Vector Calculus: Advanced (MAST20032)
Undergraduate level 2Points: 12.5On Campus (Parkville)
Overview
| Availability | Semester 1 |
|---|---|
| Fees | Look up fees |
This subject covers the material presented in MAST20009 Vector Calculus plus additional material designed to provide deeper insight into interesting areas of calculus and has a greater emphasis on mathematical rigour and proof.
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, implicit and inverse function theorems, 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 moments of inertia, centre of mass; Green's theorem, Divergence theorem in the plane, Gauss' divergence theorem, Stokes' theorem; and curvilinear coordinates. Possible additional topics include differential geometry of surfaces.
Intended learning outcomes
On completion of this subject, students should be able to:
- Apply calculus to the functions of several variables; differential operators; line, surface and volume integrals; curvilinear coordinates; integral theorems;
- Demonstrate 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;
- Define fundamental concepts of vector calculus; the relations between line, surface and volume integrals.
- Apply and interpret theorems of calculus in a rigorous way.
Generic skills
- 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: 4 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
(with a mark of at least 75 for MAST10006 or MAST10019)
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 |
MAST10018: Linear Algebra Extension Studies
(with a mark of at least 75 for MAST10007 or MAST10018)
Corequisites
None
Non-allowed subjects
| Code | Name | Teaching period | Credit Points |
|---|---|---|---|
| MAST20009 | Vector Calculus | No longer available |
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: 4 March 2025
Assessment
| Description | Timing | Percentage |
|---|---|---|
Three to five written assignments due at regular intervals
| During the teaching period | 20% |
A written examination
| During the examination period | 80% |
Last updated: 4 March 2025
Dates & times
- Semester 1
Coordinator Gufang Zhao Mode of delivery On Campus (Parkville) Contact hours 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
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: 4 March 2025
Further information
- Texts
- 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: 4 March 2025