In this article, my focus will be on the work of Leibniz, and I will show, based mainly on the analysis in Dunham and Mena, how he derived the well-known formula for the integration by parts.
Modern calculus, *which can be defined as *“the mathematical study of continuous change,” was developed independently by two of the great thinkers of the 17th and 18th centuries, namely, Isaac Newton and Gottfried Wilhelm Leibniz.
Figure 1: A portrait and a statue (without the wig) of Leibniz.
For an article about Isaac Newton’s early mathematical achievements, see the link below.
Gottfried Wilhelm Leibniz was the quintessential polymath. He made fundamental contributions to a broad range of topics, including philosophy, mathematics, linguistics, theology, engineering, jurisprudence, law, computer science, and geology. Leibniz once remarked that he often needed to use a substantial part of his week to document the thoughts of just a single morning (for an outstanding biography of Leibniz, see Antognazza).
In English, the titles are, respectively:
The title pages are shown in Fig. 3 below.
Figure 3: The three most famous articles on the Calculus that Leibniz published in the scientific journal Acta Eruditorum (source)
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