THE UNIVERSITY OF SYDNEY Summer School, Information Sheet for MATH1013 Mathematical Modelling

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1 THE UNIVERSITY OF SYDNEY Summer School, 2015 Information Sheet for MATH1013 Mathematical Modelling Check the unit website regularly! It contains ALL important announcements and academic resources such as scanned lecture notes, etcetera. The coordinator and lecturer for this unit is Collin Zheng. Office: Carslaw 495 For your information, the Summer School coordinator (for all units) is Dr. Brad Roberts. Classes There are a total of 6 contact hours per week, comprising 4 hours of lectures and 2 hours of tutorials. Almost all classes are held on Mondays and Tuesdays in 3 hour blocks between 2-5pm. The classes each day always takes the following format: 2-4pm A 2 hour lecture in Carslaw Lecture Room 173 with Collin 4-5pm A 1 hour tutorial with Collin, George or Andrew (see below) 5-6pm Optional consultations with Collin in his tutorial room Classes commence on Monday in Week 2 of Summer School, which is the week starting 11th of Jan. Note that due to the Australia Day Public Holiday in Week 4, the Tues classes will be moved to Wed. Some info and comments on the lectures I expect you to attend lectures on a regular basis. In fact, at least 4 pieces of assessment will be sprinkled in lectures across the Summer School semester, totalling up a total of 35% of your total unit mark. Scans of the lecture notes will be placed on the website after each lecture. Some parts will not make sense unless you attend the lecture. Lectures will be recorded and placed on Blackboard. You are recommended to buy a booklet titled Mathematical Modelling by Leon Poladian, available from Kopystop (55 Mountain St. near Broadway Shopping Centre). These printed notes will be of great supplement to the physical lectures. Some info and comments on the tutorials Your tutorial allocation is based on the first letter of your surname. Tutorials are held in either the Carslaw Building or the new Sydney Neuroscience Hub (which is the glassy building right behind the Physics Building on Physics Road). Surname initial Location Tutor Contact Starting with A - F Carslaw 360 Collin Zheng [email protected] Starting with G - K SNH 4001 George Papadopoulos [email protected] Starting with L - Z SNH 3001 Andrew Crisp [email protected] It is vitally important that you participate in the tutorials. Like any other skill, to become good at mathematics you must do mathematics there is no substitute for thinking about the questions and attempting them yourself. Have you ever felt that your lecturer or tutor makes the content seem so easy, yet when you have a go yourself, you get stuck very quickly? That often means you haven t practiced the questions enough yourself. Don t make the mistake of thinking that this unit is crammable this may have worked in high school but not at university! To keep the class sizes balanced, you must attend the tutorial for which you are officially enrolled above. If for some reason you wish to formally switch tutorials, please contact me (Collin) first. Tutorial sheets are available on the website, and solutions are posted after each tutorial. You should bring the day s tutorial sheet to class with you, either printed on paper or on a tablet, etcetera. Some info and comments on the consultations After each 2-5pm lecture-tutorial block, you re recommended to see me in my tutorial room (Carslaw 360) to clear up any misunderstandings on the unit, such as difficult concepts from lectures, unsolved tutorial problems etc. Don t procrastinate Summer School goes by VERY fast. If something doesn t make sense, sort it out pronto or else you ll find yourself behind very quickly.

2 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 transform 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 complex systems; 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 relations that describe 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 slope conditions; 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 is stable; Explore sequences numerically, and classify their long-term behaviour; Determine the general solution to linear second-order equations or simultaneous pairs of first order equations with constant coefficients.

3 Assessment Your final raw mark for this unit will be calculated as follows: 50%: Final exam 30%: Quizzes (2 in total) 10%: Lecture pop quizzes (2 in total) 10%: Weekly homework (5 in total) Your final raw mark is then compared with thresholds for final grades, based on simple criteria given below: High Distinction (HD), : representing complete or close to complete mastery of the material; Distinction (D), 75 84: representing excellence, but substantially less than complete mastery; Credit (CR), 65 74: representing a creditable performance that goes beyond routine knowledge and understanding, but less than excellence; Pass (P), 50 64: representing at least routine knowledge and understanding over a spectrum of topics and important ideas and concepts in the course; Quizzes There are two quizzes, each worth 15% of your final raw mark and are held in LECTURES. Quiz 1 will be held during the Week 4 Wednesday lecture (27th January). Quiz 2 will be held in the Week 7 Tuesday lecture (16th February). Lecture Pop Quizzes To encourage students to actively attend lectures, two American-style pop quizzes worth a combined total of 10% will be held potentially in ANY lecture. The questions will be fairly routine and this represents a relatively easy way to obtain 10% just by making sure you turn up to class! Bettermark Principle Your quizzes and lecture pop quizzes are calculated using the Bettermark Principle, which means that for each quiz, the quiz counts if and only if it is better than or equal to your exam mark. (Yay!) So if your quiz mark ended up being less than your exam mark, then the exam mark will be used for that portion of your assessment instead. For instance, if you went better in the exam than, say, Quiz 1, then your exam mark will count for 70% (50% + 15%). This sympathetic policy exists to cut you some slack because we all have bad days. Note that the weighting for the homework and tutorial participation marks are not affected by the bettermark principle together they will always count for 15% towards your final raw mark. Missed quizzes due to illness or misadventure are automatically deferred to the bettermark principle there will be no opportunities for make-up sessions. For example, if you miss Quiz 2 due to an alien abduction, your exam will automatically be worth 55% + 15% = 70%. You do not have to me. Homework In addition to the quizzes and pop quizzes held in lectures, there will also be regular homework assignments to be submitted each week in tutorials. There are a total of 5 homework assignments, each worth 2% of your final raw mark. Homework will be collected at the beginning of the Tuesday tutorials (i.e. second tutorial of each week) and returned the following week. For the last homework, you are encouraged to collect it during my exam consultations. Note: you will have both a quiz AND homework due on the same day in Weeks 4 and 7! This is a good thing as the homework will greatly assist in your quiz preparations. Be sure to manage your time well! Final Exam The final exam (worth 50%) is currently planned to be held on Tuesday 23rd February with the venue yet to be confirmed. Please arrive early and bring your own University-approved calculators.

4 Lecture-by-lecture Schedule Each lecture is 2 hours in duration. Lectures commence in Week 2 of Summer School, which is the week commencing 11th Jan Introduction to Differential Equations Week 2 Mon: Introduction to differential equations. General and particular solutions of DEs. Week 2 Tues: Equilibrium (steady-state) solutions for DEs and their stability (qualitative sketch of general solution, model curve sketch, slope/stability condition). Week 3 Mon: Separation of variables. Simple linear models. Week 3 Tues: Partial fractions. The logistic function. Week 4 Tues: Applications of Logistic Models: Resource-limited Growth (peak oil, intra-species competition) and Sustainable Harvesting (constant harvesting and effort models). Difference Equations/Recurrence Relations Week 4 Wed: Introduction to difference equations (recurrence relations). General and particular solutions of RRs. QUIZ 1 HELD IN THIS LECTURE! Week 5 Mon: stability. Equilibrium (fixed-point) solutions for RRs and their Week 5 Tues: Numerical solution of equations. Fixed-point iteration (Gregory-Dary method). Week 6 Mon: Behaviour and applications of the logistic map. Second-order Equations and Pairs of First-order Equations Week 6 Tues: Second-order equations. real roots. Characteristic equations with Week 7 Mon: Interactions; pairs of first-order differential and difference equations. Week 7 Tues: Oscillations: trigonometric solutions of second-order differential equations (non-real roots). Revision. QUIZ 2 HELD IN THIS LECTURE! Note: TWO lecture pop quizzes will be randomly held in lectures.

5 Assumed Knowledge If you are feeling rusty with some of the basic mathematics required for the course, please do NOT delay and use the first two consultation hours (held right after the first two tutorials in Carslaw 360) and seek help from me! I would also advise you to attend the MATH1011 Summer School lectures which runs concurrently with those of MATH1013. A more complete list of things you need to be proficient with coming into the course will be covered in the first lecture (and is also listed in Leon s Kopystop lecture notes). Ideally, you should have passed MATH1011 Applications of Calculus in Semester 1, or obtained 65 or above for MATH1111 Introduction to Calculus. Struggling and need help? For administrative matters, please contact the lecturer. For help with mathematics, bug your lecturer or tutor. Lecturers guarantee to be available during their consulation times, but may well be available at other times as well via. appointment. If you are having difficulties with mathematics due to insufficient background, you should check out the Mathematics Learning Centre (MLC) in Carslaw Room 455 to explore your options. The MLC operates a drop-in facility whereby eligible students can drop in at anytime for what is essentially free tutoring!! They also operate an useful resources page at