Essential Mathematics
Overview
This unit of study aims to provide students with the mathematical knowledge and skills to support their concurrent and subsequent studies, providing a thorough grounding in mathematics with an emphasis of modelling and statistics. Students will be equipped to model real world applications and critique the appropriateness of the models. Students will learn to apply differentiation and integration techniques to practical problems and the solution of differential equations modelling real world phenomena. Students will gain programming experience using statistical software to quantify relationships in data, test hypotheses, and critique the validity of tested hypotheses.
Requisites
MTH00007 Preliminary Mathematics
OR
MTH00005 Applied Engineering Mathematics
OR
A study score of at least 25 in VCE Maths Methods Units 3, 4 or equivalent
02-November-2025
31-May-2026
01-November-2026
Unit learning outcomes
Students who successfully complete this unit will be able to:
- Classify continuous functions and characterise long-term behaviour of functions by calculating the limit
- Construct algebraic and geometric forms of functions to enable modelling of real-world phenomena using polynomials, rational and exponential functions
- Identify standard derivatives and integrals for simple functions and apply appropriate techniques to differentiate and integrate more complicated functions
- Solve optimisation problems for real world applications, calculate linear approximations of functions, compute areas and tangent curves using the rules of differentiation and integration
- Solve simple linear first order and second order differential equations and classify stationary points and apply these techniques to applications in science and engineering
- Analyse data using statistical software to quantify relationships between datasets using statistical techniques such as correlation, linear regression, and t-tests to perform hypothesis tests and critique the suitability of tested hypotheses
Teaching methods
Hawthorn
| Type | Hours per week | Number of weeks | Total (number of hours) |
|---|---|---|---|
| On-campus Lecture |
4.00 | 9 weeks | 36 |
| On-campus Class |
1.00 | 12 weeks | 12 |
| On-campus Class |
4.00 | 3 weeks | 12 |
| Specified Activities Various |
2.00 | 12 weeks | 24 |
| Unspecified Activities Independent Learning |
5.50 | 12 weeks | 66 |
| TOTAL | 150 |
Assessment
| Type | Task | Weighting | ULO's |
|---|---|---|---|
| Examination | Individual | 40 - 60% | 1,2,3,4,5,6 |
| Online Assignment | Individual | 5 - 25% | 1,2,3,4,6 |
| Project Report | Individual | 5 - 25% | 4,5 |
| Test | Individual | 5 - 25% | 1,2,3 |
Hurdle
As the minimum requirements of assessment to pass a unit and meet all Unit Learning Outcomes to a minimum standard, a student must achieve:
(i) an aggregate mark of 50% or more, and(ii) at least 40% in the final exam.Students who do not successfully achieve hurdle requirement (ii) will receive a maximum of 45% as the total mark for the unit.
Content
- Sets, Limits and Functions
- Modelling and Error
- Descriptive Statistics
- Inferential Statistics
- Differentiation
- Integration
- Ordinary Differential Equations
Study resources
Reading materials
A list of reading materials and/or required textbooks will be available in the Unit Outline on Canvas.