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Vector Calculus (MAST20009)
Undergraduate level 2Points: 12.5On Campus (Parkville)
About this subject
- Overview
- Eligibility and requirements
- Assessment
- Dates and times
- Further information
- Timetable(opens in new window)
Contact information
Semester 1
Email: mangel@unimelb.edu.au
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: 11 April 2024
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: 11 April 2024
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: 11 April 2024
Dates & times
- Semester 1
Principal coordinator Christine Mangelsdorf 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 4 March 2019 to 2 June 2019 Last self-enrol date 15 March 2019 Census date 31 March 2019 Last date to withdraw without fail 10 May 2019 Assessment period ends 28 June 2019 Semester 1 contact information
Email: mangel@unimelb.edu.au
- Semester 2
Principal coordinator Nora Ganter 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 29 July 2019 to 27 October 2019 Last self-enrol date 9 August 2019 Census date 31 August 2019 Last date to withdraw without fail 27 September 2019 Assessment period ends 22 November 2019 Semester 2 contact information
Time commitment details
Estimated total time commitment of 170 hours
Last updated: 11 April 2024
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 Physics Informal specialisation Science-credited subjects - new generation B-SCI Informal specialisation Applied Mathematics Informal specialisation Pure Mathematics Informal specialisation Selective subjects for B-BMED Major Pure Mathematics Major Applied Mathematics Major Physics Breadth Track Accelerated Mathematics Breadth Track Mathematics and Statistics - Breadth options
This subject is available as breadth in the following courses:
- 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: 11 April 2024