For a specific example, this recording demonstrates the process involved in multiplying two binary numbers using long mutliplication.

In this recording we calculate j to the power of j by first converting j into exponential polar form. We then also see that there are an infinite number of values for j to the power of j.

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.

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.

We show how the Cayley-Hamilton theorem can be used to give an expression for any power of a 2 by 2 matrix. The method is used to find the 4th power of a given matrix.

We use the Cayley-Hamilton method to find all four square roots of a given 2 by 2 matrix.

This recording demonstrates how to integrate rational functions where the denominator is a quadratic function and the numerator is a linear function which is a constant multiple of the derivative of the denominator. Integration by substitution is used.

This recording demonstrates how to integrate rational functions where the denominator is a quadratic function and the numerator is a linear function which is a constant multiple of the derivative of the denominator. Integration by substitution is used.

We use the Cayley-Hamilton method to find all four square roots of a given 2 by 2 matrix.

We show how the Cayley-Hamilton theorem can be used to give an expression for any power of a 2 by 2 matrix. The method is used to find the 4th power of a given matrix.