Syllabus

1. Interpretations of graphs and tables of functions of two and three variables, including contour plots. Also the sketching of simple functions in two variables and contour plots of functions of two and three variables.
2. Computation involving vectors, such as vector addition, scalar multiplication, as well as calculating dot and cross products and magnitudes and projections of vectors. Applications of vectors to solve problems in other areas.
3. Differentiation of functions of several variables. Partial and directional derivatives. Gradients and differentials in several variables, and consideration of linearisations of functions in several variables.
4. Computing critical points of functions in several variables and using the second derivative test to determine the nature of such points. Using critical point techniques to solve optimisation problems. Lagrange multipliers.
5. Double and triple integrals. Change of variables between Cartesian coordinates to cylindrical and spherical coordinates.
6. Use parametrisation to describe curves and surfaces.
7. Understand vector fields and be able to compute the flow within such a field.
8. Integrate over vector fields (including line integrals, flux etc.)