MAS182 S2 2019 Unit Info PDF

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MAS182 Applied Mathematics

Unit Information Semester 2, 2019

This information should be read in conjunction with the online learning materials which can be found on your MyUnits page.

Unit Coordinator Mrs Ha Nguyen Office: Science and Computing SC 3.024 (245.3.024) Tel: (08) 9360 2374 Email: [email protected] Mathematics & Statistics College of Science, Health, Engineering & Education

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MAS182 Unit Information

Previous Unit Coordinators 1986-87 Assoc Prof Peter Kloeden 1988 Dr J Carminati with Dr Ian Wright 1989 Assoc Prof Peter Kloeden 1990 Dr J Carminati with Dr Ian Wright 1991 Assoc Prof Peter Kloeden 1992 Mr Robert Dunne (First Semester) 1993 Dr Chris Reason (First Semester) 1994 Dr Chris Reason (First Semester) 1995 Dr Ken Harrison (First Semester) 1996 Prof Walter Bloom (First Semester) 1997 Mrs Jen Bradley (First Semester) 1998 Prof Walter Bloom (First Semester) 1999 Dr Graeme Hocking (First Semester) 2000 Dr Duncan Farrow (First Semester) 2001 Dr Duncan Farrow (First Semester) 2002 Dr Duncan Farrow (First Semester) 2003 Dr Duncan Farrow (First Semester) MAS182: Applied Mathematics 2004 Dr Duncan Farrow (First Semester) 2005 Dr Duncan Farrow (First Semester) 2006 Dr Duncan Farrow (First Semester) 2007 Dr Duncan Farrow (First Semester) 2008 A/Prof Ken Harrison (First Semester) 2009 Dr Duncan Farrow (First Semester) 2010 Dr Duncan Farrow (First Semester) 2011 Dr Duncan Farrow (First Semester) 2012 Dr Mark Lukas (First Semester) 2013 Dr Mark Lukas (First Semester) 2014 Mrs Ha Nguyen (First Semester) 2015 Dr Mark Lukas (First Semester) 2016 Dr Mark Lukas, Mrs Ha Nguyen Mrs Ha Nguyen 2017 Mrs Ha Nguyen (First Semester) 2018 Mrs Ha Nguyen (First Semester) 2019 Mrs Ha Nguyen (First Semester)

Dr Chris Reason Dr Helen Middleton Dr Mark Short Prof Walter Bloom Dr Duncan Farrow Prof Walter Bloom Dr Graeme Hocking Dr Duncan Farrow Prof Walter Bloom Prof Walter Bloom Prof Walter Bloom Dr Duncan Farrow

(Second Semester) (Second Semester) (Second Semester) (Second Semester) (Second Semester) (Second Semester) (Second Semester) (Second Semester) (Second Semester) (Second Semester) (Second Semester) (Second Semester)

Dr Duncan Farrow Dr Duncan Farrow Prof Walter Bloom A/Prof Ken Harrison Prof Walter Bloom Prof Walter Bloom Prof Walter Bloom Mrs Ha Nguyen Mrs Ha Nguyen Mrs Ha Nguyen Prof Graeme Hocking Mrs Ha Nguyen

(Second Semester) (Second Semester) (Second Semester) (Second Semester) (Second Semester) (Second Semester) (Second Semester) (Second Semester) (Second Semester) (Second Semester) (Second Semester) (Second Semester) (First Semester) (Second Semester) (Second Semester) (Second Semester) (Second Semester)

Mrs Ha Nguyen Mrs Ha Nguyen Mrs Ha Nguyen

© Published by Murdoch University, Perth, Western Australia, July 2019.

This publication is copyright. Except as permitted by the Copyright Act no part of it may in any form or by any electronic, mechanical, photocopying, recording or any other means be reproduced, stored in a retrieval system or be broadcast or transmitted without the prior written permission of the publisher.

MAS182 Unit Information

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Unit Coordinator and contacts

Unit Coordinator

Mrs Ha Nguyen Mathematics & Statistics College of Science, Health, Engineering & Education Tel: (08) 9360 2374 Office: Science and Computing Building, 245.3.024 Email*: [email protected] (*Note: please include the unit code MAS182 and your name or student number in the subject line so that your email can be easily identified.)

As the Unit Coordinator and Lecturer, I would like to welcome you to the study of Applied Mathematics. I hope you will find the unit both interesting and useful. Please do not hesitate to contact me if you have any difficulties with the unit, or if you would just like to talk over the work to receive some encouragement to press on!

Tutor

Internal students will meet their tutor during the first week of semester, in the tutorial. External students will be informed of their assigned tutor in week 1. During the semester your tutor will mark your assignments and assist you with your study. Do not hesitate to contact your tutor if you have any questions.

Administration

If you have any queries about your enrolment in this unit, or if you need information about the University in general, please contact the Student Centre on 9360 6000 or submit your query through http://askmurdoch.custhelp.com/

Technical help

For technical difficulties with accessing the Online Unit, contact the IT Service Desk: [email protected] or phone 9360 2000 For other difficulties with the online materials, contact the Unit Coordinator.

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Unit overview

Introduction

The ideas and techniques considered in this unit are basic to many applications of mathematics in engineering and in the biological, physical and social sciences. Mastery of these ideas and techniques at this stage will greatly help later on with an understanding of these disciplines where they are used. They also form a background prerequisite for the units MAS161 Calculus and Matrix Algebra and MAS221 Mathematical Modelling.

Prerequisites

MAS164 Fundamentals of Mathematics OR at least a pass in the Year 11 course Introduction to Calculus together with a final scaled score of 55% or more in TEE Applicable Mathematics OR a final scaled score of 55% or higher in ATAR

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MAS182 Unit Information

Mathematics Methods or WACE Mathematics (3C/3D). Students who have not studied mathematics for some time or who have a weak background in mathematics should complete MAS164 Fundamentals of Mathematics before enrolling in this unit. If you are in any doubt about your qualifications or background preparation, you should get in touch with the Unit Coordinator as soon as possible.

Aim

Provide an introduction to the techniques and applications of calculus and differential equations.

Learning outcomes On successful completion of this unit you should be able to: 

Use the basic ideas, rules and techniques of differentiation and integration.



Analyse problems and use a range of calculus techniques to solve them.



Apply differential equations to mathematical models of physical and biological phenomena.



Use simple differential equations to describe growth and decay and to solve problems.

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Use trigonometric functions in various applications.

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Express complex numbers in Cartesian and polar form.

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Present coherent written solutions to various problems related to the material in the unit.

Graduate Attributes This unit will contribute to the development of the following Graduate Attributes (see http://our.murdoch.edu.au/Educational-Development/Preparing-to-teach/Graduate-attributes/): 

Communication: The ability to communicate effectively and appropriately in a range of contexts using communication, literacy, numeracy and information technology skills.



Critical and Creative Thinking: The ability to collect, analyse and evaluate information and ideas and solve problems by thinking clearly, critically and creatively.

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Independent & Lifelong Learning: A capacity to be a self-directed learner and thinker and to study and work independently.



Interdisciplinarity: A capacity to acquire knowledge and understanding of fields of study beyond a single discipline.

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In-depth Knowledge of a Field of Study: A comprehensive and in-depth knowledge of a field of study and defined professional skills where appropriate.

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Resources

Textbook

Lial, Margaret L., Greenwell, Raymond N. and Ritchey, Nathan P.: Calculus with Applications, 11th edition, Pearson (2017) (Earlier editions can be used) The scope and level of the unit are closely related to the textbook. The textbook is available by personal or mail purchase from the Murdoch University Bookshop.

Learning Guide (Unit Notes) This outlines the content of the unit and provides a guide to using the textbook. There are also more detailed notes on material not covered by the textbook along with a list of practice problems and tutorial exercises.

References

There are a number of books available in the Murdoch University Library that could be useful when studying this unit. Some of these are listed below. Swokowski, E.: Calculus with Analytic Geometry, 4th edn, Prindle, Weber & Schmidt (1988). (515.15 S979) Arya, Jagdish C. & Lardner, R.: Mathematics for the Biological Sciences, Prentice-Hall (1979). (510.24574) Edwards, C. & Perrey, D.: Calculus & Analytic Geometry, Prentice-Hall (1982) (515.15 E26) Lang, Serge: A First Course in Calculus, 4th edn, Addison-Wesley (1978).

(515 L269)

Salas, S. & Hille, E.: Calculus: One and several variables, 4th edn, Wiley (1982). (515 S161 3)

Online Resources The MAS182 Online Unit and the LCS (Lecture Capture System) Echo360 lecture recordings can be accessed from your MyUnits page. The recordings will be available within a few hours of each lecture. Copies of the lecture notes will be posted on LMS at the end of each week or chapter.

Past Exam Papers

Some sample tests and past exam papers (with solutions) will be posted on LMS to give you an idea of the standard required and for you to try as practice during your revision. In addition, more exam papers are available online at http://wwwlib.murdoch.edu.au/exams/. However, note that the contents and the types of questions may change from year to year.

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Unit organization

Structure

The structure of the unit follows the textbook closely. There are some topics not covered in the textbook, the notes for which are included in the Learning Guide (Unit Notes).

Lectures per section

The approximate number of lectures devoted to each section of the unit is

given below. Use this information to work out a self-paced study plan so that you can submit assignments regularly. Include in your plan time for revision.

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MAS182 Unit Information

Chapter

No. of lectures

R 1

Algebra Reference Linear Functions

0.5 0.5

2 3

Nonlinear Functions The Derivative

1 2

4 5

Calculating the Derivative Graphs and the Derivative

2 2

6 6a*

Applications of the Derivative Exponential and Logarithmic Functions

5 2

7 8

Integration Further Techniques and Applications of Integration

5 2

10 13

Differential Equations The Trigonometric Functions

5 4

14

Complex Numbers

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* Chapter 6a above actually consists of parts from Chapters 2 and 4. ** Chapter 14 is NOT covered in the textbook. See the Unit Notes/Learning Guide for more information. *** Chapter R and Chapter 1 cover revision topics – you should work through these chapters to refresh your memory. Some practice problems are listed for each topic. The lists of practice problems have two functions. Firstly, working the problems will facilitate your learning, and secondly, the listing of problems is another way of specifying the kinds of skills and knowledge you are to gain from this unit. You should work through all of the listed practice problems, as a bare minimum. However, it is recommended that you also choose others from the textbook. The best way to learn mathematics is to do mathematics.

Learning activities Internal students: This unit has three different lectures per week (see the timetable on the web) and you should attend as many of these as possible. If you miss a lecture, you should read the appropriate section in the Learning Guide and textbook, and/or catch up via the lecture recordings before the next lecture. Each internal student will also have a 50 minute tutorial each week starting in Week 1. It is expected that students will attend all or almost all twelve of their tutorials in the semester, and tutorial participation is a component of the assessment (see under Assessment). Students need to enrol online at one of the available tutorial times.

External students: There is no on-campus attendance requirement for external students. However, you are welcome to attend as many of the on-campus lectures as you wish. Recordings of the lectures will be available online. External students should work steadily through the Learning Guide and textbook and do the practice exercises to help their understanding. If you have any questions about the material after making an attempt to understand it, you should contact your external tutor as soon as possible. A good way to do this is to email your tutor, and include in your email your phone number and the times you would be

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available to talk on the phone. If it is a straightforward question, your tutor may answer your question by email.

Advice on how to study this unit Some of you will have already developed effective studying habits. What works well for one person may not for another, and so it is important that you find a method that suits you. However, the system described below seems to work well for most people.

Work in sections

Tackle the work in sections, trying to master each one before going on to the next. In each section read the unit material, making sure that you are familiar with the definitions, techniques and results included. To help reinforce these ideas, follow through the worked examples and read the relevant sections of the textbook or any reference book that you are using. You might try to relate the section to the unit objectives (see Section 2 above) and to your previous knowledge.

Try writing a summary If you want to test whether or not you have mastered a section, try writing out a summary of its contents without looking at the unit material. If you succeed (and subsequent comparison with the unit material shows that you got it correct) then you certainly know the work. If you do not quite manage all of it, at least you will know what to revise.

Try the problems as you meet them As you work through the unit material, you should attempt some or all of the exercises that you meet. Sometimes, if you cannot do one of the problems, it pays to lay it aside and come back to it another day.

Contact your tutor You should not spend an unreasonably long time on one problem. Go on to something else and get in touch with your tutor for some help. Prepare a list of questions you wish to ask. When you telephone your tutor, you should have your Learning Guide, textbook and the list of questions with you, so that you do not waste time (and money) searching for information during your conversation with the tutor.

Complete the following information yourself: My tutor: ......................................................................................................................................................... Phone: .................................................................................

Internet access

If you have problems with connection to the University, visit the IT service desk in the library or telephone (08) 9360 2000, or email [email protected]

Change of enrolment Students are expected to change their enrolment over the web through MyInfo, accessible from http://myinfo.murdoch.edu.au/. However you should discuss your progress with your tutor before you make any change.

Withdrawals

Withdrawals are recorded on a student’s academic transcript as follows:

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MAS182 Unit Information

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Withdrawal on or before the census date: withdrawal is not formally recorded on the academic record. An administrative record is kept.

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Withdrawal after the census date, but on or before the last date for withdrawal without penalty in the teaching period in which the unit is to be completed: withdrawal is recorded and fees incurred. For Commonwealth-supported students, Student Learning Entitlement is consumed.



Withdrawals after the last date for withdrawal without penalty: fail is recorded and fees incurred.

For important deadlines regarding withdrawals, see http://our.murdoch.edu.au/Student-life/Get-organised/Important-dates-and-events/

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Required coursework and assignment timetable

Workload

Full-time students usually take 12 points per semester and so, with 3 points credit, MAS182 Applied Mathematics represents about one quarter of a full-time load, or about 10 hours per week.

Assignments how many?

There are five assignments. Assignment questions will be posted on the LMS.

approach

You should look ahead at the assignment questions whilst working on the practice problems, but avoid the temptation to work "backwards" from assignment questions to the required reading from the textbook. The practice problems are sequenced to develop each topic from a beginning and work up to the level of the assignment questions, which are similar to the practice problems. Students should bear in mind that it is better to neatly handwrite their assignments rather than to type them, as typing mathematics correctly is time consuming.

how to submit?

Internal students: Assignments should be placed in your tutor’s pigeonhole in the Assignment Box in the Maths & Statistics Foyer (3rd level, North wing, Science & Computing Building). Make sure you attach a completed Assignment Cover Sheet, which is available on top of the Assignment Box, to each assignment.

External students: Submit your assignments online via the Assignments page on LMS. The submission process includes a declaration that what you are submitting is your own work. Each submission must be a single PDF document no more than 10 MB in size. Please use a clear naming convention for your submission files incorporating your name, student number and unit code, e.g. Surname 12345678 MAS182 Assign 1. keep a copy

Be sure to keep a copy of all assignments submitted for assessment.

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Assignment timetable (internal and external students) It is in your interest to work steadily rather than leave the work to the last minute. If you submit work regularly, then you will receive feedback from your tutor at times when it is most useful (and not after you’ve taken the final examination, for example). NOTE: Extensions will be possible only in special cases. Unless you have prior approval from the Unit Coordinator, late assignments will lose half their marks for the first day they are late. This means that an assignment that would otherwise receive 80 marks out of 100 will receive only 40 marks out of 100 if it is submitted up to a day late. If it is submitted more than a day late it will receive 0 marks.

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Assignment

Submission Date

Week

1

4:00 pm, Friday 16 August

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2

4:00 pm, Friday 6 September

6

3

4:00 pm, Friday 27 September

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4

4:00 pm, Monday 14 ...