MATH2069 is a Mathematics Level II course which is only available to students for whom it is specifically required as part of their program. See the course overview below.

**Units of credit:** 6

**Prerequisites:** MATH1231 or Math1241 or MATH1251.

**Exclusions:** MATH2011, MATH2111, MATH2510, MATH2610, MATH2520, MATH2620.

**Cycle of offering: **Yearly in Semester 1.

**Graduate attributes:** The course will enhance your research, inquiry and analytical thinking abilities.

**More information:**

This recent course outline (pdf) contains information about course objectives, assessment, course materials and the syllabus.

The Online Handbook entry contains up-to-date timetabling information.

If you are currently enrolled in MATH2069, you can log into UNSW Moodle for this course.

#### Course Overview

**Several Variable Calculus:**

Vectors, differential calculus of curves in R3 and surfaces, Taylor series for functions of two variables, critical points, local maxima and minima. Lagrange multipliers, integral calculus for functions of several variables using various co-ordinate systems, conservative vector fields and line integrals, Green's Theorem in the plane, divergence and curl, surface integrals, Stokes' Theorem, Gauss' divergence Theorem.

**Complex Analysis:**

Complex numbers, simple mapping problems, differentiation theory for complex functions, Cauchy Riemann equations, analytic functions, the elementary functions, Integration Theory for complex functions, Cauchy's Theorem and the Cauchy integral formulae, Taylor series and Laurent Series, residues, evaluating real integrals and trigonometric integrals using residues.