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Unit of Study MAT10721 - Multivariate Calculus and Differential Equations (2014)

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Unit Snapshot

  • Unit typeo

    UG Coursework Unit

  • Credit points

    12

  • AQF level

    7

  • Level of learning

    Advanced

  • Former School/College

    Former School of Education

Unit description

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

Availabilities

Location Domestic International
Online Session 2 N/A

Learning outcomes and graduate attributes

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:
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:

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

Prescribed learning resources

Prescribed Texts
  • No prescribed texts.

Prescribed Learning Resources may change in future Teaching Periods.