THE UNIVERSITY OF SYDNEYSemester 2, 2014

Information Sheet for MATH1013 Mathematical Modelling

Web SitesIt is important that you regularly check both the Junior Mathematics web site

http://www.maths.usyd.edu.au/u/UG/JM/

and the MATH1013 web site

http://www.maths.usyd.edu.au/u/UG/JM/MATH1013

LecturesThere are 2 different lecture streams. You should attend one stream (that is, two lectures per week), asshown on your personal timetable.

Times Location Lecturer Consultations

8 am Thu & Fri Wallace Leon Poladian THU at 10:00 in Carslaw 713

11 am Thu Merewether LT1 Collin Zheng WED at 13:00 in Carslaw 49511 am Fri New Law LT 101

Lectures run for 13 weeks. The first lecture will be on Thursday 31 July. The last lecture will be onFriday 31 October.

Duty TutorsDuty tutors will also be available from Week 2, from 1 pm to 2 pm on Tuesdays and Thursdays, inCarslaw 830 (level 8 of the Carslaw Building).

TutorialsTutorials (one per week) start in Week 2. You should attend the tutorial given on your personal timetable.Attendance at tutorials will be recorded. Your attendance will not be recorded unless you attend thetutorial in which you are enrolled.

The tutorial sheets for a given week will be available on the MATH1013 webpage. You should take thecurrent weeks sheet to your tutorial. The sheet is available for printing or viewing (for example,using a laptop, if you take one to class) using a link from the webpage.Solutions to tutorial exercises for week n will usually be posted on the web by the afternoon of the Fridayof week n.

Lecture notesL. Poladian. Mathematical Modelling. School of Mathematics and Statistics, University of Sydney,Sydney, NSW, Australia. Available from Kopystop.

Reference booksSee the Junior Mathematics and Statistics Handbook.

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AssessmentYour final mark for this unit will be calculated as follows:

55%: Exam at end of semester 1.15%: Quiz 1 mark (using the bettermark principle).15%: Quiz 2 mark (using the bettermark principle).10%: Online homework mark.5%: Assignment mark.

The bettermark principle means that for each quiz, the quiz counts if and only if it is better than or equalto your exam mark. If your quiz mark is less than your exam mark the exam mark will be used for thatportion of your assessment instead. So for example if your quiz 1 mark is better than your exam markwhile your quiz 2 mark is worse than your exam mark then the exam will count for 55 + 15 = 70%, quiz1 will count for 15% and the homework will count for 10% and assignment for 5% of your overall mark.The homework and assignment marks are always counted directly regardless of whether they are betterthan your exam mark or not.Final grades are returned within one of the following bands:

High Distinction (HD), 85100: representing complete or close to complete mastery ofthe material; Distinction (D), 7584: representing excellence, but substantially less thancomplete mastery; Credit (CR), 6574: representing a creditable performance that goesbeyond routine knowledge and understanding, but less than excellence; Pass (P), 5064:representing at least routine knowledge and understanding over a spectrum of topics andimportant ideas and concepts in the course.

A student with a passing or higher grade should be well prepared to undertake further studies in math-ematics on which this unit of study depends.

ExaminationThere is one examination of 1.5 hours duration during the examination period at the end of semester 2.Further information about the exam will be made available at a later date.

QuizzesThere are two quizzes, each worth 15% of your final mark. Quizzes are held during LECTURES, on thefollowing two dates

Week 6 (THURSDAY 4 September) and Week 12 (FRIDAY 24 October).

You should put those dates in your diary now! You should sit for the quiz during the lecture stream inwhich you are enrolled. Your quiz mark may not be recorded if you sit for the quiz in a lecture streamin which you are not enrolled (unless you have first made an arrangement with the Mathematics StudentOffice). If you miss a quiz, then you must go to the Mathematics Student Office as soon as possibleafterwards.

Online HomeworkThere will be ten online homework quizzes each worth 1% and count in total for 10% of your final mark.Online homework is provided to support your learning and give you the opportunity to practice thebasic skills introduced in this course. Each online item may be attempted as many times as desired,only your best attempt is counted. You may do the homework at whatever time and pace suits youbut all items must be completed before the end of the study week (5PM on Friday 7 November). Moreinformation about online homework will be given in lectures and on the MATH1013 webpage.

AssignmentThere will be one assignment worth 5% of your final mark. Information about the assignment will begiven in lectures and on the MATH1013 webpage. Your assignment should be handed to your tutor atthe beginning of your tutorial in Week 11 (Monday 13, Tuesday 14 or Wednesday 15 October). You mustgive your assignment to the tutor of the tutorial in which you are enrolled otherwise you mark may notbe recorded. Assignments will be marked and returned at the end of the tutorial in Week 13.

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Any questions? Before you contact us with any enquiry, please check the FAQ page:

http://www.maths.usyd.edu.au/u/UG/JM/FAQ.html

Where to go for help: For administrative matters, go to theMathematics Student Office, Carslaw520. For help with mathematics, see your lecturer, your tutor or a duty tutor. Lecturers guarantee tobe available during their indicated office hour, but may well be available at other times as well. If youare having difficulties with mathematics due to insufficient background, you should contact the MathsLearning Centre Drop-in at Carslaw 455.

Objectives

The objectives of this course are to:

Classify, interpret and construct simple mathematical models,

Compare and discuss the results of applying different models to the same data or situation,

Understand the limitations of models and mathematical methods,

Recognise the same information or model when presented in different forms, and convert or trans-form between equivalent forms,

Extract qualitative information from a model, including the use of graphical methods,

Apply simple techniques in unfamiliar situations, including generalising from simple to complexsystems,

Use numerical exploration to understand models, including estimation and approximation.

Outcomes

Students who successfully complete this course should be able to:

Write down general and particular solutions to simple differential equations and recurrence relationsdescribing models of growth and decay

Determine the order of a differential equation or recurrence relation,

Find equilibrium solutions and analyse their stability using both graphical methods and slopeconditions

Recognise and solve separable first-order differential equations

Use partial fractions and separation of variables to solve certain nonlinear differential equations,including the logistic equation.

Use a variety of graphical and numerical techniques to locate and count solutions to equations

Solve equations numerically by fixed-point iteration, including checking if an iteration method isstable.

Explore sequences numerically, and classify their long-term behaviour

Determine the general solution to linear second-order equations or simultaneous pairs of first orderequations with constant coefficients

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Lecture-by-lecture Outline

1. Assumed knowledge for differential equations

2. intro to differential equations (general and particular solutions)

3. equilibrium (steady-state) solutions for differential equations

4. stability of equilibria for differential equations (graphical method)

5. separation of variables

6. simple linear models

7. partial fractions

8. the logistic function

9. applications of logistic models

10. more applications + assumed knowledge for arithmetic and geometric sequences

11. QUIZ 1

12. intro to recurrence relations (general and particular solutions)

13. equilibrium (fixed-point) solutions

14. stability of fixed points

15. numerical solution of equations

16. fixed-point iteration (Gregory-Dary method)

17. behaviour of logistic map

18. applications of logistic map

MID SEMESTER BREAK

19. second-order equations

20. the characteristic quadratic (positive discriminants only)

21. pairs of first-order differential equations

22. pairs of first-order recurrence equations

23. oscillating (trigonometric) solutions (negative discriminants)

24. QUIZ 2

25. review of the unit of study

26. review of past exam

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