MATH2011 Several Variable Calculus

MATH2011 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

Exclusions: MATH2018, MATH2019, MATH2069, MATH2111

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.

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

If you are currently enrolled in MATH2011, you can log into UNSW Moodle for this course.

Course Aims

This course introduces the mathematics crucial to mechanics, dynamics, electromagnetism, fluid flow, financial modelling and many areas of pure and applied mathematics. The course combines and extends the ideas from one variable calculus and linear algebra to develop the calculus of functions in R2 and R3. The final topic is an introduction to Fourier series, which concerns the representation of functions of a single real variable by infinite trigonometric series. In this course, the connection between diagrams/visualization and symbols is particularly important. Understanding that relationship is one of the main aims of the course.

 

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. Vector calculus, line integrals, parametrised surfaces, surface integrals, del, divergence and curl, Stokes' theorem, Green's theorem in the plane, applications to fluid dynamics and electrodynamics. Fourier Series.