Linear Mathematics and Vector Calculus (MATH2061)
UNIT OF STUDY
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.
Further unit of study information
Three 1 hour lectures, one 1 hour tutorial and one 1 hour practice class per week.
One 2 hour exam, assignments, quizzes (100%)
Faculty/department permission required?
Unit of study rules
Prerequisites and assumed knowledge
(MATH1011 or MATH1001 or MATH1901 or MATH1906) and (MATH1014 or MATH1002 or MATH1902) and (MATH1003 or MATH1903 or MATH1907)
MATH2001 or MATH2901 or MATH2002 or MATH2902 or MATH2961 or MATH2067
Study this unit outside a degree
If you wish to undertake one or more units of study (subjects) for your own interest but not towards a degree, you may enrol in single units as a non-award student.
If you are from another Australian tertiary institution you may be permitted to underake cross-institutional study in one or more units of study at the University of Sydney.