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 S333
Advanced Mathematical Methods
Welcome to MATH S333 Advanced Mathematical Methods. We hope that you will find studying it enjoyable and rewarding.
This Course Guide contains information about the content and components of MATH S333 Advanced Mathematical Methods that you should be aware of before starting to study the course. Like most Hong Kong Metropolitan University courses, MATH S333 combines the study of texts (for this course, 'blocks' containing 'units') with some other activities.
The course provides an introduction to the subject of fluid mechanics, and teaches the methods required to solve simple flow problems. The course extends the theory of ordinary and partial differential equations and of vector calculus begun in the prerequisite course (MATH S221 and MATH S222). The course is based around 7 units within two blocks.
If you are to study MATH S333 successfully, then you will need to have succeeded in studying the prerequisite course MATH S221 and MATH S222, or to have gained similar experience from another source.
A typical fortnight's work will consist mainly of reading a course unit and working through the exercises that it contains. But also you may be expected to listen to an audio activity or to study using a DVD at your computer, either to watch sections of video material or to undertake interactive exercises. These other activities reinforce and enhance the subject matter of the units.
Each unit has continuous assessment associated with it. There are 2 assignments. The course ends with a three-hour examination.
4.1 Course units
There are 7 course units. Each unit is divided typically into five sections. A typical section might be studied in a single session (in an evening, for example). Each unit begins with a Study guide, which indicates what you will need to recall from the prerequisite course or from previous units to study the current one, which sections may be most or least time- consuming, when you will need to listen to audio, and how best to organise your study of the unit. Towards the end of the unit you will find a short section headed Outcomes, which consists of a checklist of the things that you should be able to do as a result of having studied the unit. This will help you to ensure that you have mastered the contents of one unit before moving on to the next.
Examples and Exercises
The course units contain various types of question for you to work through as part of your study.
First, there are Examples, which show you how to carry out some technique or method. The solution to an example is given in the text immediately below it; your task is to read and to follow the working, so as to learn how to apply that technique for yourself. (The end of each solution is marked with a square.)
Next, Exercises are designed to give you practice in what the preceding text teaches. You should attempt to solve these by yourself, consulting the solutions (which are given at the back of the unit) only in order to check that your own answer is correct. If you are stuck, then look at the solution as a last resort, but look at just enough of it to see how to proceed, before returning to complete the solution of the problem for yourself. It cannot be emphasised too strongly that doing exercises in this way is an essential part of studying mathematics; nobody learns much mathematics just by reading texts.
You should try each exercise within a section as you come to it. At the end of most sections you will find additional groups of exercises called End-of-section exercises. These provide extra practice if you need it, and may be a little more demanding than the majority of the exercises within the sections. You may regard these end-of-section exercises as optional, but it is recommended that you do as many of them as you can find the time for.
Audio sessions
Some units feature an audio session, which entails listening to tracks from a CD, accessed either on your computer or on a separate audio player, while working through 'audio frames' provided within the unit text. The audio includes instructions for particular exercises to be undertaken while you are listening. Audio sessions are flagged within the unit by the icon shown on the right.
4.2 Exercise Booklet
Two additional Exercise Booklets are provided with the course, covering Block 1 and Block 2. These may be obtained from the course website (see Section 5). No hard copy is provided.
The Exercise Booklets are entirely optional, but provide further practice if you wish to undertake it. You might, for example, wish to tackle these exercises in the consolidation weeks indicated in the Study Calendar. Alternatively, they could be used for revision purposes at the end of the course
4.3 MATH S333 Handbook
This is designed as a work of reference, and provides a convenient source of basic definitions and formulas for use throughout the course. In addition, you will be allowed to take it with you into the examination room.
The Handbook has two main components: a collection of useful formulas and definitions, many of which you will have come across already in prerequisite courses, and summaries of the main concepts, definitions and techniques in each of the course units. Two pages at the back of the Handbook summarise particular formulas from the course which need to be called upon regularly, for rapid reference.
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.
4.4 Stop Press Notices
The stop presses act as a course newsletter containing useful and often essential information such as: errata and details of tutorial arrangement. 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).
4.5 Academic Timetable
This gives the starting date for each unit, the dates when assignments are due and weekends when tutorials are scheduled.
4.6 Tutorials
Dates for tutorials are 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.
4.7 The Online Learning Environment (OLE)
The Online Learning Environment Guide (http://ole.hkmu.edu.hk/help.html) 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.
4.8 Assessment
The assessment of the course includes 2 Assignments and a TWO-hour final examination. MATH S333 does not have any multiple choice assignments.
The continuous assessment and the final examination contribute 30% and 70% to the course score. Students will be awarded the 5 credits on MATH S333 if they can get at least 40 marks in both the OCAS and the final examination score. Read the Student Handbook for information on the award of course results.
Each study block has a Tutor Marked 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.
4.9 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.
Familiarize yourself with the Online Learning Environment. Then start your work on Unit 2. Unit 1 Properties of a Fluid is not examinable.
(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]
