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MAT1512/001/0/2021of 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 regularaccess 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

CONTENTSPage1INTRODUCTION..................................................................................................................31.1Getting started................................................................................................................32OVERVIEW of MAT1512......................................................................................................32.1Purpose...............................................................................................................................52.2Outcomes........................................................................................................ 53LECTURER(S) AND CONTACTDETAILS..........................................................................83.1Lecturer(s)............................................................................................................................83.2Department...........................................................................................................................93.3University..............................................................................................................................94RESOURCES.......................................................................................................................94.1Joining myUNISA..................................................................................................................94.2Prescribed book(s)...............................................................................................................104.3Recommended book(s).....................................................................................................104.4Electronic reserves (e-reserves)..........................................................................................104.5Library services and resources........................................................................... 105STUDENT SUPPORTSERVICES.....................................................................................116HOW TO STUDY ONLINE ?............................................................................................. 126.1What does it mean to study fully online?.......................................................................... 126.2myUNISA tools..............................................................................................137ASSESSMENT.............................................................................................. 147.1Assessment plan............................................................................................. 147.2Year mark and final examination/other options....................................................... 168CONCLUSION................................................................................................ 17APPENDIX: GLOSSARY OF TERMS.................................................................. 17

MAT1512/001/0/20211INTRODUCTIONDear StudentWelcome to theMAT1512module. We trust that you will find the mathematics studied in this moduleinteresting and useful, and that you will enjoy doing it.This tutorial letter contains important information about the scheme of work, resources andassignments for this module as well as exam admission. We urge you to read it carefully beforeworking through the study material, preparing the assignment(s), preparing for the examinationand addressing questions to your lecturers.In this tutorial letter, you will find the assignments as well as instructions on the preparation andsubmission of the assignments. This tutorial letter also provides all the information you need withregard to the prescribed study material and other resources. Please study this informationcarefully 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 onmyUnisa, under AdditionalRe-sources and Lessons tools onmyUnisaplatform. A tutorial letter is our way of communicatingwith 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 accessfrom the module site immediately and carefully, as they always contain important and, sometimesurgent information.Because this is a fully online module, you will need to use myUnisa to study and complete thelearning 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 startedOwing to the nature of this module, you can read about the module and find your study materialonline. Go to the website athttps://my.unisa.ac.zaand log in using your student number andpassword. Click on “myModules” at the top of the webpage and then on “Sites” in the top rightcorner. In the new window, click on the grey Star icon next to the modules you want displayed onyour navigator bar. Close the window in the right corner. The select the option “Reload to seeyour updated favorite sites”. Now go to your navigation bar and click on the module you want toopen.We wish you every success with your studies!2OVERVIEW of MAT15122.1 PurposeThis module will be able useful to students interested in developing the basic skills in Calculuswhich can be applied in the natural sciences and social sciences. Students who have completedthismodulesuccessfullywillhaveanunderstandingofthebasicideasofCalculus.

MAT1512/00152 PURPOSE ANDOUTCOMES2.1 PurposeThis module is useful to students interested in developing the basic skills in differential and integralcalculus. 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 arealready 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 learningenvironment–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 policyand guidelines. Recognition takes place, where prior learning corresponds to the re-quired NQF-HEQF level and in terms of applied competencies relevant to the contentand 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. Thisintroductory calculus module covers differentiation and integration of functions of onevariable, with applications.2.2 Outcomes2.2.1Specific 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 morevariables.

6Assessment criteria–A formal definition of the limit with the correct mathematical notation is given whichembraces an understanding of the limit as the y-value of a function.–A distinction between the limits of a function asxapproaches{limx→af(x)}andthe value of the function atx=ais 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 continuousor discontinuous at a point.–The Squeeze Theorem is used to determine certain undefined limits.2.2.2Specific 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 madecorrectly.–A representation of the first derivative as the slope of the tangent line at the point oftangency is given.2.2.3Specific 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 rulesare 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 findderivatives of composite functions.

MAT1512/00172.2.4Specific outcome4:–Use derivatives to solve applied problems.Assessment criteria–For the problem solving, the differentiation technique chosen is appropriate to theproblem.–Mathematical notations and language are used appropriately.–The derivative is used to find equations of tangent and normal lines of differentcurves.–Where appropriate, the Mean Value Theorem is applied.2.2.5Specific outcome5:–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 fromx = atox = biff(x) is the rate of change ofthe quantity with respect tox.–A functionFis defined as an anti-derivative (indefinite integral) of the function f ifthe derivativefF.Anti-differentiation (integration) is recognised as the inverseof the differentiation process._ The Fundamental Theorem of Calculus for a functionfon an intervalba,as:aFbFdxxfbawherexFis such thatxfxFis reproduced and used to:-∗explain the way in which differentiation and integration are related.∗evaluate given integrals.–Integral notation is used appropriately.2.2.6Specific outcome6:–Use integrals of simple functions to solve applied problemsRange: Simple integrals are applied but not limited to problems involving the lengthof 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 determinedcorrectly.–For the problem solving process:-∗The estimations of the definite integrals of the functions are correct.∗The solution is consistent with the problem.2.2.7Specific outcome 7–Analyse logarithmic and exponential functions.

8Assessment criteria–The graphs of the functionsy=exandy=lnxare reproduced.–Therelationshipbetweenexandlnxas inversedifferentiablefunctions is recognisedand used as a device for simplifying calculations.–Rules of differentiation and integration are applied to functions involving logarithmicand exponential functions.–Logarithmic differentiation is used correctly.–Exponentials and logarithmic models for solving applied problems are identified.2.2.8Specific 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 differentialequation.–A suitable method for determining the solution is chosen.–Initial or boundary conditions are identified and used to determine the constant ofintegration.–The differential equation is solved correctly.–Partial derivatives are computed where necessary.–Mathematical notation is used to communicate the results clearly3LECTURER(S) AND CONTACTDETAILS3.1Lecturer(s)The lecturer responsible for this module is Dr. SB Mugisha. You can contact her at:Dr. SBMugishaTel:(011)670-9154Room no: C6-54GJ GerwelBuildinge-mail:mugissb@unisa.ac.zaA notice will be posted onmyUnisaif there are any changes and/or an additional lectureris 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 personalvisit to his/her office.Please arrange an appointment in advance (by telephone or by e-mail)toensurethatyourlecturerwillbeavailablewhenyouarrive.

MAT1512/0019Please come to these appointments well prepared with specific questions that indicated your ownefforts to have understood the basic concepts involved. If these difficulties concern exerciseswhich you are unable to solve, you must send us your attempts so that we can see where you aregoing wrong.If you should experience any problems with the exercises in the study guide, your lecturer willgladly help you with them, provided that you send in your bona fide attempts.When sending inany queries or problems, please do so separately from your assignments and address themdirectly to your lecturer.3.2 DepartmentYou can contact the Department of Mathematical Sciences as follows:Department of Mathematical SciencesFax 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.za3.3 UniversityTo 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 subjectline to enable the lecturer to help you effectively.4RESOURCES4.1JoiningmyUnisaThe myUnisa learning management system is the University’s online campus which will help youcommunicate 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 athttps://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 toenter your student number. Please enter yourstudent number and click “continue”.4.Enter your surname, your full name, your date of birth and, finally, your South African IDnumber (for South African citizens) OR your passport number (for foreign students). Thenclock “continue”.Remember to enter either an ID number or a passport number, NOTboth.5.Please read through the guidelines and click all the check boxes to acknowledge that youhave read all the information provided. Once you are done, click the “Acknowledge” button toredirect you to the final page in the process.6.The final page will display your myLife e-mail address, and yourmyLife AND myUnisapassword. This password will also be sent to the cellphone number displayed on the page forsafekeeping.7.Please note that it can take up to 24 hours for your myLife e-mail account to be created.

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