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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
Managing faculty or University school:
Science
| Study level | Undergraduate |
|---|---|
| Academic unit | Mathematics and Statistics Academic Operations |
| Credit points | 6 |
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Prerequisites:
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{(MATH1X61 or MATH1971) or [(MATH1X21 or MATH1931 or MATH1X01 or MATH1906 or MATH1011) and (MATH1014 or MATH1X02)]} and (MATH1X62 or MATH1972 or MATH1013 or MATH1X23 or MATH1X03 or MATH1933 or MATH1907) |
|---|---|
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Corequisites:
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None |
| Prohibitions:
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MATH2961 or MATH2067 or MATH2021 or MATH2921 or MATH2022 or MATH2922 |
| Assumed knowledge:
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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 ? |
|---|---|---|---|
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Semester 1 2024
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Normal day | Camperdown/Darlington, Sydney | |
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Intensive January 2024
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Block mode | Camperdown/Darlington, Sydney |
| Session | MoA ? | Location | Outline ? |
|---|---|---|---|
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Semester 1 2025
|
Normal day | Camperdown/Darlington, Sydney |
Outline unavailable
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Intensive January 2025
|
Block mode | Camperdown/Darlington, Sydney |
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Modes of attendance (MoA)
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Important enrolment information
Additional advice
This unit of study is only available to Faculty of Engineering and Information Technologies students.
