We choose a simple scalar function f(x,y,z) and calculate its gradient.

We calculate the divergence and curl of a simple vector field

Six short examples useful as preparation for implicit differentiation. Some require the chain rule, others are straightforward differentiations.

We ask if a matrix can be raised to the power of a matrix and do a simple 2 by 2 example.

We show how complex number arithmetic can be performed using matrices for the complex numbers.

We look at cases when we can add and subtract surds- namely when terms can be re-written with the same number under the square root sign. Two examples are given- in the second example the surds need to be simplified before adding/ subtracting them.

We look at a numerical example for an RLC circuit and calculate the complex impedance and phase difference.

We continue investigation of the RLC circuit, introducing complex versions of voltage and current. The complex impedance results naturally from these quantities and gives a clear picture of why the current and voltage differ by a phase, and by how much.

We look at several examples of adding and subtracting fractions, by first obtaining a common denominator.

We investigate the RLC circuit and obtain a relation between voltage and current without use of complex quantities. We see that the relation is rather cumbersome and not transparent.