Detailed discussion of using Laplace transform to solve a 1st order ODE.

Sketch of y =(x+1)^3-2.

In this recording we look at an example of differentiation using the inverse function rule.

Standard pair of linear, coupled 1st order DE's solved by Laplace transform method.

Demonstration of using Laplace transform to solve a 2nd order, linear, non-homogeneous, constant coefficient DE with boundary conditions and with right hand side appearing in the CF.

Sketch of y = 2(x+2)(x-2)(x+3).

We solve a non-homogeneous 2nd order constant coefficient ODE with boundary conditions using the Laplace transform method. A check is applied to the solution. The process of solving is then repeated with a deliberate error and it is demonstrated that not all checks can identify the error. We identify the feature that boundary conditions can be more effective than the original ODE in identifying errors.

Brief and simple introduction to the first shift theorem for Laplace transforms.

Sketch of y = 2(x+1)^2-3.

Brief introduction to why we use Laplace transforms, with mention of tables.