Vector Calculus

Subject MAST20009 (2013)

Note: This is an archived Handbook entry from 2013.

Credit Points: 12.50
Level: 2 (Undergraduate)
Dates & Locations:

This subject is not offered in 2013.

Time Commitment: Contact Hours: 3 x one hour lectures per week, 1 x one hour practice class per week
Total Time Commitment:

Estimated total time commitment of 120 hours

Prerequisites:

One of

Subject
Study Period Commencement:
Credit Points:
Not offered in 2013
12.50
Not offered in 2013
12.50

and one of

Subject
Study Period Commencement:
Credit Points:
Not offered in 2013
12.50
Not offered in 2013
12.50
  • MAST10013 UMEP Maths for High Achieving Students

Or

  • 620-143 Applied Mathematics (prior to 2009)
Corequisites:

None

Recommended Background Knowledge:

None

Non Allowed Subjects:

Students may only gain credit for one of

  • MAST20009 Vector Calculus
  • 620-296 Multivariable and Vector Calculus (prior to 2010)
  • 620-233 Vector Analysis Advanced (prior to 2009)

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.

Core Participation Requirements:

For the purposes of considering request for Reasonable Adjustments under the Disability Standards for Education (Cwth 2005), and Students Experiencing Academic Disadvantage Policy, academic requirements for this subject are articulated in the Subject Description, Subject Objectives, Generic Skills and Assessment Requirements of this entry.
The University is dedicated to provide support to those with special requirements. Further details on the disability support scheme can be found at the Disability Liaison Unit website: http://www.services.unimelb.edu.au/disability/

Contact

Second Year Coordinator

Email: sycoord@ms.unimelb.edu.au

Subject Overview:

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.

Objectives:

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.
Assessment:

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%).

Prescribed Texts:

None

Breadth Options:

This subject potentially can be taken as a breadth subject component for the following courses:

You should visit learn more about breadth subjects and read the breadth requirements for your degree, and should discuss your choice with your student adviser, before deciding on your subjects.

Fees Information: Subject EFTSL, Level, Discipline & Census Date
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.
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.

Previously known as 620-231 Vector Analysis (prior to 2009).

Related Majors/Minors/Specialisations: Applied Mathematics
Physics
Pure Mathematics
Science credit subjects* for pre-2008 BSc, BASc and combined degree science courses
Science-credited subjects - new generation B-SCI and B-ENG. Core selective subjects for B-BMED.
Related Breadth Track(s): Accelerated Mathematics
Mathematics and Statistics

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