(MAT1512) - Calculus A Tutorial Letter: Important Information, Purpose, Outcomes, Resources, and Support at University of South Africa
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University of South Africa
Calculus A (MAT1512)
Added on 2021-07-13
About This Document
This is a tutorial letter for the MAT1512 Calculus A module at the University of South Africa. It contains important information about the module and is only available on myUnisa. The letter provides an overview of the module, including its purpose and outcomes, lecturer and contact details, resources such as prescribed and recommended books, student support services, and assessment plan. Students are urged to read it carefully before working through the study material and preparing for assignments and exams.
(MAT1512) - Calculus A Tutorial Letter: Important Information, Purpose, Outcomes, Resources, and Support at University of South Africa
University of South Africa
Calculus A (MAT1512)
Added on 2021-07-13
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MAT1512/001/0/2021 of south africaTutorial Letter 001/0/2021CALCULUS AMAT1512Year moduleDepartment of Mathematical SciencesIMPORTANT INFORMATION: This tutorial letter contains important information about your module. Please activate your myUNISA and myLife e-mail account(s) and make sure that you have regular access to the myUNISA module website MAT1512-21-Y1, as well as your group site. Note: This is a fully online module. It is therefore, only available on myUnisa. BAR CODEDefine tomorrow. universityOpen Rubric
CONTENTS Page1 INTRODUCTION.................................................................................................................. 31.1 Getting started................................................................................................................ 32 OVERVIEW of MAT1512...................................................................................................... 3 2.1 Purpose............................................................................................................................... 5 2.2 Outcomes........................................................................................................ 5 3 LECTURER(S) AND CONTACT DETAILS.......................................................................... 83.1 Lecturer(s)............................................................................................................................ 8 3.2 Department........................................................................................................................... 9 3.3 University.............................................................................................................................. 9 4 RESOURCES....................................................................................................................... 94.1 Joining myUNISA.................................................................................................................. 9 4.2 Prescribed book(s)...............................................................................................................10 4.3 Recommended book(s).....................................................................................................10 4.4 Electronic reserves (e-reserves)..........................................................................................10 4.5 Library services and resources........................................................................... 10 5 STUDENT SUPPORT SERVICES..................................................................................... 11 6 HOW TO STUDY ONLINE ?............................................................................................. 12 6.1 What does it mean to study fully online?.......................................................................... 12 6.2 myUNISA tools.............................................................................................. 13 7 ASSESSMENT .............................................................................................. 14 7.1 Assessment plan............................................................................................. 14 7.2 Year mark and final examination/other options....................................................... 16 8 CONCLUSION................................................................................................ 17 APPENDIX: GLOSSARY OF TERMS.................................................................. 17
MAT1512/001/0/2021 1 INTRODUCTIONDear Student Welcome to the MAT1512 module. We trust that you will find the mathematics studied in this module interesting and useful, and that you will enjoy doing it. This tutorial letter contains important information about the scheme of work, resources and assignments 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 semester/ year. These tutorial letters will be uploaded on myUnisa, under Additional Re-sources 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 MAT1512 on myUnisa frequently. The website for your module is MAT1512-21-Y1. 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 webpage 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 navigator bar. Close the window in the right corner. The 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 MAT1512 2.1 Purpose This module will be able useful to students interested in developing the basic skills in Calculus which can be applied in the natural sciences and social sciences. Students who have completed this module successfully will have an understanding of the basic ideas of Calculus.
MAT1512/001 5 2 PURPOSE AND OUTCOMES2.1 PurposeThis module is useful to students interested in developing the basic skills in differential and integral calculus. Differential and integral calculus are essential for physical, life and economic sciences. Students credited with this module will have a firm understanding of the limit, continuity at a point, differentiation and integration, together with a background in the basic techniques and some appli- cations of Calculus. 2.1.1 Learning Assumptions: The learning is based on the assumption that students are already competent in terms of the following outcomes or areas of learning and must: – Have a Senior Certificate or equivalent qualification (as required) for further study. – Have obtained an NQF/HEQF Level equivalent to 4 with the ability to: – Be able to learn from predominantly written material in the language of tuition – Take responsibility for their own progress and independently adjust to the learning environment – Have basic computer skills like using a mouse, keyboard and windows features – Demonstrate an understanding of the most current topics in mathematics including ∗ Functions∗ The ability to algebraically manipulate real numbers and solve equations.∗ An ability to sketch graphs and find equations from these graphs.∗ Substantive knowledge about basic trigonometry∗ Knowledge about the following mathematical concepts: absolute values, partialfractions and inequalities. Recognition of prior learning will take place in accordance with the institution’s policy and guidelines. Recognition takes place, where prior learning corresponds to the re- quired NQF-HEQF level and in terms of applied competencies relevant to the content and outcomes of the qualification, at the discretion of the department. 2.1.2 Range statement for the module: The techniques selected involve polynomial, ratio- nal, trigonometric, exponential and logarithmic functions and their composites. This introductory calculus module covers differentiation and integration of functions of one variable, with applications. 2.2 Outcomes2.2.1 Specific outcome 1:Demonstrate knowledge of the concept of a limit of a function and its application. Range:The knowledge includes limits of one variable and an introduction to limits of two or more variables.
6 Assessment criteria– A formal definition of the limit with the correct mathematical notation is given which embraces an understanding of the limit as the y-value of a function. – A distinction between the limits of a function as x approaches {limx →a f (x)} andthe value of the function at x = a is made correctly. – Laws governing limits are stated and used to determine and evaluate limits of sums, products, quotients and composition of functions. – The limits of functions are evaluated graphically and numerically. – The limit definition of continuity is used to determine whether a function is continuous or discontinuous at a point. – The Squeeze Theorem is used to determine certain undefined limits. 2.2.2 Specific outcome 2:Demonstrate an understanding of differentiation. Assessment criteria– The derivative is defined as an instantaneous rate of change of a function. – The first principle of differentiation is presented using different expressions. Range: These different expressions include: hxfhxfxfh0lim; xxfxxfxfx0limxyxfx0lim; axafxfafaxlim– Alternate derivative notations are given. Range: These include: xfdxddxdfdxdyyxf– A distinction between continuity and differentiability of a function at point is made correctly. – A representation of the first derivative as the slope of the tangent line at the point of tangency is given. 2.2.3 Specific outcome 3: – Calculate derivatives. Assessment criteria– The derivative of a function is computed from the first principle of differentiation. – The basic rules of differentiation such as the power rule, product and quotient rules are used to compute derivatives of different functions. – Range: The functions are in the form:][xgxfxh; xgxfxh.xgxfxh.The chain rule is used, together with other rules of differentiation to find derivatives of composite functions.
MAT1512/001 7 2.2.4 Specific outcome 4:– Use derivatives to solve applied problems.Assessment criteria– For the problem solving, the differentiation technique chosen is appropriate to the problem. – Mathematical notations and language are used appropriately. – The derivative is used to find equations of tangent and normal lines of different curves. – Where appropriate, the Mean Value Theorem is applied. 2.2.5 Specific outcome 5:– Demonstrate understanding of basic integration and the Fundamental Theo- rem of CalculusAssessment criteria– The definite integral is defined and interpreted using: ∗ the concept of definite integral to obtain areas under the curve.∗ as the net change in a quantity from x = a to x = b if f(x) is the rate of change ofthe quantity with respect to x.– A function F is defined as an anti-derivative (indefinite integral) of the function f if the derivative fF.Anti-differentiation (integration) is recognised as the inverse of the differentiation process. _ The Fundamental Theorem of Calculus for a function fon an interval ba,as: aFbFdxxfbawhere xFis such that xfxFis reproduced and used to:- ∗ explain the way in which differentiation and integration are related.∗ evaluate given integrals.– Integral notation is used appropriately. 2.2.6 Specific outcome 6:– Use integrals of simple functions to solve applied problems Range: Simple integrals are applied but not limited to problems involving the length of a curve, area between curves, velocity and acceleration. Assessment criteria – Substitution or term by term integration techniques are used appropriately. – The anti-derivatives of basic algebraic and trigonometric functions are determined correctly. – For the problem solving process:- ∗ The estimations of the definite integrals of the functions are correct.∗ The solution is consistent with the problem. 2.2.7 Specific outcome 7– Analyse logarithmic and exponential functions.
8 Assessment criteria – The graphs of the functions y = ex and y = lnx are reproduced. – The relationship between ex and lnx as inverse differentiable functions is recognised and used as a device for simplifying calculations. – Rules of differentiation and integration are applied to functions involving logarithmic and exponential functions. – Logarithmic differentiation is used correctly. – Exponentials and logarithmic models for solving applied problems are identified. 2.2.8 Specific outcome 8– Solve exponential growth and decay problems using elementary differential equa- tions. Range: The solutions are limited to first-order, separable, constant coefficient initial- value problems, with contextual situations involving exponential growth and decay. Assessment criteria – The contextual situation (problem) is analysed and represented with a differential equation. – A suitable method for determining the solution is chosen. – Initial or boundary conditions are identified and used to determine the constant of integration. – The differential equation is solved correctly. – Partial derivatives are computed where necessary. – Mathematical notation is used to communicate the results clearly 3 LECTURER(S) AND CONTACT DETAILS3.1 Lecturer(s)The lecturer responsible for this module is Dr. SB Mugisha. You can contact her at: Dr. SB MugishaTel: (011) 670-9154Room no: C 6-54GJ Gerwel Buildinge-mail: mugissb@unisa.ac.zaA notice will be posted on myUnisa if there are any changes and/or an additional lecturer is appointed to this module. Please do not hesitate to consult your lecturer whenever you experience difficulties with your stud- ies. You may contact your lecturer by phone or through correspondence or by making a personal visit to his/her office. Please arrange an appointment in advance (by telephone or by e-mail) to ensure that your lecturer will be available when you arrive.
MAT1512/001 9 Please come to these appointments well prepared with specific questions that indicated your own efforts to have understood the basic concepts involved. If these difficulties concern exercises which you are unable to solve, you must send us your attempts so that we can see where you are going wrong. If you should experience any problems with the exercises in the study guide, your lecturer will gladly help you with them, provided that you send in your bona fide attempts. When sending in any queries or problems, please do so separately from your assignments and address them directly to your lecturer.3.2 Department You can contact the Department of Mathematical Sciences as follows: Department of Mathematical Sciences Fax number: 011 670 9171 (RSA) +27 11 670 9171 (International) Departmental Secretary: 011 670 9147 (RSA) +27 11 670 9147 (International) e-mails: mathsciences@unisa.ac.za or swanem@unisa.ac.za 3.3 University To contact the University, follow the instructions on the Contact us page on the Unisa website. Remember to have your student number available whenever you contact the University. Whenever you contact a lecturer via e-mail, please include your student number in the subject line to enable the lecturer to help you effectively. 4 RESOURCES4.1 Joining myUnisaThe myUnisa learning management system is the University’s online campus which will help you communicate with your lecturers, other students, and the administrative departments within Unisa. To claim your myUnisa account, Please follow the steps below: 1. Visit the myUnisa website at https://my.unisa.ac.za/portal2. Click on the “Claim Unisa login” link on the top of the screen under the orange use ID box. 3. A new screen will load, prompting you to enter your student number. Please enter your student number and click “continue”. 4. Enter your surname, your full name, your date of birth and, finally, your South African ID number (for South African citizens) OR your passport number (for foreign students). Then clock “continue”. Remember to enter either an ID number or a passport number, NOT both.5. Please read through the guidelines and click all the check boxes to acknowledge that you have read all the information provided. Once you are done, click the “Acknowledge” button to redirect you to the final page in the process. 6. The final page will display your myLife e-mail address, and your myLife AND myUnisa password. This password will also be sent to the cellphone number displayed on the page for safekeeping. 7. Please note that it can take up to 24 hours for your myLife e-mail account to be created.
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