Analysis and the calculus
Branch · 1660s-1870s, Europe · Mathematics, stage 2: Map the branches
Newton and Leibniz independently assembled the calculus in the 1670s and 1680s, giving a systematic way to compute rates of change and accumulated quantities and showing that the two operations are inverse to each other. The methods worked and the justification did not: both relied on quantities that were treated as nonzero and then discarded as zero. Analysis is the branch that put the subject on a footing, replacing infinitesimals with limits in the nineteenth century and then re-examining what functions, continuity, and integration actually mean.
What it claims
- Change and area can be computed exactly by taking limits of approximations that are individually inexact.
- Differentiation and integration are inverse operations.
- The concepts of calculus have to be defined by limits rather than by appeals to infinitely small quantities.
Key ideas
People
Sources
- Mathematical analysis Wikipedia
- Calculus history MacTutor History of Mathematics
