Vector Calculus (MAST20009)
Undergraduate level 2Points: 12.5On Campus (Parkville)
About this subject
Contact information
Semester 1
Semester 2
Overview
| Availability | Semester 1 Semester 2 |
|---|---|
| Fees | Look up fees |
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: 14 March 2025
Eligibility and requirements
Prerequisites
One of
| Code | Name | Teaching period | Credit Points |
|---|---|---|---|
| MAST10006 | Calculus 2 | No longer available | |
| MAST10009 | Accelerated Mathematics 2 | No longer available | |
| MAST10021 | Calculus 2: Advanced | No longer available |
MAST10019 Calculus Extension Studies
AND
One of
| Code | Name | Teaching period | Credit Points |
|---|---|---|---|
| MAST10007 | Linear Algebra | No longer available | |
| MAST10008 | Accelerated Mathematics 1 | No longer available | |
| MAST10022 | Linear Algebra: Advanced | No longer available |
MAST10013 UMEP Maths for High Achieving Students
MAST10018 Linear Algebra Extension Studies
Corequisites
None
Non-allowed subjects
| Code | Name | Teaching period | Credit Points |
|---|---|---|---|
| MAST20032 | Vector Calculus: Advanced | No longer available |
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 lodge an enrolment variation via their student portal to request enrolment). 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: 14 March 2025
Assessment
| Description | Timing | Percentage |
|---|---|---|
Three to five written assignments due at regular intervals amounting to a total of up to 50 pages
| During the teaching period | 20% |
A written examination
| During the examination period | 80% |
Additional details
Last updated: 14 March 2025
Dates & times
- Semester 1
Coordinator Yaping Yang Mode of delivery On Campus (Parkville) Contact hours 3 x one hour lectures per week, 1 x one hour practice class per week Total time commitment 170 hours Teaching period 26 February 2024 to 26 May 2024 Last self-enrol date 8 March 2024 Census date 3 April 2024 Last date to withdraw without fail 3 May 2024 Assessment period ends 21 June 2024 Semester 1 contact information
- Semester 2
Coordinator Ting Xue Mode of delivery On Campus (Parkville) Contact hours 3 x one hour lectures per week, 1 x one hour practice class per week Total time commitment 170 hours Teaching period 22 July 2024 to 20 October 2024 Last self-enrol date 2 August 2024 Census date 2 September 2024 Last date to withdraw without fail 20 September 2024 Assessment period ends 15 November 2024 Semester 2 contact information
Time commitment details
Estimated total time commitment of 170 hours
What do these dates mean
Visit this webpage to find out about these key dates, including how they impact on:
- Your tuition fees, academic transcript and statements.
- And for Commonwealth Supported students, your:
- Student Learning Entitlement. This applies to all students enrolled in a Commonwealth Supported Place (CSP).
Subjects withdrawn after the census date (including up to the ‘last day to withdraw without fail’) count toward the Student Learning Entitlement.
Last updated: 14 March 2025
Further information
- Texts
- Subject notes
- Related Handbook entries
This subject contributes to the following:
Type Name Major Applied Mathematics Major Pure Mathematics Major Physics Informal specialisation Physics Informal specialisation Pure Mathematics Informal specialisation Science Discipline subjects - new generation B-SCI Informal specialisation Applied Mathematics Breadth Track Accelerated Mathematics Breadth Track Mathematics and Statistics - Breadth options
This subject is available as breadth in the following courses:
- Bachelor of Arts
- Bachelor of Commerce
- Bachelor of Design
- Bachelor of Environments
- Bachelor of Fine Arts (Acting)
- Bachelor of Fine Arts (Animation)
- Bachelor of Fine Arts (Dance)
- Bachelor of Fine Arts (Film and Television)
- Bachelor of Fine Arts (Music Theatre)
- Bachelor of Fine Arts (Production)
- Bachelor of Fine Arts (Screenwriting)
- Bachelor of Fine Arts (Theatre)
- Bachelor of Fine Arts (Visual Art)
- Bachelor of Music
- Available through the Community Access Program
About the Community Access Program (CAP)
This subject is available through the Community Access Program (also called Single Subject Studies) which allows you to enrol in single subjects offered by the University of Melbourne, without the commitment required to complete a whole degree.
Please note Single Subject Studies via Community Access Program is not available to student visa holders or applicants
Entry requirements including prerequisites may apply. Please refer to the CAP applications page for further information.
- Available to Study Abroad and/or Study Exchange Students
Last updated: 14 March 2025