MTH2010 · Multivariable calculus

Overview

Functions of several variables, partial derivatives, extreme values, Lagrange multipliers. Multiple integrals, line integrals, surface integrals. Vector differential calculus; grad, div and curl. Integral theorems of Gauss and Stokes.

Areas of study: Applied mathematics Astrophysics Climate and atmospheric science Financial and insurance mathematics Mathematical statistics Mathematics Physics Pure mathematics

Offerings

Assessment

The Handbook lists an examination for this unit.

Assessment details may change. Please refer to the assessment information in Moodle closer to the start of the teaching period.

Requisites

Learning outcomes

1. Apply multivariable calculus techniques to solve problems in mathematics, physics, and related disciplines;
2. Explain the definition of the derivative of a multivariable function and its geometric interpretation as the tangent plane, as well as its relation to the gradient and directional derivative;
3. Find and classify extrema of functions of several variables, including constrained optimisation using Lagrange multipliers;
4. Evaluate and interpret line, surface, and volume integrals in Cartesian, cylindrical, and spherical coordinates, and apply the integral theorems of Green, Gauss, and Stokes;
5. Communicate mathematical reasoning effectively, both orally and in writing, and collaborate to analyse and solve problems using multivariable calculus techniques.

Workload

• Three 1-hour seminars; • One 2-hour applied class (in weeks 2-12) and • 7 hours of independent study per week.

Student experience, not official rules. Nothing here changes what the Handbook says.