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

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

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.

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

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.

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

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

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

The quotient rule for differentiation is proved from first principles.

Integration by parts is used to integrate the product of two polynomials.