We derive a formula to simplify the process of taking the curl of the curl of a vector field. The algebra is rather complicated!

We continue the theme of half range series and examine how the integrations can be simplified using the symmetry of the function. Here we examine a half-range sine series for a linear f(t).

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.