We investigate linear independence for a set of three vectors in four dimensions and demonstrate how to decide on their (in)dependence using Gaussian elimination.

This recording demonstrates the general method for solving an equation of form sqrt(ax^2+bx+c) = cx+d and then illustrates this with an example, including checking solutions that were generated by squaring both sides to see which ones satisfy the original equation.

An introduction to the Newton-Raphson method for finding a numerical solution of f(x) = 0, explaining what the method is (including graphical illustration of the method)

A demonstration of how to use the Newton-Raphson method: to find the positive solution of the equation x^2 = 2

An example of using integration and the 'disk method' to find the volume of a 3D solid that is obtained when the region bounded by 2 curves is revolved about the x-axis

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

An example of using integration to find the area of a region that is bounded by 2 curves

An example of using integration and the 'disk method' to find the volume of a 3D solid that is obtained when the region between a curve, the x-axis and two vertical lines is revolved about the x-axis

An example of integrating a function that is a product of an even power of sec x and a power of tanx

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