Visualization of the Riemann–Stieltjes Integral

Summary

It is desirable to have geometric interpretations of difficult mathematical concepts. In this paper, we present an intuitive geometric interpretation of the Riemann–Stieltjes integral. It can be summarized as follows: the Riemann–Stieltjes integral can be interpreted as an infinite sum of infinitesimally small non-rectangular integration strips. This interpretation is surprisingly similar to the geometric interpretation of the ordinary Riemann integral. It is therefore likely that students, when encountering the Riemann–Stieltjes integral for the first time, would find this new geometric framework a useful visualization tool.

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Notes on contributors

Trienko Grobler

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Trienko Grobler ([email protected]) received his PhD in Engineering at the University of Pretoria in 2013. He was a postdoctoral fellow at Rhodes University from 2013 to 2016. He joined the Computer Science Division of Stellenbosch University in 2017. His research interests include remote sensing and interferometry.