Mathematical methods

Home Admissions Course Guide Mathematical methods

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 S221

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.]

MST207 and MST204 are no longer offered. You should note that
MST 204 = MATH S204
MST 207 = MATH S207

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)

Please note that all the materials for this course have been uploaded to the OLE for easy access and no physical CDs will be provided.

 

4.1 Course Units

There are 15 study units in the course.

 

Unit 1Getting startedUnit 9Fourier series
Unit 2First-order differential equationsUnit 10Partial differential equations
Unit 3Second-order differential equationsUnit 11Scalar and vector fields
Unit 4Vector algebraUnit 12Vector calculus
Unit 5Matrices and determinantsUnit 13Multiple integrals
Unit 6 Eigenvalues and eigenvectorsUnit 14Laplace Transforms
Unit 7Systems of differential equations Unit 15Numerical methods for differential equations (Reference unit, no assessment involved)
Unit 8Functions of several variables  

 

 

Unit 15This is provided for self-study. It will not be assessed in the continuous assessment and the final examination.  If you have time, you may read it for own interest.

 

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.

 

Unit 1This is designed to revise the prerequisite mathematics for MATH S221 and will be assessed in the first assignment. The Academic Timetable specifies a starting date for Unit 1 but there is no reason why you should not begin studying Unit 1 as soon as you can. You are strongly urged to devote as much time as you can.

 

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
Note

In order to use Mathcad in your home computer, you need an individual license file for installation. HKMU will send you a registration link to register your license' via your HKMU email. [Please check your email for it].
The Mathcad license runs only for one-year period.

  • 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:

 

Adopt from MST 209 Mathcad worksheetsFor MATH S221 Mathcad worksheets
Block 0: MST 209 Unit 0Essential Mathcad tutorial
Block 1: MST 209 Units 1 to 3MATH S221 Units 1 to 3
Block 3: MST 209 Units 9 to 12MATH S221 Units 5 to 8
Block 6: MST 209 Units 21 to 22MATH S221 Units 9 to 10
Block 7: MST 209 Units 25 to 26MATH S221 Units 13 and 15

 

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

 

Note

Mathcad worksheets are available to download on the MATH S221 OLE.

Go to MATH S221 OLE <Course Material/MATHS221 Mathcad Files >

You will need to download the whole Zip file < MATHS221_Mathcad_File.zip > to your home computer, and unzip it to use.

 

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.

 

Note

A Mathcad User's Guide containing a comprehensive description of all the features of Mathcad skills is posted on MATH S221 OLE. You may download it.

Go to MATH S221 OLE <Course Material/Mathcad User's Guide >

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.

NoteYou will not be allowed to bring MATH S221 Formula Handbook to the exam. Another copy of the MATH S221 Formula Handbook will be given to you together with the exam paper.

 

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:

 

TypeNumberRequirementMaximum percentagePart of course covered
Assignment4 (assignments 01, 02, 03, 04)All assignments are required30 %One assignment for each Block
Examination1 70 %All units, except the mathematical modelling exercises
Total marks  100 % 

 

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:

 

Assignment 01
Assignment 02
Assignment 03
Assignment 04
Covers Units 1,2,3 and 4
Covers Units 5, 6 and 7
Covers Units 8, 9 and 10
Covers Unit 11, 12, 13 and 14

 

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.

 

There will not be any questions, which require the use of a computer, in the examination.

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:

Unit 1 : Getting Started

  • Revise some of the prerequisite mathematics which include:
  • Numbers and sequences
  • Trigonometric functions
  • Complex numbers
  • Differentiation and integration

Unit 2: First-order differential equations

  • Direction field
  • Euler's method
  • Separation of variables
  • Integrating factor method
  • Finding analytic and numerical solutions of a system of linear equations

Unit 3: Second-order differential equations

  • Linear constant coefficient second-order differential equation
  • Homogeneous equations
  • Inhomogeneous equations
  • Principle of superposition
  • Boundary-value problems
  • Initial-value problems

Unit 4: Vector algebra

  • Scaling and adding a vector
  • Cartesian form vectors
  • Polar representation of 2-D vectors
  • Right-hand screw rule
  • Dot and cross product
  • Vectors in 2-D and 3-D

Unit 5 : Matrices and determinants

  • Manipulating equations and matrices
  • Scaling and addition of a matrix
  • Matrix multiplication
  • Using Gaussian elimination method
  • Transformations
  • Matrix inverses and determinants
  • Polynomial and least square interpolation
  • Partial pivoting and induced instability
  • Rounding and Ill-conditioning problem

Unit 6: Eigenvalues and Eigenvectors

  • Eigenvectors in the plane
  • Relation of Eigenvalues and Eigenvectors
  • Use basic method finding Eigenvalues
  • Iterative method approximating Eigenvectors
  • Inverse iteration method

Unit 7: Systems of differential equations

  • System of differential equations as models
  • Linear first-order homogeneous and inhomogeneous systems
  • Linear second-order homogeneous systems
  • Application of Eigenvalues/Eigenvectors solution
  • solving simultaneous differential equations
  • Simple harmonic motion
  • Finding particular integrals

Unit 8: Functions of several variables

  • Geometric interpretation
  • First-order partial derivatives
  • Slope in an arbitrary direction
  • Taylor approximations
  • Tangent plane
  • Higher-order partial derivatives
  • Classification of stationary points
  • Maxima, minima and saddle points
  • Applications of the methods

Unit 9: Fourier analysis

  • Period functions: saw-tooth function and a square-wave function
  • Determine of cosine and sine functions
  • Fourier series for odd and even functions
  • Fourier series for any periodic functions
  • Trigonometric integrals

Unit 10: Partial differential equations

  • Linear second-order PDEs
  • Modelling using the wave equation
  • Modelling using the diffusion equation
  • Separation of variables
  • Partial differential equations for heat transfer problems
  • Transverse vibrations of a string

Unit 11: Scalar and vector fields

  • Orthogonal matrices
  • Scalar and vector fields, Contours curves and surfaces
  • Gradient function
  • Gradient function in three dimensions
  • Gradient as a vector operator
  • Gradient function in plane polar coordinates
  • Three-dimensional polar coordinate systems
  • Cylindrical polar coordinates
  • Grad in cylindrical polar coordinates
  • Spherical polar coordinates

Unit 12: Vector calculus

  • Divergence of a vector field
  • Calculating divergence
  • Curl of a vector field, calculating curl
  • Curl and local rotation
  • Scalar line integrals, the length of a curve
  • Linking line integrals, curl and gradient
  • Conservative vector fields

Unit 13: Multiple integrals

  • Scalar line integrals
  • Conservative vector fields
  • Area integrals over rectangular and non-rectangular
  • Applications of area integrals
  • Integrating surface density functions
  • Changing to plane polar coordinates
  • Volume integral
  • Moment of inertia of rigid bodies
  • Spherical polar coordinates
  • Cylindrical polar coordinates

Unit 14: Laplace Transforms

  • Laplace transform
  • Differential transform
  • Inverse transform

Unit 15: Numerical methods for differential equations (Reference Unit)

  • Taylor's theorem
  • Euler's method
  • Improvement of the Euler's method
  • Runge-Kutta method and Trapezoidal method
  • Ill-conditioning
  • Stability and convergence
  • Determination of step size
  • Solve system of differential equations

(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]

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