MTH2015 Multivariable calculus (advanced)

When you finish this unit, you should be able to:

1. 1

   Apply multivariable calculus techniques to solve problems in mathematics, physics, and related disciplines;

2. 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. 3

   Find and classify extrema of functions of several variables, including constrained optimisation using Lagrange multipliers;

4. 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. 5

   Communicate mathematical reasoning effectively, both orally and in writing, and collaborate to analyse and solve problems using multivariable calculus techniques;

6. 6

   Extend and deepen understanding of multivariable calculus through advanced theoretical concepts, rigorous proofs, and exposure to additional topics such as curvature and torsion, stereographic projection, uniform convergence, and analytic functions.