Availabilities:

LocationDomesticInternational
OnlineN/A

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

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:GA1GA2GA3GA4GA5GA6GA7
1demonstrate a sound knowledge and understanding of multivariate calculus and differential equations conceptsKnowledge of a discipline
2demonstrate a proficiency in applying techniques from multivariate calculus and differential equationsIntellectual rigourCommunication and social skills
3use appropriate multivariate calculus or differential equation techniques to solve 'real world' problemsKnowledge of a disciplineCommunication and social skills
4communicate mathematical ideas, processes and results effectively at different levels of formality.Intellectual rigourCommunication 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.

Teaching and assessment

Teaching method
Tutorial online 1 hour (8)
Assessment
QuizSR
Calculations25%
Calculations25%
Exam: closed book50%
Notice

Intensive offerings may or may not be scheduled in every session. Please refer to the timetable for further details.

Southern Cross University employs different teaching methods within units to provide students with the flexibility to choose the mode of learning that best suits them. SCU academics strive to use the latest approaches and, as a result, the learning modes and materials may change. The most current information regarding a unit will be provided to enrolled students at the beginning of the study session.

Fee information

Domestic

Commonwealth Supported courses
For information regarding Student Contribution Amounts please visit the Student Contribution Amounts.

Fee paying courses
For postgraduate or undergraduate full fee paying courses please check Domestic Postgraduate Fees OR Domestic Undergraduate Fees

International

Please check the international course and fee list to determine the relevant fees.

+