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Unit Summary

Unit type

UG Coursework Unit

Credit points

12

AQF level

7

Level of learning

Advanced

School/College

School of Education

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.

GA1: Intellectual rigour, GA2: Creativity, GA3: Ethical practice, GA4: Knowledge of a discipline, GA5: Lifelong learning, GA6: Communication and social skills, GA7: Cultural competence
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 Knowledge of a discipline
2 demonstrate a proficiency in applying techniques from multivariate calculus and differential equations Intellectual rigour Communication and social skills
3 use appropriate multivariate calculus or differential equation techniques to solve 'real world' problems Knowledge of a discipline Communication and social skills
4 communicate mathematical ideas, processes and results effectively at different levels of formality. Intellectual rigour Communication and social skills

On completion of this unit, students should be able to:

  1. demonstrate a sound knowledge and understanding of multivariate calculus and differential equations concepts
    • GA4: Knowledge of a discipline
  2. demonstrate a proficiency in applying techniques from multivariate calculus and differential equations
    • GA1: Intellectual rigour
    • GA6: Communication and social skills
  3. use appropriate multivariate calculus or differential equation techniques to solve 'real world' problems
    • GA4: Knowledge of a discipline
    • GA6: Communication and social skills
  4. communicate mathematical ideas, processes and results effectively at different levels of formality.
    • GA1: Intellectual rigour
    • GA6: Communication and social skills

Prescribed texts

  • Hughes-Hallett, D, 2008, Calculus: Single and multivariate, 5th (or 6th) edn, Wiley.
Prescribed texts may change in future study periods.