Mathematical methods

This Course Guide contains essential information about the content and components of MATH S221 that you will need to know before you start to study the course.

MATH S221 Mathematical Methods is about applied mathematics featuring on the mathematical methods and techniques. You will find the course contents of great use in the higher level courses in computing, engineering and technology programmes, and in many scientific professions.

The course teaches the commonly used mathematical methods that are required in most science and engineering, financial and quantitative disciplines, but also covers many examples involving skills in the application of mathematical techniques. About 20% of the material involves the use of computer algebra software Mathcad that can be used to solve a variety of complicated mathematical and numerical problems.

This course includes 15 units, starting with a preparatory unit to review the foundation mathematics, then two units on first-order and second-order differential equations, and one unit on vector algebra, going on to matrices and determinants; Eigenvalues and Eigenvectors; simultaneous and non-linear differential equations.  There are 3 units on mathematical methods for three-dimensional problems: one on partial differentiation, one on vector calculus and one on multiple integrals. Two units are devoted to Fourier transforms and Laplace transforms. One unit is concerned with numerical methods for differential equations. Most of the numerical mathematical methods have practical computing activities associated with it. These activities will be carried out using the softwareMathcad. No programming skills are required.

[NOTE: MATH S221, MST 204 AND MST 207 FORM AN EXCLUDED COMBINATION.]

At the completion of this course, students will be able to:

1. Explain the methods of linear and vector algebra, numerical analysis, ordinary differential equations, vector calculus, multiple-variable functions and  the Fourier series.
2. Describe the basic principles of applied mathematics used in engineering and technology disciplines;
3. Explain an understanding of the use of mathematical methods to solve certain types of real-life applications; as well as graph, analyze and interpret results.
4. Construct appropriate mathematical models, and solve the resulting equations by appropriate methods.
5. Use a computer algebra package to help in solving complex equations, as well as graph and interpret the results.

To study MATH S221 successfully, you should have studied the foundation mathematics courses (or have otherwise gained the similar knowledge) MATH S111/MATH S121 or MATH S121/MATH S122. These foundation mathematics courses cover all essential mathematical topics that are required for your study of MATH S221.

If you have not studied either one of the foundation mathematics courses, and you have left school for many years, you are advised to study the Preparatory Unit well before you begin this course. This preparatory material gives you a revision of some fundamental mathematics essential to your study of MATH S221. Refer to Subsection 5.1 of this guide for more details of this item.

MATH S221 combines the study of course units with a number of activities.

You will see in the Academic Timetable that two weeks are assigned for the reading of a course unit and working through some computing exercises on your computer. You will also need to watch a video or a multimedia activity, which are designed to illustrate the mathematical concepts.

The course material consists of the following:

• 15 study units;
• Preparatory Unit;
• Three Exercise Booklets;
• Diagnostic Quiz;
• Course Guide;
• One Formula Booklet
• Computing Worksheets (It is available for downloading on MATH 221 OLE)
• Course Software (Mathcad)

4.1 Course Units

There are 15 study units in the course.

The outlines of each unit are summarized in Appendix A of this Course Guide.

The content of each unit is typically divided into four to five sections, each of which is de­signed to be studied in a single session (for example, study a section in an evening). Each unit begins with a study guide, which tells you what you will need to recall from previous units, when you will need to use your computer or watch a video, and how best to organize your study of the unit. Towards the end of the unit, you will find a short section headed 'Outcomes', which consists of a list of learning outcomes for studying the unit; this will help you to ensure that you have mastered the contents of one unit before moving on to the next unit.

4.2 Examples and exercises in study unit

Each study unit contains various types of exercises for you to work through as part of your study. These questions are divided into four types:

• Examplesshow you how to carry out some techniques or methods. The solution to an example is given in the text immediately below it; your task is to read it and follow it, to learn how to apply that technique for yourself.
• Exercisesare designed to give you practice in what the preceding text teaches. You should attempt to solve by yourself, consulting the solutions (which are given at the end of the unit) to check your own answer. 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, and then go back to solving the problem.
  We cannot emphasize too strongly that doing exercises in this way is an essential part of studying mathematics; nobody learns mathematics just by reading texts and watching videos. You should try as many of exercises within each section as you can. If you find that you do not have enough time to work through all exercises, you are advised to attempt the most important exercises that have been signified with an asterisk * in the unit.
• End-of-section Exercises, 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 sections. You may regard these end-of-section exercises as optional; but at the risk of being repetitious, we recommend that you do as many of them as you can find the time for doing them.
• Computer Activities are provided for you to use the computer algebra package to consolidate your work in this unit.

4.3 Course software and Computer activities

This course consists of computer software Mathcad and computer activities.

• Software: Mathcad

• Computer activities

There are some computer activities for you to do throughout the course, each of which is signposted by an icon in the margin of the associated course unit. The computer activities require you to use the preset Mathcad worksheets. No programming skills are required. You can only run the computer activities after installed the Mathcad software.

MATH S221 is half of the course MST209 from OUUK. MATH S221 only adopts the following Mathcad activities from MST209 for the respective units in MATH S221:

When working through the computer activities, you will come across references to MST 209; these can all be safely ignored in your study.

4.4 Mathcad User's Guide

Mathcad techniques and a glossary of useful tips for making best use of the Mathcad are also included in this booklet.

5.1 Preparatory Unit

The Preparatory Unit is sent to all students enrolled for MATH S221 and MATH S222 (Note that MATH S221 and MATH S222 share the same Preparatory Unit.)

The aim of this unit is intended for students who have not studied M112/M122, or an equivalent foundation mathematics course. It contains an account of the important topics that will be needed for MATH S221.

• The first section covers differentiation and some of its applications.
• The second section covers integration and the associated techniques.
• The third section introduces the basic concept of Complex Number.

The study of this preparatory unit is optional and it will not be assessed in both assignment and examination. If you need to learn the basic calculus, you should do it well before studying Unit 1.

5.2 Formula Handbook and its Regulations

The Formula Handbook is for reference. It provides a convenient source of basic definitions and formulas for use throughout the year of your study.

5.3 MATH S221 Exercise Booklets

This course will provide you with three Exercise Booklets. These booklets contain some additional exercises on some units. These will provide extra practice throughout the course, and may be useful for revision before the examination.

5.4 Academic Timetable

The Academic Timetable, which provides you with a course timetable, is available on the Online Learning Environment (OLE). The organization of the calendar is meant as an indication on how you should arrange your study of the course and you must aim to submit your assignments by the indicated cut-off dates.

5.5 Assignment Booklets

The course contains 4 assignments and each contains 4 questions. They are all required by the course. The assignment booklets will be posted to OLE later.

5.6 Stop Presses

Throughout the presentation, I will send you Stop Presses, which contain important up-to-date information about various aspects of the course. You should read each of these as soon as you receive it.

5.7 Errata

The Errata contains corrections of the study material and assignment questions. You should check and amend your text immediately as soon as you receive it.

6.1 Starting work

If you have not studied MATH S111/MATH S121 or MATH S112/MATH S122, or have not covered the relevant topics from it in another course, your first task is to study the Bridging Material. It is essential that you start working on this at the earliest possible opportunity, because no time is allocated for it in the Academic Timetable.

The study of the Computing Booklet and the introductory com­puter activities are assigned for the first week of the Academic Timetable. You should aim to work through this before you begin your study of Unit 1. As mentioned previously, the Mathcad tutorials are provided for you inside the computing package. You should work through them if you do not have any experience in using Mathcad software.

Whatever your situation, there is no need to wait for the starting date given in the Academic Timetable before starting work on the course, which begins with Unit 1. All preparation and revision of relevant topics from prerequisite courses will be invaluable, and you are strongly advised to spend as much time as you need on Unit 1, which revises many of the topics from the prerequisite courses that are important to MATH S221.

6.2 Tutorials and Surgeries

There are about 10 tutorials, and 8 surgeries provided for this course. All tutorials and surgeries will be a 2-hour session and will be conducted by the tutor.

You should refer to the Stop Press and the Academic Timetable about tutorial and surgeries arrangements. Although none of the tutorial and surgeries is compulsory, you are strongly advised to attend.

6.3 Keeping up to schedule

It is important to keep as close to the schedule laid down in the Academic Timetable as you can (of course there is no harm in being ahead of it, but few students are in the fortunate position of being able to keep that up for any length of time). The main reason for keeping up to schedule is that you will lose marks if you miss any question of assignments. For many of the assignments, the cut-off date is very soon after the end of the study week for the last of the relevant units. We recommend that you finish the assignment questions for each unit as soon as you finish the unit, otherwise you will have a lot of work to do in a few days before the cut-off date.

If you have not done all the work in time for an assignment, you should still submit as much of the assignment as you can do, and start the new unit on time. As a matter of survival, it is more important to start each unit on time than to do every assignment question.

If it becomes apparent during your study that you will not have enough time to do all the work in it, you will have to make some decisions about which parts of which units to leave out. Such omissions will, in general, cost you to lose marks in your assignment but this is better than to get hopelessly behind and drop out.

You should refer to the HKMU Student Handbook for the regulations relating to assignments; in particular, you should ensure that you understand the procedures for the late submission of assignments.

This course comprises four assignments and a three-hour examination. The details of each are described below:

The passing minimum threshold is 40 marks for both assignment and examination.

7.1 Assignment

All 4 assignments are required for the final assessment score. Each assignment is worth 7.5% of the overall assessment score. In general, each assignment contains 3-4 questions and is marked out of 100 marks.  The contents of each assignment are shown below:

Your answers to each assignment should be sent directly to your tutor before the official cut-off date for marking.   (This course contains no project assignment.)

7.2 Final examinations

There is a 3-hour examination at the end of the course. To help you to prepare the examination, two specimen examination papers are posted on the MATH S221 OLE for reference.

7.3 Assessment in computer activities

About 20% of the overall marks available for each assignment will involve the use of the computer, though the amount of computer work involved will vary widely with each assignment. A part of a question in which the computer has to be used will be indicated in the Assignment Booklet. You may freely use any of the Mathcad worksheets provided with the course material to answer the computing parts of assignment questions: in fact, you will usually be expected to use one (or more) of the worksheets given to answer the related question.

For computing-related questions, you are required to include some computer printout for marking. So please send the absolute minimum of required computer printout to your tutor. Your tutor should never have to search through the printout for the information he/she needs to be able to mark your solution, so please circle or underline the equation you entered (for example, use a highlighter to point it out), and annotate the printout results.

To study the course, you are required to a have

• a computer, and
• a calculator.

8.1 Calculator

A calculator will be required to answer certain questions in the examination, as well as being useful for numerical work during the year. If you have studied one of the recommended prerequisite foundation courses, the calculator you used there should be suitable for MATH S221. If you decide to buy a new calculator, make sure that it is an approved model by the Hong Kong Examination Authority. (An approved calculator list is attached in MATH S221 OLE.)

MATH S221 students are provided with online support called the Online Learning Environment (OLE).

The OLE is a web-based learning system (Internet system) developed by the HKMU and is an interactive online learning environment used for communication among students, tutors and the Course Coordinator. This system can enhance students' learning experience through its interactive tools. To help you to use the OLE system, refer to the Online Learning Environment User Guide (http://ole.hkmu.edu.hk/help.html).

When entering the OLE system you will see the following topics in the system:

News Course News

Schedules Course Schedules Calendar

Interactive Tools Discussion Board

Course Materials Course Guide MATH S221 Study Units Specimen Exam Paper Errata Stop Press Approved Exam Calculator Formula Handbook

Assignments Multimedia Demonstrations Instructions Instructions(Tutor) Assignment File Submission & Extension Assignment Solution

This presentation, MATH S221 OLE includes “Assignment Submission and Extension”. This component allows you to:

• Submit your assignments
• Check the status of your assignment scores;
• View the assignment files;
• Apply for a late submission extension of assignment.

Other details related to the use of OLE will be given in the later Stop Presses.

(i) From your tutor

Your tutor is the contact person to help you in your study. Your tutor will mark your assignment and answer all your queries. When your assignment is returned, you should go through the assignment comments marked on the assignment script and take note of the comments written by your tutor to avoid similar errors in later assignments and in the examination. Make every effort to attend your tutorials and surgeries; there you will have the opportunity to talk to your tutor directly and to discuss with other students.

(ii) From your fellow students

One of the best ways of learning is by discussing your study with other fellow students. Unfortunately, you will see them only at the infrequent tutorials during the year. You should collect the address and telephone number of other students in your class; this way, you can keep in touch with them all the time. You may form a self-help group among students to meet regularly; this is a good way of getting people together to discuss common study difficulties, especially in the assignment questions.

(iii) From the Course Coordinator: Dr. Anita Wong

If there is any academic query which your tutor cannot settle for you, then your tutor will probably advise you to contact the Course Coordinator.
The Course Coordinator of this course is Dr. Tony Chan, in Room A0921 of the HKMU Ho Man Tin campus.  Her office telephone number is 2768 6867; email: tmtchan@hkmu.edu.hk.

(iv) From the OLE

The OLE provides you with an interactive learning environment for communication among students, tutors and the Course Coordinator. When you find problems that you would like to discuss with other students, you are welcome to post your problem on the OLE Discussion Board. Details of how to use the OLE component are in the OLE User Guide.

The content of each of the units is summarized in the following table:

(In addition to the following models, calculators bearing the 'HKEA/HKEAA Approved' labels are also allowed.)

A.MAX

ATABA/AURORA

BISTEC

BLT

CANON

CASIO

CITIZEN

HEWLETT‑PACKARD

KARCE

SHARP

TEXAS INSTRUMENTS

TRULY

 [End of calculator list]