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
Academic unit | Mathematics and Statistics Academic Operations |
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Credit points | 6 |
Prerequisites
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[(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]) |
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 |
Available to study abroad and exchange students | Yes |
Teaching staff
Coordinator | Laurentiu Paunescu, laurentiu.paunescu@sydney.edu.au |
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Lecturer(s) | Ruibin Zhang, ruibin.zhang@sydney.edu.au |
Laurentiu Paunescu, laurentiu.paunescu@sydney.edu.au |