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Vector Calculus (MAST20009)
Undergraduate level 2Points: 12.5On Campus (Parkville)
From Semester 1, 2023 our undergraduate programs will be delivered on campus. Graduate programs will mainly be delivered on campus, with dual-delivery and online options available to a select number of subjects within some programs.
To learn more, visit 2023 Course and subject delivery.
About this subject
- Overview
- Eligibility and requirements
- Assessment
- Dates and times
- Further information
- Timetable(opens in new window)
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: 20 May 2023
Eligibility and requirements
Prerequisites
One of
| Code | Name | Teaching period | Credit Points |
|---|---|---|---|
| MAST10006 | Calculus 2 |
Summer Term (Dual-Delivery - Parkville)
Semester 2 (On Campus - Parkville)
Semester 1 (On Campus - Parkville)
|
12.5 |
| MAST10009 | Accelerated Mathematics 2 | Semester 2 (On Campus - Parkville) |
12.5 |
| MAST10021 | Calculus 2: Advanced | 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 (Dual-Delivery - Parkville)
|
12.5 |
| MAST10008 | Accelerated Mathematics 1 | Semester 1 (On Campus - Parkville) |
12.5 |
| MAST10022 | Linear Algebra: Advanced | Semester 1 (On Campus - Parkville) |
12.5 |
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 | Semester 1 (On Campus - Parkville) |
12.5 |
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: 20 May 2023
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: 20 May 2023
Dates & times
- Semester 1
Principal coordinator Chenyan Wu 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 27 February 2023 to 28 May 2023 Last self-enrol date 10 March 2023 Census date 31 March 2023 Last date to withdraw without fail 5 May 2023 Assessment period ends 23 June 2023 Semester 1 contact information
- Semester 2
Principal coordinator Gufang Zhao 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 24 July 2023 to 22 October 2023 Last self-enrol date 4 August 2023 Census date 31 August 2023 Last date to withdraw without fail 22 September 2023 Assessment period ends 17 November 2023 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).
- Completion rate. Students who started their course from 2022 and are in a CSP or receiving a HELP Loan (eg FEE-HELP) must meet the completion rate to continue to receive Commonwealth Support for that course.
Subjects withdrawn after the census date (including up to the ‘last day to withdraw without fail’) count toward the Student Learning Entitlement, and as a fail toward the completion rate, unless there are approved ‘special circumstances’.
Last updated: 20 May 2023
Further information
- Texts
Prescribed texts
None
- Subject notes
This subject is available for science credit to students enrolled in the BSc (both pre-2008 and new degrees), BASc or a combined BSc course.
- Related Handbook entries
This subject contributes to the following:
Type Name Informal specialisation Applied Mathematics Informal specialisation Physics Informal specialisation Pure Mathematics Informal specialisation Science Discipline subjects - new generation B-SCI Major Applied Mathematics Major Pure Mathematics Major Physics Breadth Track Mathematics and Statistics Breadth Track Accelerated Mathematics - 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.
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
This subject is available to students studying at the University from eligible overseas institutions on exchange and study abroad. Students are required to satisfy any listed requirements, such as pre- and co-requisites, for enrolment in the subject.
Last updated: 20 May 2023