1. Solve geometric problems in three dimensional space using vectors and their operators.
2. Calculate derivatives and integrals of vector functions to solve problems involving arc length and curvature of space curves.
3. Apply the concept of the limit, continuity and partial derivative of a function of many variables as well as calculate tangent planes, linear approximations and differentials.
4. Apply the chain rule, directional derivatives and the gradient vector to solve problems, particularly multivariable optimisation problems either with or without constraints.
5. Calculate double & triple integrals over general regions, and also in polar, cylindrical and spherical coordinates.
6. Apply the change of variables technique to simplify the evaluation of a double or triple integral.
7. Evaluate line integrals both in space and of vector fields, plus solve problems involving the curl and divergence of a vector field.
8. Calculate the surface integral of a scalar function or of a vector field, plus use Green’s theorem, Stokes’ Theorem and the Divergence Theorem to solve problems.
9. Use mathematical software to visualise, analyse and solve problems in multivariable calculus.