# 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

### Classes

Three 1 hour lectures, one 1 hour tutorial and one 1 hour practice class per week.

### Assessment

One 2 hour exam, assignments, quizzes (100%)

No

## Unit of study rules

### Prerequisites

(MATH1011 or MATH1001 or MATH1901 or MATH1906) and (MATH1014 or MATH1002 or MATH1902) and (MATH1003 or MATH1903 or MATH1907)

### Prohibitions

MATH2001 or MATH2901 or MATH2002 or MATH2902 or MATH2961 or MATH2067

## Study this unit outside a degree

### Non-award/non-degree study

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.

### Cross-institutional study

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.