This Course Guide has been taken from the most recent presentation of the course. It would be useful for reference purposes but please note that there may be updates for the following presentation.
MATH S216
Mathematical Analysis
Welcome to MATH S216 Mathematical Analysis. We hope that you will find studying it enjoyable and rewarding.
This Course Guide contains information about the content and components of MATH S216 Mathematical Analysis that you should be aware of before starting to study the course.
The course provides an introduction to the subject of analysis In analysis we examine the foundations of calculus and discuss in detail what it means for a function from R to R to be 'well-behaved'. There are various approaches to analysis. In this course we choose to regard sequences as our basic tool and, after carefully discussing the convergence of sequences, we use sequences to study the three crucial concepts of analysis:
If you are to study MATH S216 successfully, then you will need to have succeeded in studying the prerequisite course MATH S121 and MATH S122, or to have gained similar experience from another source.
At the start of the course you will receive a Study Calendar for the year. This provides precise information about when you are expected to be studying each element of the course, and when you must submit your assignments. You will need to adjust this calendar for your personal circumstances and commitments, remembering that the dates by which you must submit your assignments are fixed.
Each unit has continuous assessment associated with it. In all there are two assignments. The course ends with a three-hour examination.
4.1 Course units
There are six course units (study texts) which vary in length but should each take you about 2-3 weeks to study. Each unit starts with an Introduction, which gives a brief outline of the various sections of that unit and indicates how the sections depend on one another. The Introduction finishes with a study guide, which helps you to plan your study of the unit. Most units have four or five sections, each corresponding approximately to an evening's work. The learning outcomes for the whole course are listed at the end of this booklet. In addition, each section in the units has a list of learning outcomes at its start, which should help you to focus your study on the most important ideas in that section.
Audio sessions
Most units contain an audio section, indicated by an audio symbol in the text margin. Each audio section contains a sequence of audio frames, which you should look at while listening to the associated audio. All these recordings can be accessed via the Online Environment (OLE) under 'Multimedia'.
You will need to pause the audios regularly to solve exercises or answer questions and we have indicated these points by a few bars of music. You may want to pause the audios more frequently than indicated--for example, whenever you need to think about the material.
Video programmes
Some units have an associated video programme. There may be some preparatory material to read, or exercises to work through before watching the programme. There may also be material to study after watching the programme. All the video programmes can be accessed via the OLE under 'Multimedia'. Each unit with an associated video programme includes a review which summarises the material presented in the programme.
4.2 MATH S216 Handbook
This is designed as a work of reference, and provides a convenient source of basic definitions and formulas for use throughout the course. Youwill not be allowedto bring the Course Handbook to the exam. Another copy of the handbook will be given to you together with the exam paper.
The course Handbook is a summary of the course. It provides a convenient source of the most important definitions, results, theorems and strategies in the units, presented section by section and indexed.
It is a good idea to start using the Handbook right from the beginning of the course, so that you become familiar with its contents.
4.3 Stop Press Notices
Each course mailing will contain a Stop Press which will give important up-to-date information about various aspects of the course. You should read each Stop Press carefully as soon as you receive it, as it may contain corrections to errors in assignments or units, or changes to the running of the course. It is important that you read each Stop Press as soon as you receive it. These notices are also posted in the Online Learning Environment (OLE).
4.4 Academic Timetable
This gives the starting date for each unit, the dates when assignments are due and weekends when tutorials are scheduled.
4.5 Tutorials
Dates for tutorials are as given in the presentation schedule. Other details, such as tutorial venue and exact timing, will be given to you through emails and the OLE. Attend tutorials to meet your tutor and the other students on the course. Be active to share your views in tutorials.
4.6 The Online Learning Environment (OLE)
The Online Learning Environment User Guide explains to you the hardware and the software requirements for you to access the course electronically. It also helps you to use the components in the OLE. Through the OLE, you can get more information on the course and communicate with other students and tutors of the course.
4.7 Assessment
The assessment of the course includes two assignments and a TWO-hour final examination. MATH S216 does not have any multiple choice assignments.
The continuous assessment will account for 30% of the total score for the course, and the examination will account for 70% of weights on your course score. The student passed the requirement on continuous assessment for the course. Registered students will be awarded the 5 credits on MATH S216 if they can get at least 40 marks in both the OCAS and the examination score. Read the Student Handbook for information on the award of course results.
Each study block has an assignment associated with it. In each assignment there will be a question on each of the units of the block. These questions will generally test main concepts, methods of proof and techniques taught in the course, and will range from the fairly straightforward to the quite difficult ones.
The examination covers the whole course. The specimen examination paper and solutions give you a general idea about the examination.
Questions in assignments and in the examination carry both accuracy marks and method marks. You should therefore, as a general practice, show all your working.
We expect you to leave numbers like π as they are √2 but you should simplify expressions such as sin(π/2). If you need to use decimal fractions at any time, two decimal places will normally be sufficient.
4.8 Calculators and mathematics software
You can use a calculator, or mathematics software such as Scientific Notebook, to evaluate mathematical functions such as exponential, logarithmic, trigonometric (and their inverses) and hyperbolic (and their inverses) when you study the course.
Calculators are allowed in the examination. The University has a List of Approved Models of Calculators so that students realise what types of calculators are allowed in the examination. This List is updated according to the types of calculators approved by the Hong Kong Examinations and Assessment Authority. You will receive the List from Registry before the examination.
You are not allowed to use a non-approved calculator or a calculator without 'HKEA/HKEAA Approved' label in the examination. For your early information, a copy of approved calculator list is attached at the back of this guide.
You should receive your first batch of materials at least one week before the start of the course. (The exact time may depend on when you registered for the course.) There is no need to wait for the start date given in the Study Calendar before starting work on the course, which begins with Unit AA3. If you are able to start earlier it will give you a cushion for weeks when you find the unit particularly long, or you have other commitments.
Notification of the name and contact details of your tutor, and the tutorial timetable, will be sent to you shortly before the start of the course.
(In addition to the following models, calculators bearing the "HKEA/HKEAA Approved" labels are also allowed.)
A.MAX
| SC-801 | SC-802 | SC-809 | SC-813 |
ATABA/AURORA
| AC‑688 | AC‑689 | AC‑690 | AC‑692 | ||||||
| AC‑693 | AC‑694 | AT‑1 | AT‑105 | ||||||
| AT‑106 A | AT‑108 A | AT‑168 | AT‑208 N/B | ||||||
| AT‑231 A/B/C/D | AT‑232 /S | AT‑233 | AT‑241 T | ||||||
| AT‑244 H | AT‑256 H | AT‑268 | AT‑281 /S | ||||||
| AT‑282 | AT‑283 | AT‑368 | AT‑508 | ||||||
| AT‑510 | AT‑512 | AT‑518 | AT‑520 | ||||||
| AT‑522 | AT‑601 A | AT‑620 A | AT‑630 | ||||||
| AT‑687 | AT‑2129 A/B | AT‑6120 | AT‑6320 | ||||||
| AT‑9300 | BD‑1 | BD‑2 | D‑8 /N | ||||||
| D‑10 /N | D‑12 N | SC-170 | SC-180 | ||||||
| SC-200 | SC-500 |
BISTEC
| B300 | B500 | B600 | B700 | ||||||
| B900 |
BLT
| BT-206 | BT-2016-12 | BT-2018-12 | DC-308-8S/12 | ||||||
| DC-318-8S/12 | DC-338-8S/12 | DC-408 | DC-508 | ||||||
| SC-183 |
CANON
| BS‑100 | BS-102 | BS‑120 | BS 122 | ||||||
| BS-123 | BS‑200 | BS‑300 | BS-1200TS | ||||||
| CB II BK/G | CB III | F‑45 | F‑65 | ||||||
| F‑73 /P | F‑402 | F-500 | F-502 | ||||||
| F-600 | F‑602 | F-604 | F-612 | ||||||
| F-700 | F‑800 P | F‑802 P | FC-4 S | ||||||
| FC-42 S | FINANCIAL/II | FS-400 | FS-600 | ||||||
| HS-20H | HS-100 | HS-102H | HS-120L | ||||||
| HS-1200RS/T/TV/TS | KC-20 | KS-10 | KS‑20 | ||||||
| KS‑30 | KS‑80 | KS-100 | KS-102 | ||||||
| KS‑120 | KS-122 | KS-123 | L‑20 II W AD | ||||||
| L‑30 II W AD | L-813 II | L‑1011 | L‑1214II/AD | ||||||
| L‑1218 | LC-22 | LC‑23 | LC‑34 /T | ||||||
| LC-44 | LC‑63 | LC‑64 T | LC-101 | ||||||
| LC-500H | LC‑1016 | LC-1222 | LC-1620H | ||||||
| LS‑8 | LS‑21 | LS-25H II | LS‑31 II | ||||||
| LS-32 | LS-39H | LS‑41 II | LS‑42 | ||||||
| LS‑43 B/S | LS-51 | LS‑52 BK/W | LS‑54 W | ||||||
| LS‑61 | LS-62 BK/W | LS‑80/H | LS-81 Z | ||||||
| LS‑82 H/Z | LS-88Hi/V | LS‑100 II/H/TS | LS-102 Z | ||||||
| LS-120H/L/RS/V | LS-151 | LS‑500 | LS‑510 | ||||||
| LS‑550 G/B1 | LS‑552 | LS‑553 | LS‑560 | ||||||
| LS-562 | LS‑563 | LS-566H | LS-716H | ||||||
| LS-1000H | LS-1200H | M‑10 | M‑20 | ||||||
| M-30 | OS‑1200 | PS‑8 BK/W | PS‑10BK/W | ||||||
| SK-100H | T-14BK/G/W | T‑19 | TR-10H | ||||||
| TR-1200H | TS‑81/H | TS‑83 | TS-85H | ||||||
| TS-101 | TS‑103 | TS-105H | TS-120TL | ||||||
| TX-1210Hi | WS‑100 | WS‑120 | WS-121H | ||||||
| WS-200H | WS-220H | WS-1200H | WS-1210Hi | ||||||
| WS-2222 | WS-2224 | WS-2226 |
CASIO
| AZ-45F | BF‑80 | BF‑100 | CV‑700 | ||||||
| D-20A | D-20D/M | D-40D | D‑100 W/L/LA | ||||||
| D-120 L/W/T/LA/TE | DF-10L | DF-20L | DF-120TE | ||||||
| DJ-120 | DN‑10 | DN‑20 | DN‑40 | ||||||
| DS‑1 B/L | DS‑2 B/L | DS‑3/L | DS‑8 E | ||||||
| DS‑10E/L/G | DS‑20 E/L/G | DS‑120 | FC‑100 | ||||||
| FN‑10 | FN‑20 | FX‑8 | FX‑10 F | ||||||
| FX‑39 | FX‑50 F | FX-55 | FX‑61 F | ||||||
| FX‑68 /B | FX‑78 | FX‑82/B/C/D/L/LB/SUPER/SX/W | FX‑85 /M/N/V | ||||||
| FX‑100/A/B/C/V/D | FX‑115 /M/N/V/D | FX‑120 | FX‑135 | ||||||
| FX‑140 | FX‑210 | FX‑350/A/C/D/H/HA/W | FX‑451 M | ||||||
| FX-500 /A | FX‑550 /S | FX‑570 A-/C‑/V/D/S | FX-911S/SA | ||||||
| FX‑991/M/N/V/D/H/S | FX‑992 V/VB/S | FX‑3400 P | FX‑3600 P/V/A/PV | ||||||
| FX-3650P | FX‑3800 P | FX-3900PV | FX-3950P | ||||||
| HL‑100 L | HL‑122/L | HL‑812 /E/L | HL-820 A/LU/D | ||||||
| HS-4A | HS‑8 G/L/LU/D | HS‑9 | HS‑88 | ||||||
| HS‑90 | J-10 A/D | J‑20 | J‑30 C | ||||||
| J‑100W/L/LA | J‑120 L/W/T | JE‑2 | JE‑3 | ||||||
| JF-100/TE | JF-120TE | JL‑210 | JN‑10 | ||||||
| JN‑20 | JN‑40 | JS‑8 C | JS‑10 /C/M/L/LA | ||||||
| JS‑20/C/M/L/LA | JS‑25 | JS-40 L/LA | JS‑110 | ||||||
| JS‑120 | JS‑140 | LC-401A | LC‑403 C/E/L/LU/LB | ||||||
| LC-700 | LC-710 | LC‑787 G/GU | LC‑797 G/GU | ||||||
| LC‑798 G | LC‑1000 /L | LC‑1210 | MC‑40 S | ||||||
| MC‑801 S | MJ‑20 | MJ-120 | MS-5A | ||||||
| MS-6 | MS‑7/LA | MS‑8 W/A | MS‑9 | ||||||
| MS-10 W/L | MS-20W/TE | MS‑70 L | MS‑100 A/TE/V | ||||||
| MS‑120 A/TE/V | MS‑140 A | MS‑170 L/LA | MS180 | ||||||
| MS‑270 L/LA | MS-470 L | NS‑3 | NS-10L | ||||||
| NS-20L | RC‑770 | S‑1 | S‑2 | ||||||
| S‑20 L | SJ‑20 | SL‑80 E | SL‑100 A/B | ||||||
| SL‑110 A/B | SL‑120 A/B | SL-200 | SL‑210 | ||||||
| SL‑220 | SL‑240/L | SL‑300H/J/L/LH/LU/LB | SL‑310 M | ||||||
| SL‑330 | SL‑350 | SL‑450 | SL‑510 /A | ||||||
| SL‑704 | SL‑720 /L | SL‑760 A/C/LU/LB | SL-787 | ||||||
| SL-790L | SL-797 | SL-805A | SL‑807 /A/L/LU | ||||||
| SL-817 L | SL-850 | SL-910L | SL‑1000 M | ||||||
| SL-1200L | SL‑1510 | SL-1530T | SL‑2000 M | ||||||
| US‑20 | US‑100 | WD-100L | WD-120L | ||||||
| WJ‑10 | WJ‑20 | WJ-100L | WJ120L |
CITIZEN
| CT-500 | CT‑600 | ELS-301 | ELS-302 | ||||||
| ELS-501 | F‑908 /N | F‑920 | F-940 N | ||||||
| F‑950 | FT‑200 | LC‑505 | LC‑508 N | ||||||
| LC‑510 N | LC‑516 N | LC‑531 | LC-5001 | ||||||
| LH-700 | LH-830 | SB‑741 P | SDC‑810 | ||||||
| SDC‑814 | SDC‑826 | SDC‑830 | SDC‑833 | ||||||
| SDC‑834 | SDC-836 | SDC‑839 | SDC-848 | ||||||
| SDC‑850 | SDC‑865 | SDC-868 | SDC‑875 | ||||||
| SDC-878 | SDC‑880 | SDC-888 | SDC-8001 | ||||||
| SDC-8150 | SDC-8360 | SDC-8401 | SDC-8460 | ||||||
| SDC-8480 | SDC-8780/L | SDC-8890 | SLD‑702 | ||||||
| SLD‑705 B | SLD‑707 | SLD-708 | SLD‑711 /N | ||||||
| SLD‑712 /N | SLD‑720 | SLD‑722 | SLD‑723 | ||||||
| SLD‑725 | SLD‑732 | SLD‑735 | SLD-737 | ||||||
| SLD‑740 | SLD-742 | SLD‑750 | SLD-760 | ||||||
| SLD-767 | SLD‑781 | SLD-7001 | SLD-7401 | ||||||
| SR‑30 | SR‑35 | SR‑70 | SR-260 | ||||||
| SRP‑40 | SRP‑45 | SRP‑60 | SRP‑65 | ||||||
| SRP‑75 | SRP-80 | SRP-285II |
HEWLETT‑PACKARD
| HP-6S | HP-6S Solar | HP-9S | HP‑10 B/BII | ||||||
| HP‑11 C | HP‑12 C | HP‑15 C | HP‑16 C | ||||||
| HP‑20 S | HP‑21 S | HP-30S |
KARCE
| KC-107 | KC-117 | KC-119 | KC121 | ||||||
| KC127 | KC-153 | KC159 |
SHARP
| EL-231C/L | EL-233G | EL-240C | EL-310A | ||||||
| EL-326L/S | EL-330A | EL331A | EL-334H/A | ||||||
| EL-337M | EL338A | EL-344G | EL-354L | ||||||
| EL-373 | EL376G | EL386L | EL387L | ||||||
| EL-480G | EL-501V | EL-506A/G/R/V | EL‑509G/D/S/L/R/V | ||||||
| EL‑520 D/G/L/R/V | EL‑530 A | EL-531 GH/H/P/LH/RH/VH | EL‑546D/G/L | ||||||
| EL-556G/L | EL‑731 | EL-733A | EL-771C | ||||||
| EL-782C | EL-792C | EL-879L | EL-2125 | ||||||
| EL-2128H | EL-2135 | EL‑5020 |
TEXAS INSTRUMENTS
| BA-III | BA-SOLAR | BA-II/PLUS | BA-35 | ||||||
| BUSINESS-EDGE | FINANCIAL-INVESTMENT-ANALYST | MATH EXPL0RER | TI-COLLEGIATE | ||||||
| TI-25X SOLAR | TI-30 /Xa/Xa Solar/XIIB | TI-31 | TI-32 | ||||||
| TI-34 /II | TI-35 /X | TI‑36 /X Solar | TI‑60 | ||||||
| TI‑65 |
TRULY
| 101 /A | 102 | 103 | 105 | ||||||
| 106 | 107 | P-127 | SC-106A | ||||||
| SC-107B/C/F | SC-108 | SC-109 /X | SC-110 /X | ||||||
| SC-111 /X | SC-118 /A/B | SC-128 |
[End of calculator list]
