MATH2111 is a Pure Mathematics Level II course which applies the ideas of calculus and linear algebra to functions of several variables. See the course overview below.

**Units of credit:** 6

**Prerequisites: **MATH1231 or MATH1241 or MATH1251 or DPST1014 each with a mark of at least 70

**Exclusions:** MATH2018, MATH2019, MATH2069, MATH2011

**Cycle of offering:** Term 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.

MATH2111 (alternatively MATH2011) is a compulsory course for Mathematics majors and for Statistics majors.

If you are currently enrolled in MATH2111, you can log into UNSW Moodle for this course.

#### Course Aims

The aim of this course is to deepen your understanding of the ideas and techniques of integral and differential calculus for functions of several variables. These ideas and techniques are crucial to mechanics, dynamics, electromagnetism, fluid flow and many other areas of pure and applied mathematics. The course combines and extends ideas from one variable calculus and linear algebra to establish the calculus of vector - valued functions: from differentiation through multiple integration to integration over curves and surfaces and the classical Stokes' and Divergence Theorems. The emphasis is on understanding fundamental concepts, developing spatial understanding and acquiring the ability to solve concrete problems.

#### Course Description

Functions of several variables, limits and continuity, differentiability, gradients, surfaces, maxima and minima, Taylor series, Lagrange multipliers, chain rules, inverse function theorem, Jacobian derivatives, double and triple integrals, iterated integrals, Riemann sums, cylindrical and spherical coordinates, change of variables, centre of mass, curves in space, line integrals, parametrised surfaces, surface integrals, del, divergence and curl, Stokes' theorem, Green's theorem in the plane, applications to fluid dynamics and electrodynamics, orthogonal curvilinear coordinates, arc length and volume elements, gradient, divergence and curl in curvilinear coordinates.