# DEs and Vector Calculus for Engineers (MATH2067)

## UNIT OF STUDY

MATH2067 starts by introducing students to solution techniques of ordinary and partial differential equations (ODEs and PDEs) relevant to the engineering disciplines: it provides a basic grounding in these techniques to enable students to build on the concepts in their subsequent engineering classes. The main topics are Fourier series, second order ODEs, including inhomogeneous equations and Laplace transforms, and second order PDEs in rectangular domains (solution by separation of variables).
The unit 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's 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 examination, assignments and 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 MATH2005 or MATH2905 or MATH2061 or MATH2961 or MATH2065 or MATH2965

## 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.