Explains the concept of a right angled triangle and introduces pythagoras theorem.

We introduce the points of the compass and solve a simple example using distances and basic directions (N,S,E,W) to find resulting distance and angle.

The general principle of the trapezoidal rule of numerical integration is given. A specific example of applying it is then given.

Part 3 of 3. Continuation from part one, looking at increasingly complicated examples of reversal of integration order.

Gives the definition and conditions for the inverse of a function to exist, and then applies this to an example the case of finding the inverse of a one-to-one function.

We expand the binomial series for the case n = 1/2 to evaluate an approximation for the square root of 2. Convergence is discussed briefly then we deal with the case when the first term in the binomial expression is a constant other than one.

Gives the definition and conditions for the inverse of a function to exist, and then applies this to an example where the original function is not one-to-one and where the domain of f(x) hence needs to be restricted in order to define the inverse function.

Introduction to 'head to tail' vector subtraction in the geometric sense. This is then applied to an example of working out a boat's velocity relative to water given the velocity of the current and the velocity of the boat relative to land are both known.

Introduction to "head to tail" vector addition in the geometric sense. This is then applied to an example of working out a boat's velocity relative to land given the velocity of the current and the velocity of the boat relative to water are both known.

We investigate the linear dependence or independence of a set of 3 vectors in 3 dimensions. We show how the determinant of a 3 by 3 matrix can assist in this process.