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'.

This screencast demonstrates how to solve a first-order separable differential equation in the case where the right hand side of the equation is a mixture of x and y terms that needs to be factorised so that the equation can be separated and solved.

This screencast gives an example of how to solve the first order separable differential equation: 2x/((1+x^2)y)

Explains graphically what it means to multiply a matrix and a vector. Then introduces eigenvectors as vectors belonging to the matrix with a special property in matrix vector multiplication. Eigenvalues are also explained in this context.

We explain what is meant by an even function in terms of symmetry, then give a rule satisfied by the function. We show how to test for evenness then discuss the area under the graph of an even function between points an equal distance of the y axis.

We explain what is meant by an odd function in terms of symmetry, then give a rule satisfied by the function. We show how to test for oddness then discuss the area under the graph of an even function between points an equal distance of the y axis.

We continue the theme of half range series and examine how the integrations can be simplified using the symmetry of the function. Here we examine a half-range cosine series for a linear f(t).

This recording shows how velocity and acceleration of a particle travelling through 3D space are calculated given we have a general vector expression for the position vector at time t - this is then illustrated with a specific example.

Solve a question about finding the roots of a complex number.