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 or DPST1014

**Exclusions:** MATH2011, MATH2111, MATH2521, MATH2621

**Cycle of offering: **Term 3

**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 Aims

This course has two strands, Vector Calculus and Complex Analysis, both of which are important for engineering students. These topics bring together calculus and linear algebra and have many applications to physics, engineering and mathematics, and are particularly important for electrical engineers.

Vector Calculus deals with calculus in two and three dimensions, and develops the theory of curves, vector functions and partial derivatives, two and three dimensional integration, line integrals and curl and divergence. [Applications include mechanics and dynamics, electrostatics, graphics and design.]

Complex Analysis extends calculus from real numbers to complex numbers, and develops the theory of analytic functions, complex integration and Cauchys theorem, series expansions, the residue theorem and applications to real improper integrals and trigonometric integrals. [Applications include fluid flow, electrostatics, circuit theory, and heat flow.]

#### Course Description

**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. Note: Available only to students for whom it is specifically required as part of their program.