Unit of study_

# MATH1013: Mathematical Modelling

### 2023 unit information

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

#### Science

Study level Undergraduate Mathematics and Statistics Academic Operations 3
 Prerequisites: ? None None MATH1003 or MATH1903 or MATH1907 or MATH1023 or MATH1923 or MATH1933 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

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.

## Unit availability

This section lists the session, attendance modes and locations the unit is available in. There is a unit outline for each of the unit availabilities, which gives you information about the unit including assessment details and a schedule of weekly activities.

The outline is published 2 weeks before the first day of teaching. You can look at previous outlines for a guide to the details of a unit.

There are no availabilities for this year.
Session MoA   Location Outline
Intensive January 2020
Block mode Camperdown/Darlington, Sydney
Outline unavailable
Semester 2 2020
Normal day Camperdown/Darlington, Sydney
Intensive February 2021
Block mode Camperdown/Darlington, Sydney
Intensive February 2021
Block mode Remote
Semester 2 2021
Normal day Camperdown/Darlington, Sydney
Semester 2 2021
Normal day Remote
Intensive January 2022
Block mode Camperdown/Darlington, Sydney
Intensive January 2022
Block mode Remote
Semester 2 2022
Normal day Camperdown/Darlington, Sydney
Semester 2 2022
Normal day Remote
Intensive January 2023
Block mode Camperdown/Darlington, Sydney
Intensive January 2023
Block mode Remote

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### Modes of attendance (MoA)

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