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Unit of study_

MATH2061: Linear Mathematics and Vector Calculus

2024 unit information

This unit starts with an investigation of linearity: linear functions, general principles relating to the solution sets of homogeneous and inhomogeneous linear equations (including differential equations), linear independence and the dimension of a linear space. The study of eigenvalues and eigenvectors, begun in junior level linear algebra, is extended and developed. The unit then moves on to topics from vector calculus, including vector-valued functions (parametrised curves and surfaces; vector fields; div, grad and curl; gradient fields and potential functions), line integrals (arc length; work; path-independent integrals and conservative fields; flux across a curve), iterated integrals (double and triple integrals; polar, cylindrical and spherical coordinates; areas, volumes and mass; Green's Theorem), flux integrals (flow through a surface; flux integrals through a surface defined by a function of two variables, though cylinders, spheres and parametrised surfaces), Gauss' Divergence Theorem and Stokes' Theorem.

Unit details and rules

Managing faculty or University school:

Mathematics and Statistics Academic Operations

Code MATH2061
Academic unit Mathematics and Statistics Academic Operations
Credit points 6
Prerequisites:
? 
(MATH1X21 or MATH1011 or MATH1931 or MATH1X01 or MATH1906) and (MATH1014 or MATH1X02) and (MATH1X23 or MATH1933 or MATH1X03 or MATH1907)
Corequisites:
? 
None
Prohibitions:
? 
MATH2961 or MATH2067 or MATH2021 or MATH2921 or MATH2022 or MATH2922

At the completion of this unit, you should be able to:

  • LO1. solve a system of linear equations
  • LO2. apply the subspace test in several different vector spaces
  • LO3. calculate the span of a given set of vectors in various vector spaces
  • LO4. test sets of vectors for linear independence and dependence
  • LO5. find bases of vector spaces and subspaces
  • LO6. find a polynomial of minimum degree that fits a set of points exactly
  • LO7. find bases of the fundamental subspaces of a matrix
  • LO8. test whether an n × n matrix is diagonalisable, and if it is find its diagonal form
  • LO9. apply diagonalisation to solve recurrence relations and systems of DEs
  • LO10. extended (from first year) their knowledge of vectors in two and three dimensions, and of functions of several variables
  • LO11. evaluate certain line integrals, double integrals, surface integrals and triple integrals
  • LO12. evaluate certain line integrals, double integrals, surface integrals and triple integrals
  • LO13. understand the physical and geometrical significance of these integrals
  • LO14. know how to use the important theorems of Green, Gauss and Stokes.

Unit availability

This section lists the session, attendance modes and locations the unit is available in. There is a unit outline for each of the unit availabilities, which gives you information about the unit including assessment details and a schedule of weekly activities.

The outline is published 2 weeks before the first day of teaching. You can look at previous outlines for a guide to the details of a unit.

Session MoA ?  Location Outline ? 
Semester 1 2023
Normal day Camperdown/Darlington, Sydney
Semester 1 2023
Normal day Remote
Intensive January 2023
Block mode Camperdown/Darlington, Sydney
Intensive January 2023
Block mode Remote
Session MoA ?  Location Outline ? 
Semester 1 2024
Normal day Camperdown/Darlington, Sydney
Outline unavailable
Intensive January 2024
Block mode Camperdown/Darlington, Sydney
Outline unavailable
Session MoA ?  Location Outline ? 
Semester 1 2020
Normal day Camperdown/Darlington, Sydney
Intensive January 2020
Block mode Camperdown/Darlington, Sydney
Outline unavailable
Intensive August 2020
Block mode Camperdown/Darlington, Sydney
Semester 1 2021
Normal day Camperdown/Darlington, Sydney
Semester 1 2021
Normal day Remote
Semester 1 2022
Normal day Camperdown/Darlington, Sydney
Semester 1 2022
Normal day Remote
Intensive January 2022
Block mode Camperdown/Darlington, Sydney
Intensive January 2022
Block mode Remote

Modes of attendance (MoA)

This refers to the Mode of attendance (MoA) for the unit as it appears when you’re selecting your units in Sydney Student. Find more information about modes of attendance on our website.

Important enrolment information

Additional advice

This unit of study is only available to Faculty of Engineering and Information Technologies students.