Learning Outcomes:
On completion of this module students should be able to
1. Write down parametric equations for lines and planes, and perform standard calculations based
on these equations (e.g. points/lines of intersection, condition for lines to be skew);
2. Compute the Frenet-Serret vectors for an arbitrary differentiable curve;
3. Compute the series expansion of important functions using Taylor's theorem;
4. Differentiate scalar and vector fields expressed in a Cartesian framework;
5. Perform operations involving div, grad, and curl;
6. Perform line, surface, and volume integrals. The geometric objects involved in the integrals
may be lines, arbitrary curves, simple surfaces, and simple volumes, e.g. cubes, spheres,
cylinders, and pyramids;
7. State precisely and prove Gauss's and Stokes's theorems;
8. Derive corollaries of these theorems, including Green's theorems and the necessary and sufficient condition for a vector fueld to be derivable from a potential;
9. Compute the scale factors for arbitrary orthogonal curvilinear coordinate systems;
10. Apply the formulas for div, grad, and curl in arbitrary orthogonal curvilinear coordinate systems;