Unit of study_

# MATH1013: Mathematical Modelling

## Overview

MATH1013 is designed for science students who do not intend to undertake higher year mathematics and statistics. In this unit of study students learn how to construct, interpret and solve simple differential equations and recurrence relations. Specific techniques include separation of variables, partial fractions and first and second order linear equations with constant coefficients. Students are also shown how to iteratively improve approximate numerical solutions to equations.

### Unit details and rules

Unit code MATH1013 Mathematics and Statistics Academic Operations 3 MATH1003 or MATH1903 or MATH1907 or MATH1023 or MATH1923 or MATH1933 None None HSC Mathematics or a credit or higher in MATH1111. Students who have not completed HSC Mathematics (or equivalent) are strongly advised to take the Mathematics Bridging Course (offered in February). Please note: this unit does not normally lead to a major in Mathematics or Statistics or Financial Mathematics and Statistics. No

### Teaching staff

Coordinator Daniel Hauer, daniel.hauer@sydney.edu.au Pantea Pooladvand

## Assessment

Type Description Weight Due Length
Assignment Assignment 1
written calculations
2.5% Week 02
Due date: 26 Jan 2021 at 23:59

Closing date: 02 Feb 2021
7 days
Outcomes assessed:
12.5% Week 03
Due date: 03 Feb 2021 at 17:00
40 minutes
Outcomes assessed:
Assignment Assignment 2
written calculations
7.5% Week 04
Due date: 09 Feb 2021 at 23:59

Closing date: 16 Feb 2021
7 days
Outcomes assessed:
12.5% Week 05
Due date: 18 Feb 2021 at 17:00
40 minutes
Outcomes assessed:
Final exam (Open book) Final exam
65% Week 06
Due date: 24 Feb 2021 at 14:00
1.5 hours
Outcomes assessed:
= Type C final exam

### Assessment summary

• Quizzes: Two quizzes will be held online through Canvas. The quizzes are 40 Minutes and are scheduled during one of the tutorials. The better mark principle will be used for the quizzes so do not submit an application for Special Consideration or Special Arrangements if you miss a quiz. The better mark principle means that for each quiz, the quiz counts if and only if it is better than or equal to your exam mark. If your quiz mark is less than your exam mark, the exam mark will be used for that portion of your assessment instead.
• Assignments: There are two assignments. Each assignment must be submitted electronically, as one single typeset or scanned PDF file only, via Canvas by the deadline. Note that your assignment will not be marked if it is illegible or if it is submitted sideways or upside down. It is your responsibility to check that your assignment has been submitted correctly and that it is complete (check that you can view each page). Late submissions will receive a penalty.
• Final Exam: There is one final exam to this unit of study scheduled in week 6. Further information about the exam will be made available at a later date on Canvas.

Detailed information for each assessment can be found on Canvas.

### Assessment criteria

The University awards common result grades, set out in the Coursework Policy 2014 (Schedule 1).

As a general guide, a high distinction indicates work of an exceptional standard, a distinction a very high standard, a credit a good standard, and a pass an acceptable standard.

Result name

Mark range

Description

High distinction

85 - 100

Representing complete or close to complete mastery of the material.

Distinction

75 - 84

Representing excellence, but substantially less than complete mastery.

Credit

65 - 74

Representing a creditable performance that goes beyond routine knowledge and understanding, but less than excellence.

Pass

50 - 64

Representing at least routine knowledge and understanding over a spectrum of topics and important ideas and concepts in the course.

Fail

0 - 49

When you don’t meet the learning outcomes of the unit to a satisfactory standard.

### Late submission

In accordance with University policy, these penalties apply when written work is submitted after 11:59pm on the due date:

• Deduction of 5% of the maximum mark for each calendar day after the due date.
• After ten calendar days late, a mark of zero will be awarded.

The Current Student website  provides information on academic integrity and the resources available to all students. The University expects students and staff to act ethically and honestly and will treat all allegations of academic integrity breaches seriously.

We use similarity detection software to detect potential instances of plagiarism or other forms of academic integrity breach. If such matches indicate evidence of plagiarism or other forms of academic integrity breaches, your teacher is required to report your work for further investigation.

You may only use artificial intelligence and writing assistance tools in assessment tasks if you are permitted to by your unit coordinator, and if you do use them, you must also acknowledge this in your work, either in a footnote or an acknowledgement section.

Studiosity is permitted for postgraduate units unless otherwise indicated by the unit coordinator. The use of this service must be acknowledged in your submission.

## Learning support

### Simple extensions

If you encounter a problem submitting your work on time, you may be able to apply for an extension of five calendar days through a simple extension.  The application process will be different depending on the type of assessment and extensions cannot be granted for some assessment types like exams.

### Special consideration

If exceptional circumstances mean you can’t complete an assessment, you need consideration for a longer period of time, or if you have essential commitments which impact your performance in an assessment, you may be eligible for special consideration or special arrangements.

Special consideration applications will not be affected by a simple extension application.

### Using AI responsibly

Co-created with students, AI in Education includes lots of helpful examples of how students use generative AI tools to support their learning. It explains how generative AI works, the different tools available and how to use them responsibly and productively.

## Weekly schedule

WK Topic Learning activity Learning outcomes
Week 01 1. Assumed knowledge for differential equations; 2. Intro to differential equations (general and particular solutions) Block teaching (2 hr)
1. Equilibrium (steady-state) solutions for differential equations; 2. Stability of equilibria for differential equations (graphical method) Block teaching (2 hr)
Week 02 1. Separation of variables; 2. Simple linear models Block teaching (2 hr)
1. Partial fractions; 2. The logistic function Block teaching (2 hr)
Week 03 1. Applications of logistic models; 2. More applications of logistic models Block teaching (2 hr)
1. Assumed knowledge for arithmetic and geometric sequences; 2. Intro to recurrence relations (general and particular solutions) Block teaching (2 hr)
Week 04 1. Equilibrium (fixed-point) solutions; 2. Stability of fixed points Block teaching (2 hr)
1. Numerical solution of equations; 2. Fixed-point iteration (Gregory–Dary method) Block teaching (2 hr)
1. Behaviour of logistic map; 2. Applications of logistic map Block teaching (2 hr)
Week 05 1. Second-order equations; 2. The characteristic quadratic (positive discriminants only) Block teaching (2 hr)
1. Pairs of first-order differential equations; 2. Pairs of first-order recurrence equations Block teaching (2 hr)
1. The characteristic equation (negative discriminants); 2. Oscillating (trigonometric) solutions Block teaching (2 hr)

### Attendance and class requirements

• Attendance: Students are expected to attend a minimum of 80% of timetabled activities for a unit of study, unless granted exemption by the Associate Dean. For some units of study the minimum attendance requirement, as specified in the relevant table of units or the unit of study outline, may be greater than 80%.
• Tutorial attendance:  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 the tutorial in which you are enrolled.  While there is no penalty if 80% attendance is not met we strongly recommend you attend tutorials regularly to keep up with the material and to engage with the tutorial questions. Since there is no assessment associated with the tutorials do not submit an application for Special Consideration or Special Arrangements for missed tutorials.

### Study commitment

Typically, there is a minimum expectation of 1.5-2 hours of student effort per week per credit point for units of study offered over a full semester. For a 3 credit point unit, this equates to roughly 60-75 hours of student effort in total.

• L. Poladian. Mathematical Modelling. School of Mathematics and Statistics, University of Sydney, Sydney, NSW, Australia, 2011. Available from Kopystop. (also available as a PDF through Canvas)

## Learning outcomes

Learning outcomes are what students know, understand and are able to do on completion of a unit of study. They are aligned with the University's graduate qualities and are assessed as part of the curriculum.

At the completion of this unit, you should be able to:

• LO1. write down general and particular solutions to simple differential equations and recurrence relations describing models of growth and decay
• LO2. determine the order of a differential equation or recurrence relation
• LO3. find equilibrium solutions and analyse their stability using both graphical methods and slope conditions
• LO4. recognise and solve separable first-order differential equations
• LO5. use partial fractions and separation of variables to solve certain nonlinear differential equations, including the logistic equation
• LO6. use a variety of graphical and numerical techniques to locate and count solutions to equations
• LO7. solve equations numerically by fixed-point iteration, including checking if an iteration method is stable
• LO8. explore sequences numerically, and classify their long-term behaviour
• LO9. determine the general solution to linear second-order equations or simultaneous pairs of first order equations with constant coefficients.

The graduate qualities are the qualities and skills that all University of Sydney graduates must demonstrate on successful completion of an award course. As a future Sydney graduate, the set of qualities have been designed to equip you for the contemporary world.

 GQ1 Depth of disciplinary expertise Deep disciplinary expertise is the ability to integrate and rigorously apply knowledge, understanding and skills of a recognised discipline defined by scholarly activity, as well as familiarity with evolving practice of the discipline. GQ2 Critical thinking and problem solving Critical thinking and problem solving are the questioning of ideas, evidence and assumptions in order to propose and evaluate hypotheses or alternative arguments before formulating a conclusion or a solution to an identified problem. GQ3 Oral and written communication Effective communication, in both oral and written form, is the clear exchange of meaning in a manner that is appropriate to audience and context. GQ4 Information and digital literacy Information and digital literacy is the ability to locate, interpret, evaluate, manage, adapt, integrate, create and convey information using appropriate resources, tools and strategies. GQ5 Inventiveness Generating novel ideas and solutions. GQ6 Cultural competence Cultural Competence is the ability to actively, ethically, respectfully, and successfully engage across and between cultures. In the Australian context, this includes and celebrates Aboriginal and Torres Strait Islander cultures, knowledge systems, and a mature understanding of contemporary issues. GQ7 Interdisciplinary effectiveness Interdisciplinary effectiveness is the integration and synthesis of multiple viewpoints and practices, working effectively across disciplinary boundaries. GQ8 Integrated professional, ethical, and personal identity An integrated professional, ethical and personal identity is understanding the interaction between one’s personal and professional selves in an ethical context. GQ9 Influence Engaging others in a process, idea or vision.

### Outcome map

GQ1 GQ2 GQ3 GQ4 GQ5 GQ6 GQ7 GQ8 GQ9

## Responding to student feedback

This section outlines changes made to this unit following staff and student reviews.

The weighting of assignment 2 was increased.