Unit of study_

# MATH2061: Linear Mathematics and Vector Calculus

### 2025 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

#### Science

 Prerequisites: ? [(MATH1061 or MATH1961 or MATH1971) and (MATH1062 or MATH1962 or MATH1972)] or ([MATH1921 or MATH1931 or MATH1901 or MATH1906 or MATH1021 or MATH1001 or MATH1011] and [MATH1902 or MATH1002 or MATH1014] and [MATH1013 or MATH1023 or MATH1003 or MATH1923 or MATH1933 or MATH1903 or MATH1907]) None MATH2961 or MATH2067 or MATH2021 or MATH2921 or MATH2022 or MATH2922 None

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 2024
Normal day Camperdown/Darlington, Sydney
Intensive January 2024
Block mode Camperdown/Darlington, Sydney
Session MoA   Location Outline
Semester 1 2025
Normal day Camperdown/Darlington, Sydney
Outline unavailable
Intensive January 2025
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
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

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### Modes of attendance (MoA)

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