A discussion of how to sketch complex regions of form Iz-z0I<r, lz-zol>r and related cases, This is then demonstrated with a specific example.

This recording demonstrates use of the quadratic formula in relation to three examples: one with 2 distinct solutions, one with a repeated solution and one with no real solutions. The discrminant function is introduced in relation to this.

A demonstration of how to apply the identity (cosh(x))^2-(sinh(x))^2 = 1 and the graphical properties of sinh(x) and cosh(x) to finding sinh(x) if cosh(x) is known and vice versa.

3 examples based on differentiating logs with questions at the end for students to try themselves, solutions given also.

We investigate the significance of differentiating a Laplace transform and relate the derivative to the inclusion of an extra factor of 't' in the original transform. The idea is extended to multiple derivatives and powers of t.

We introduce the Heaviside step function and show how it can be used to turn other functions on and off at different positions along the t-axis.

Worked example for solving limits where x is approaching infinity. Includes graph of the function, explanation of the steps involved and why these steps are taken.

Shows how to check if a polynomial is even or odd, and extends this to a rational function.

We investigate the Laplace transform of a function when multiplied by the Heaviside step-function. The 2nd shift theorem is introduced. It is shown how to prepare a function for use with the 2nd shift theorem.

Defines the Laplace transform. Briefly describes the uses of a Laplace transform then deals with technical issues such as what is meant by infinity integration limit. Concludes with explanation of the restrictions on the Laplace variable 's'.