MAT2615/101/0/2023
Tutorial letter 101/0/2023
CALCULUS IN HIGHER DIMENSIONS
MAT2615
Year module
Department of Mathematical Sciences
IMPORTANT INFORMATION:
Please activate your myUnisa and myLife e-mail account and
make sure that you have regular access to the myUnisa module
website MAT2615-23-Y1, as well as your group website
BARCODE
university
Define tomorrow. of south africa
, CONTENTS
Page
1 INTRODUCTION ..................................................................................................................4
1.1 Getting started......................................................................................................................4
2 OVERVIEW OF MAT2615 ....................................................................................................4
2.1 Purpose ................................................................................................................................4
2.2 Outcomes .............................................................................................................................5
3 CURRICULUM TRANSFORMATION ..................................................................................5
4 LECTURER(S) AND CONTACT DETAILS ..........................................................................5
4.1 Lecturer(s) ............................................................................................................................5
4.2 Department ..........................................................................................................................6
4.3 University..............................................................................................................................6
5 RESOURCES.......................................................................................................................6
5.1 Joining myUnisa ...................................................................................................................6
5.2 Prescribed books..................................................................................................................7
5.3 Recommended book(s) ........................................................................................................7
5.4 Electronic reserves (e-reserves) ..........................................................................................7
5.5 Library services and resources ............................................................................................7
6 STUDENT SUPPORT SERVICES .......................................................................................8
7 HOW TO STUDY ONLINE? .................................................................................................9
7.1 What does it mean to study fully online?..............................................................................9
7.2 myUnisa tools .......................................................................................................................9
8 MODULE SPECIFIC STUDY PLAN.....................................................................................9
9 MODULE PRACTICAL WORK AND WORK INTEGRATED LEARNING .........................10
10 ASSESSMENT...................................................................................................................10
10.1 Assessment plan ................................................................................................................10
10.2 General assignment numbers ............................................................................................11
10.3 Submission of assignments................................................................................................11
10.4 Assignments.......................................................................................................................11
10.5 The examination .................................................................................................................11
2
, MAT2615/101/0/2023
11 OTHER ASSESSMENT METHODS ..................................................................................12
12 CONCLUSION ...................................................................................................................12
ADDENDUM A: SELF ASSESSMENT TASK FOR UNITS 1–3 ...................................................13
A.1 QUESTIONS ......................................................................................................................13
A.2 ANSWERS AND SOLUTIONS...........................................................................................18
ADDENDUM B: ASSIGNMENTS .................................................................................................26
3
, 1 INTRODUCTION
Welcome to the MAT2615 module. We trust that you will find it both interesting and rewarding.
This tutorial letter contains important information about the scheme of work, resources and as-
signments for this module as well as exam admission. We urge you to read it carefully before
working through the study material, preparing the assignment(s), preparing for the examination and
addressing questions to your lecturers.
In this tutorial letter, you will find the assignments as well as instructions on the preparation and
submission of the assignments. This tutorial letter also provides all the information you need with
regard to the prescribed study material and other resources. Please study this information carefully
and make sure that you obtain the prescribed material as soon as possible.
You will access all files online, a number of tutorial letters for example, solutions to assignments,
during the year. These tutorial letters will be uploaded on myUnisa, under Additional Resources
and Lessons tools on myUnisa platform. A tutorial letter is our way of communicating with you
about teaching, learning and assessment.
Right from the start we would like to point out that you must read all the tutorial letters you
access from the module site immediately and carefully, as they always contain important and,
sometimes urgent information.
Because this is a fully online module, you will need to use myUnisa to study and complete the
learning activities for this course. Please visit the website for MAT2615 on myUnisa frequently.
1.1 Getting started
Owing to the nature of this module, you can read about the module and find your study material
online. Go to the website at https://my.unisa.ac.za and log in using your student number and
password. Click on ”myModules” at the top of the web page and then on ”Sites” in the top right
corner. In the new window, click on the grey Star icon next to the modules you want displayed on
your navigation bar. Close the window in the top right corner. Then select the option ”Reload to see
your updated favorite sites”. Now go to your navigation bar and click on the module you want to
open.
We wish you every success with your studies!
2 OVERVIEW OF MAT2615
2.1 Purpose
The main purpose of this module is to extend concepts such as limits, continuity, differentiation and
integration, studied in first year calculus, to functions of several variables. Furthermore, the purpose
includes improving the problem solving skills of students and forming a basis of knowledge that is
necessary for further studies in Mathematics and applications in Physics.
4
Tutorial letter 101/0/2023
CALCULUS IN HIGHER DIMENSIONS
MAT2615
Year module
Department of Mathematical Sciences
IMPORTANT INFORMATION:
Please activate your myUnisa and myLife e-mail account and
make sure that you have regular access to the myUnisa module
website MAT2615-23-Y1, as well as your group website
BARCODE
university
Define tomorrow. of south africa
, CONTENTS
Page
1 INTRODUCTION ..................................................................................................................4
1.1 Getting started......................................................................................................................4
2 OVERVIEW OF MAT2615 ....................................................................................................4
2.1 Purpose ................................................................................................................................4
2.2 Outcomes .............................................................................................................................5
3 CURRICULUM TRANSFORMATION ..................................................................................5
4 LECTURER(S) AND CONTACT DETAILS ..........................................................................5
4.1 Lecturer(s) ............................................................................................................................5
4.2 Department ..........................................................................................................................6
4.3 University..............................................................................................................................6
5 RESOURCES.......................................................................................................................6
5.1 Joining myUnisa ...................................................................................................................6
5.2 Prescribed books..................................................................................................................7
5.3 Recommended book(s) ........................................................................................................7
5.4 Electronic reserves (e-reserves) ..........................................................................................7
5.5 Library services and resources ............................................................................................7
6 STUDENT SUPPORT SERVICES .......................................................................................8
7 HOW TO STUDY ONLINE? .................................................................................................9
7.1 What does it mean to study fully online?..............................................................................9
7.2 myUnisa tools .......................................................................................................................9
8 MODULE SPECIFIC STUDY PLAN.....................................................................................9
9 MODULE PRACTICAL WORK AND WORK INTEGRATED LEARNING .........................10
10 ASSESSMENT...................................................................................................................10
10.1 Assessment plan ................................................................................................................10
10.2 General assignment numbers ............................................................................................11
10.3 Submission of assignments................................................................................................11
10.4 Assignments.......................................................................................................................11
10.5 The examination .................................................................................................................11
2
, MAT2615/101/0/2023
11 OTHER ASSESSMENT METHODS ..................................................................................12
12 CONCLUSION ...................................................................................................................12
ADDENDUM A: SELF ASSESSMENT TASK FOR UNITS 1–3 ...................................................13
A.1 QUESTIONS ......................................................................................................................13
A.2 ANSWERS AND SOLUTIONS...........................................................................................18
ADDENDUM B: ASSIGNMENTS .................................................................................................26
3
, 1 INTRODUCTION
Welcome to the MAT2615 module. We trust that you will find it both interesting and rewarding.
This tutorial letter contains important information about the scheme of work, resources and as-
signments for this module as well as exam admission. We urge you to read it carefully before
working through the study material, preparing the assignment(s), preparing for the examination and
addressing questions to your lecturers.
In this tutorial letter, you will find the assignments as well as instructions on the preparation and
submission of the assignments. This tutorial letter also provides all the information you need with
regard to the prescribed study material and other resources. Please study this information carefully
and make sure that you obtain the prescribed material as soon as possible.
You will access all files online, a number of tutorial letters for example, solutions to assignments,
during the year. These tutorial letters will be uploaded on myUnisa, under Additional Resources
and Lessons tools on myUnisa platform. A tutorial letter is our way of communicating with you
about teaching, learning and assessment.
Right from the start we would like to point out that you must read all the tutorial letters you
access from the module site immediately and carefully, as they always contain important and,
sometimes urgent information.
Because this is a fully online module, you will need to use myUnisa to study and complete the
learning activities for this course. Please visit the website for MAT2615 on myUnisa frequently.
1.1 Getting started
Owing to the nature of this module, you can read about the module and find your study material
online. Go to the website at https://my.unisa.ac.za and log in using your student number and
password. Click on ”myModules” at the top of the web page and then on ”Sites” in the top right
corner. In the new window, click on the grey Star icon next to the modules you want displayed on
your navigation bar. Close the window in the top right corner. Then select the option ”Reload to see
your updated favorite sites”. Now go to your navigation bar and click on the module you want to
open.
We wish you every success with your studies!
2 OVERVIEW OF MAT2615
2.1 Purpose
The main purpose of this module is to extend concepts such as limits, continuity, differentiation and
integration, studied in first year calculus, to functions of several variables. Furthermore, the purpose
includes improving the problem solving skills of students and forming a basis of knowledge that is
necessary for further studies in Mathematics and applications in Physics.
4
