The general formulae for multiplication and division of complex numbers in polar form are given and their use is then demonstrated in relation to a particular example

This recording shows that it is possible to multiply by an expression containing a variable in an inequality - as long as one keeps track of when the expression is positive or negative.

Defines the factorial function and shows examples where it is used: e.g. in the MacLaurin series for exp(x), for cos(x), but also in nCr (n choose r). It concludes with a proof that 0!=1, using the Gamma function.

Example of how to use the Guide Number method to solve a quadratic equation

Example of how to use the Guide Number method to solve a quadratic equation

Starts with an introduction to the equation of a straight line in 3D in both Cartesian and vector form. An example is then given of converting the Cartesian equations of a straight line into its scalar parametric equations and hence its vector equation.

A discussion of when matrix addition, subtraction and multiplication are defined, and when it is possible to calculate matrix determinants and inverses, based on the order of the matrices concerned.

We examine the integration involved in calculating some Fourier coefficients and discuss the approach to be taken when one has a formula sheet in comparison with having to calculate the integral on paper.

We introduce geometric series in which the variable is a quantity other than x or the constant is not 1. Convergence is discussed and we show how to get a series that converges when the absolute value of x is greater than 1 or some other number.

We introduce the basic geometric series in powers of x, investigate the partial sums and demonstrate that the series sums to 1/(1-x) for x between -1 and 1.