After you complete this *Course Guide*, the *Diagnostic Quiz *and the *Preparatory Package*, you should continue your study as suggested in the *Presentation Schedule*.

The main study materials for *MATH S122 *are 13 printed study units. The units are supplemented by reading selections from a set textbook and teaching presented through audio and video programmes. To deepen your understanding, each unit is also provided with a *Problem Booklet*.

General administrative information is supplied through a number of documents. In particular, the *Presentation Schedule *helps you pace yourself through the presentation; *Tutorial Schedules *give the date, time and venue of your tutorials and other optional activities; *Stop Presses *provide the latest news about this course; and *Errata *correct typographical mistakes in course texts.

Having so many bits and pieces to the course may be a bit frightening, but you'll see that it really isn't so hard to follow. To give you a better picture of the components, we now discuss in detail the study materials and some of the supplementary elements.

**3.1 Study units**

These units are the core course materials. You are expected to complete one unit over a two-week period including the associated assessment questions. The following gives a brief description of the units:

*Unit 1 *Relations and functions – this unit is concerned with algebraic and graphical representations of relations and functions; and considers the properties of Cartesian equations, parametric equations, and polar equations and their relationships.

*Unit 2 *Systems of equations – this unit presents graphical and algebraic methods for solving linear and simple non-linear systems; and discusses the errors introduced in numerical operations and the problem of ill-conditioning.

*Unit 3 *Matrices – this unit introduces matrices and their operations including addition, subtraction, multiplication and matrix inversion; and solves the matrix equations for linear systems by performing row operations and inversion method.

*Unit 4 *Modelling and models – this unit describes a mathematical modelling cycle and the roles of mathematical models; it also explains how linear, non-linear and simultaneous models can be set up and solved and how the results can be interpreted.

*Unit 5 *Diﬀerentiation – this unit presents the concept of limits and derivatives and various rules of diﬀerentiation, including constant multiple rule, power rule, sum rule, product rule, quotient rule and chain rule. The technique of implicit diﬀerentiation and higher order derivatives will also be discussed.

*Unit 6 *Transcendental functions and their derivatives – this unit discusses the properties and diﬀerentiation of transcendental functions including trigonometric, exponential, logarithmic and hyperbolic functions. The concept of inverse functions and the technique of logarithmic diﬀerentiation will be presented.

*Unit 7 *Applications of diﬀerentiation – this unit applies techniques of diﬀerentiation to obtain information for graph sketching. It also discusses the formulation and solution of optimization problems, rate of change problems and related rate of change problems.

*Unit 8 *Integration – this unit introduces the concept of indefinite and definite integrations and their evaluation. The Fundamental Theorems of Calculus will be presented.

*Unit 9 *Techniques of integration – this unit discusses various methods of integration including the method of substitution, the integration-by-parts formula, the method of partial fractions for rational functions and the method of trigonometric substitutions.

*Unit 10 *Applications of integrals – this unit considers applications of integration including finding areas, volumes and lengths of curves.

*Unit 11 *Vectors – this unit considers geometrical and algebraic representations of vectors and discusses their operations including addition, subtraction, scalar multiplication, scalar (dot) product, decomposition and projection.

*Unit 12 *Position and motion – this unit focuses on physical applications of the techniques presented in the previous units. In particular, applications on position and motion relating to linear motions and projectiles will be considered. First order ordinary diﬀerential equations will be introduced.

*Unit**13 *Introduction to statistics – this unit presents the basic concepts of statistics and considers the graphical and algebraic methods for presenting data. Linear regression models and the method of least squares will be discussed.

**3.1.1 Working through the study units**

Most of the *MATH S122 *study units use information provided in earlier units. Therefore, you should study the units one at a time in a sequential order. It will help if you work through the *Preparatory Package*, where you'll learn more techniques for being a successful distance learner in the section called 'How to study an HKMU course'.

The units are divided up into sections that provide natural breaks for your study. Each unit begins with an introduction giving guidelines on what you will study and the objectives of the unit. It will conclude with a summary of the important results. Do not skip the sections that refer to the set textbook or direct you to the audio or video programmes. If you do, you'll miss some useful teaching points and explanations.

In the units you will come across examples, exercises and activities. Section 2.2 of the *Preparatory Package *will explain their purpose and how you should use them. You should work through the exercises and activities included in the units. It is important to try solving them before looking at the suggested solution; don't just turn to the solution as the easy way out. On the other hand, don't ignore the solution – always read through it and compare it with yours.

On completing your study of a unit, you should start working on the corresponding assignment questions. Although it is tempting to use the unit or ask your tutor for help, you will gain more by making your first attempt at solving the questions without any assistance. You can, of course, refer back to the units before you finalize your solutions.

**3.2 Set textbook**

These units are the core course materials. You are expected to complete one unit over a two-week period including the associated assessment questions. The following gives a brief description of the units:

You are required to purchase the following set textbook for *MATH S122 *:

Weir, Hass and Giordano (2010)

*Thomas' Calculus,*

12th edn, Pearson Education.

Note that the textbook will be referred to as 'T&F'. Details of where you can purchase T&F (and the software for this course) will be sent to you separately. Instructions on using it will be given in the study units.

**3.3 Scientific Notebook**

You are also required to purchase the algebraic software Scientific Notebook. The software combines the ease of preparing documents mixing mathematics and text with the power of symbolic computation and the convenience of direct Internet access.

These features allow you to make discoveries with mathematics as well as to tackle more realistic problems without the burden of mechanical calculations. They also enable you to discuss mathematics with your tutor or fellow students over the Internet.

Technical details of the software are given in the booklet *Getting started with Scientific Notebook *that comes with the software. You can also refer to Section 2.5 of the *Preparatory Package *that introduces the basic functions of the software and gives guidance on exploring its features.

**3.4 Audio and video programmes**

Several of the units incorporate teaching based on audio and video programmes. These programmes should provide you with some variety in your study. The content of each programme will be briefly introduced in the corresponding unit. The unit will also tell you exactly when you should start a programme.

You will need to have your unit, a pencil and some paper to hand before you start a programme. You should stop the programme whenever you are instructed to do so, and then work on the suggested exercises or return to the unit. Of course, you may want to stop it at other times to replay parts of it in order to gain a better understanding.

As part of our language support, audio programmes are supplied in both English and Chinese. The video programmes are in English with Chinese subtitles provided.

**3.5 Other materials**

The course materials include a number of supporting documents that provide academic support as well as administrative information. Eﬀective use of these documents will make an important contribution to your success in *MATH S122*.

**3.5.1*** Checklist*

Each package of course materials for *MATH S122 *will include a *Checklist *that lists the items included in the package. As soon as you receive a package you should go through the list and make sure that all the items are there. Instructions on how to obtain the missing items will be given in the *Checklist*.

**3.5.2*** Course Handbook*

The *Course Handbook *is a summary of the standard results introduced in *MATH S122*. You will not be allowed to bring the *Course Handbook *to the exam. Another copy of the handbook will be given to you together with the exam paper.

**3.5.3*** Chinese Language Summary*

The summary aims to assist you in your transition to developing English language study skills. The level of this support will be decreased as the course progresses.

**3.5.4*** Problem Booklet*

Each unit comes with a *Problem Booklet *that provides additional practice to help reinforce your understanding of the material. The *Problem Booklet *is divided up into sections corresponding to those in the study unit so you can work through the corresponding exercises after completing each section.

**3.5.5 Presentation Schedule**

The *Presentation Schedule *sets out an overall schedule for the course presentation as well as when each assignment should be completed.

In the schedule we suggest when a unit should be studied. You don't have to follow our suggestion, but it is important to keep up your progress. You should aim to finish the units for an assignment at least one week before its cut-oﬀ date. In addition, you should start the assignment questions for a unit as soon as you finish the unit.

**3.5.6 Tutorial Schedule**

The *Tutorial Schedule *tells the exact date, time and venue of your tutorials and other optional activities for this course. One schedule will be provided for each semester before the semester begins. For *MATH S122*, the first semester begins in April and the second semester begins in October.

**3.5.7 Stop Presses**

You will receive a number of *Stop Presses *throughout the course. They are a sort of newsletter containing useful information about the course.

**3.5.8 Errata**

*Errata *will let you know of any typographical mistakes in the printed course materials (i.e. the study units and assignments). When you receive an errata, you should correct the listed items immediately.