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 |
---|---|
Credit points | 6 |
Prerequisites
?
|
{(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) |
Corequisites
?
|
None |
Prohibitions
?
|
MATH2961 or MATH2067 or MATH2021 or MATH2921 or MATH2022 or MATH2922 |
Assumed knowledge
?
|
None |
Available to study abroad and exchange students | No |
Teaching staff
Coordinator | Laurentiu Paunescu, laurentiu.paunescu@sydney.edu.au |
---|---|
Lecturer(s) | Laurentiu Paunescu, laurentiu.paunescu@sydney.edu.au |
Ruibin Zhang, ruibin.zhang@sydney.edu.au |