opportunity as approved by the faculty and Senate;
(b)
if he/she helps or tries to help another candidate, or obtains help or tries to obtain help from another
candidate, or obtains help or tries to obtain help from any written information, with the exception of
explicitly approved information as stated by the invigilator or particular lecturer;
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10.
11.
(c)
If he/she helps another candidate to commit a contravention, and all candidates are expected to ensure
that other candidates do not have access to their work;
(d)
If he/she has unauthorised information stored in a pocket calculator or any other instrument in the
assessment venue.
(a) A candidate who, in the opinion of the invigilator, commits a contravention will have his/her assessment book
and any other material or part thereof that pertains to the contravention confiscated immediately and the time
recorded. A new assessment book will immediately be issued to the candidate.
(b)
After the assessment opportunity, the invigilator reports the incident in writing to the relevant Executive
Dean, with a view to possible disciplinary action.
(c)
If the contravention is the misuse of a pocket calculator, the Chief Invigilator, in consultation with the
invigilating lecturer, will decide on the steps to be taken.
No firearms and other dangerous weapons may be taken into the assessment venues. Small purses/wallets are
permitted. The University takes no responsibility for any losses in this regard.
APK: Under B Les 101.
APB: Study Centre (Old Franks Canteen ground floor).
DFC: John Orr building, ground floor Atrium C next to exit 5 and 6.
DFC: Samsung Safekeeping, 3rd floor entrance, Q-K building (Old Perskor Building) SWC:
TW Kambule building at the back A1.
Times: From 01 November 2017 to 28 November 2017
Monday to Friday: 06.30 am – 23:00 pm
Saturdays: 06.30 am – 18:00 pm
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Cell phones must be switched off and placed face down on the assessment desk next to the candidates’ student
cards. Candidates are not allowed to touch their cell phones during the full duration of the assessment. Cell phones
may be confiscated as evidence in case of a transgression.
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Unauthorised devices are not allowed inside the assessment venue and must be left with all other unauthorised
material or electronic equipment safely at the area designated for storage of personal belongings. Transgression
of assessment regulations may lead to the confiscation of devices to serve as evidence in disciplinary
investigations.
14.
No candidate is permitted to leave the assessment venue in the last fifteen minutes of the assessment opportunity
period.
15.
These regulations also pertain to all tests.
SHELLAINE ROOI
Senior Manager: Assessments
02 November 2017