Riemann Sums App

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Dr Andrew Morris required a tool which explained the concept of the Riemann definition of integration. The app provides a visualisation of Riemann summation of a function (which limits to the area under the curve under some assumptions), and has run the app for multiple years.

Upon first teaching the course, he found that students found struggled with the difference between the supremum and infimum. The basic idea is to approximate the area under a curve using a sequence of rectangles. The width is given by the number of intervals the x-axis is split up into, but the height of the rectangle is more of a choice. One can take the largest value the function takes in the interval (the supremum or upper Darboux integral), or the smallest value (the infimum or lower Darboux integral), or indeed any point within the interval (a “tagged partition”). The app provided to Dr Andrew Morris provides students with a way of visualising this process.

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