Vector Calculus (MAST20009)

Undergraduate level 2Points: 12.5On Campus (Parkville)

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Overview

Availability
Semester 1
Semester 2
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This subject studies the fundamental concepts of functions of several variables and vector calculus. It develops the manipulation of partial derivatives and vector differential operators. The gradient vector is used to obtain constrained extrema of functions of several variables. Line, surface and volume integrals are evaluated and related by various integral theorems. Vector differential operators are also studied using curvilinear coordinates.

Functions of several variables topics include limits, continuity, differentiability, the chain rule, Jacobian, Taylor polynomials and Lagrange multipliers. Vector calculus topics include vector fields, flow lines, curvature, torsion, gradient, divergence, curl and Laplacian. Integrals over paths and surfaces topics include line, surface and volume integrals; change of variables; applications including averages, moments of inertia, centre of mass; Green's theorem, Divergence theorem in the plane, Gauss' divergence theorem, Stokes' theorem; and curvilinear coordinates.

Intended learning outcomes

On completion of this subject, the student should :



  • Understand calculus of functions of several variables; differential operators; line, surface and volume integrals; curvilinear coordinates; integral theorems
  • Have developed the ability to work with limits and continuity; obtain extrema of functions of several variables; calculate line, surface and volume integrals; work in curvilinear coordinates; apply integral theorems
  • Appreciate the fundamental concepts of vector calculus; the relations between line, surface and volume integrals.

Generic skills

In addition to learning specific skills that will assist students in their future careers in science, they will have the opportunity to develop generic skills that will assist them in any future career path. These include

  • problem-solving skills: the ability to engage with unfamiliar problems and identify relevant solution strategies;
  • analytical skills: the ability to construct and express logical arguments and to work in abstract or general terms to increase the clarity and efficiency of analysis;
  • collaborative skills: the ability to work in a team;
  • time management skills: the ability to meet regular deadlines while balancing competing commitments.

Last updated: 9 April 2025

Eligibility and requirements

Prerequisites

One of

Code Name Teaching period Credit Points
MAST10006 Calculus 2
Semester 2 (On Campus - Parkville)
Semester 1 (On Campus - Parkville)
 12.5
MAST10009 Accelerated Mathematics 2
Semester 2 (On Campus - Parkville)
 12.5

  • MAST10019 Calculus Extension Studies

and one of

Code Name Teaching period Credit Points
MAST10007 Linear Algebra
Semester 1 (On Campus - Parkville)
Semester 2 (On Campus - Parkville)
Summer Term (On Campus - Parkville)
 12.5
MAST10008 Accelerated Mathematics 1
Semester 1 (On Campus - Parkville)
 12.5

  • MAST10013 UMEP Maths for High Achieving Students
  • MAST10018 Linear Algebra Extension Studies

Corequisites

None

Non-allowed subjects

Students may only gain credit for one of

  • MAST20009 Vector Calculus
  • 620-296 Multivariable and Vector Calculus (prior to 2010)

Passing MAST20009 Vector Calculus precludes subsequent credit for MAST20029 Engineering Mathematics.

Enrolment in MAST20009 Vector Calculus is permitted for students who have passed MAST20029 Engineering Mathematics. (N.B. Students in this situation will need to contact their student centre for assistance in enrolling in MAST20009).

Concurrent enrolment in both MAST20009 Vector Calculus and MAST20029 Engineering Mathematics is not permitted.

Inherent requirements (core participation requirements)

The University of Melbourne is committed to providing students with reasonable adjustments to assessment and participation under the Disability Standards for Education (2005), and the Assessment and Results Policy (MPF1326). Students are expected to meet the core participation requirements for their course. These can be viewed under Entry and Participation Requirements for the course outlines in the Handbook.

Further details on how to seek academic adjustments can be found on the Student Equity and Disability Support website: http://services.unimelb.edu.au/student-equity/home

Last updated: 9 April 2025

Assessment

Additional details

Three to five written assignments due at regular intervals during semester amounting to a total of up to 50 pages (20%), and a 3-hour written examination in the examination period (80%).

 

Last updated: 9 April 2025

Dates & times

  • Semester 1
    Principal coordinatorChristine Mangelsdorf
    Mode of deliveryOn Campus (Parkville)
    Contact hours3 x one hour lectures per week, 1 x one hour practice class per week
    Total time commitment170 hours
    Teaching period 4 March 2019 to 2 June 2019
    Last self-enrol date15 March 2019
    Census date31 March 2019
    Last date to withdraw without fail10 May 2019
    Assessment period ends28 June 2019

    Semester 1 contact information

    Email: mangel@unimelb.edu.au

  • Semester 2
    Principal coordinatorNora Ganter
    Mode of deliveryOn Campus (Parkville)
    Contact hours3 x one hour lectures per week, 1 x one hour practice class per week
    Total time commitment170 hours
    Teaching period29 July 2019 to 27 October 2019
    Last self-enrol date 9 August 2019
    Census date31 August 2019
    Last date to withdraw without fail27 September 2019
    Assessment period ends22 November 2019

    Semester 2 contact information

    nganter@unimelb.edu.au

Time commitment details

Estimated total time commitment of 170 hours

Last updated: 9 April 2025

Further information

Last updated: 9 April 2025