Essay on the Metaphysics of the Integral Calculus

By C.A. Agardh and Carl Adolph Agardh

This is a translation of 'Essai sur la Metaphysique du Calcul Integral' by C. A. Agardh, available from www.e-rara.ch If you have ever experienced difficulty in swallowing the Integral Calculus, or even the Fundamental Theorem of Calculus, then this little work may be the digestive for you. In the author's own words: 'The theory of the integral calculus which we are going to expound in the pages following, is wholly elementary. It does not require any higher mathematical knowledge than of having made oneself well familiar with the calculus of finite differences. It does not suppose any hypothesis, either of limiting ratios, or of limits, or of infinitesimals, nor of derivative functions.' By means of a finite backward difference, the author demonstrates that the sum of those rectangles, which together represent the area under a curve, is composed of an invariable term, which is the precise integral of the curve, plus a series of residual terms dependent upon delta-x or delta-y, which represent the areas of those triangular bits and pieces salient to the curve. But those salient bits and pieces do have their use: they may be used to find an area external to the curve. The method adopted in this little work is worthy of displacing conventional methods of presenting the integral calculus.

• Format: Paperback
• Language: English
• ISBN: 1724299050
• ISBN13: 9781724299055
• Release Date: August 2018
• Publisher: CreateSpace Independent Publishing Platform
• Length: 40 Pages
• Weight: 0.24 lbs.
• Dimensions: 9.0" x 0.1" x 6.0"