Availabilities:
| Location | Domestic | International |
|---|---|---|
| Online | N/A |
Unit Summary
Unit type
UG Coursework Unit
Credit points
12
AQF level
Level of learning
Advanced
Former School/College
Pre-requisites
Unit aim
Extends the concepts developed in Calculus to functions of several variables and differential equations. Topics include differential equations, partial differentiation, optimisation, vector calculus. Applications and modelling will be considered.
Unit content
Differential Equations (Topics 1 to 3) - Ordinary differential equations - First-order linear differential equations - Systems of linear equations - Applications and modelling
Functions of Several Variables (Topics 3 to 6) - Functions of two or more variables - Limits and continuity - Partial differentiation - The chain rule - Higher order partial derivatives - Optimisation - Lagrange multipliers
Multiple Integrals (Topics 7 and 8) - Double and triple integrals - Polar, cylindrical and spherical coordinates - Change of variable - Applications
Vector Calculus (Topics 9 and 10) - Vector functions - Limits, differentiation and integration - Gradient, divergence and curl - Line integrals and Green's Theorem
Learning outcomes
Unit Learning Outcomes express learning achievement in terms of what a student should know, understand and be able to do on completion of a unit. These outcomes are aligned with the graduate attributes. The unit learning outcomes and graduate attributes are also the basis of evaluating prior learning.
| On completion of this unit, students should be able to: | GA1 | GA2 | GA3 | GA4 | GA5 | GA6 | GA7 | |
|---|---|---|---|---|---|---|---|---|
| 1 | demonstrate a sound knowledge and understanding of multivariate calculus and differential equations concepts | |||||||
| 2 | demonstrate a proficiency in applying techniques from multivariate calculus and differential equations | |||||||
| 3 | use appropriate multivariate calculus or differential equation techniques to solve 'real world' problems | |||||||
| 4 | communicate mathematical ideas, processes and results effectively at different levels of formality. | |||||||
On completion of this unit, students should be able to:
-
demonstrate a sound knowledge and understanding of multivariate calculus and differential equations concepts
- GA4:
-
demonstrate a proficiency in applying techniques from multivariate calculus and differential equations
- GA1:
- GA6:
-
use appropriate multivariate calculus or differential equation techniques to solve 'real world' problems
- GA4:
- GA6:
-
communicate mathematical ideas, processes and results effectively at different levels of formality.
- GA1:
- GA6:
Prescribed texts
- Hughes-Hallett, D, 2008, Calculus: Single and multivariate, 5th (or 6th) edn, Wiley.