This screencast defines the four second-order partial derivatives that can be calculated for a function of two variables, and then demonstrates their calculation in practice for a specific example.

We look at several examples of adding and subtracting positive and negative numbers, including examples where there are two immediately adjacent signs (e.g. two negative signs).

An example of solving a second order differential equation (where the right hand side is an exponential function), given specific initial conditions y(0) and y'(0) are also provided.

A demonstration of how to tranpose the formula y=(ae^t+be^(-t))/(ce^t+de^(-t)) to make t the subject.

An example of calculating partial fractions when one of the factors on the denominator is a repeated linear factor.

An example of integrating a function that is a product of an odd power of tan x and a power of secx.

An example of how double-angle formulae can be used to help with integrating sin^2 x and cos^2 x

An example of using integration by substitution to integrate the function (sqrt(1+sqrtx))

The general principle is explained of how to divide one complex number by another when both numbers are written in Cartesian form, so that the denominator of the final answer is a real number. A specific example of using ...

This screencast shows the general method, together with an example, of finding the equation of a straight line in 3D in vector form, scalar parametric form and Cartesian form.