Gives the general formula then applies this to an example. Cartesian form is convert to polar form, then the required power of the number is calculated, and finally the result is converted back into Cartesian form.

We look at how to simplify algebraic fractions when there is a number and/ or power of a letter that is common to all terms on the numerator and denominator, thus allowing us to simplify the original fraction by cancelling out this common factor.

Investigates the scalar triple product in the context of the volume of a parallellepiped.

We find the equation of the tangent to a curve at a specific point, by first finding the general expression for the derivative of the curve, then evaluating it at the point, and then using this information to find the equation of the tangent.

Gives a basic example of implicit differentiation to find dy/dx, and compares this to the result from explicit differentiation for the same example. Second example is a circle, with graphical interpretation of dy/dx in two points.

In this recording we look at how to rearrange a formula where the letter that we want to make the subject is in the denominator. That is, we look how to make f the subject when presented with an expression of the form a/b = c/d + e/f.

We derive a general formula for the Laplacian acting on a function f(r) then demonstrate that the Laplacian is zero in the case that f(r) = 1/r, thereby showing that 1/r is harmonic.

We show that div(curl(v)) and curl (grad f) are 0 for any vector field v(x,y,z) and scalar function f(x,y,z).

We show that div(curl(v)) and curl (grad f) are 0 for any vector field v(x,y,z) and scalar function f(x,y,z).

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