Video of the lecture.

Explained that the aim of the module is to understand and apply Stokes' formula using the language of differential p-forms in n variables. Stokes hails from just up the road in Sligo so it seems appropriate to devote a 24-lecture module to his formula.

We'll use the language of differential forms because of its elegance and simplicity. In this first lecture I focussed on n=1 variable and p=0 and gave the definition of a differential 0-form in one variable. Differential forms are defined with respect to some nice oriented region S in ℝⁿ. I explained what I mean by such a region for n=1: namely the union of a collection of disjoint oriented closed intervals. I explained what is meant by the (oriented) boundary of such a region and ended with the definition of the integral of a 0-form in 1 variable over the boundary of a 1-dimensional oriented region in ℝ.