Demonstrates the general method and two examples of using the definitions of sinh(x) and cosh(x) to prove hyperbolic function identities

We derive the formula for the Laplace transform of df/dt in terms of that for f(t) and f(0). It is then shown how to extrapolate the rule to write down the transforms for 2nd, 3rd and higher derivatives.

We examine some double integrals with Cartesian variables x and y. We investigate the integration limits and relate them to the 2D region of integration in the x-y plane. This is preparatory to reversing the order of integration.

The conditions for equality of complex numbers are given. An example of grouping and then equating real and inaginary parts of complex numbers on both sides of an equation to find unknown quantities is then given.

Gives basic arithmetic rules and index laws for working with 0 and applies them to several examples.

Provides 2 worked examples of differentiating square roots, cube roots, etc. of x. Gives the viewer 3 sample questions of a similar nature at the end with solutions.

Covers one example of finding the determinant of a 3x3 matrix. Note at the end regarding the fact that if the determinant equals zero then that matrix has no inverse.

Outlines the general formula for finding the determinant of a 2x2, then goes through one simple example. Note at the end regarding the fact that if the determinant equals zero then that matrix has no inverse.

Further example of how to apply the Quotient rule. Recapped on the steps involved also. Practice questions at the end with solutions for students to try themselves

Introduction to the Quotient rule, outlining when and how to apply it with one example. Steps involved are outlined also.