The Integral Calculus of Finite Differences

By Gregorio Fontana

This is a translation of "Opuscoli Matemateci sopra il Teorema della Composizione delle Forze; e sopra il Calcolo Integrale delle Differenze Finite" by Gregorio Fontana, available from http://www.e-rara.ch/This is a broad but challenging introduction to Finite Differences, requiring of the reader a basic knowledge of differential and integral calculus, including the solution of differential equations, plus some acquaintance with series and finite difference equations. The contents comprise the following topics:Summation of some simple series.Integration of differential fractions.Summation of inverse series.The general term of a series with constant finite difference of some order.Summation of the foregoing series.Integration of a particular form of linear finite difference equation with variable coefficients.Solution to a particular recurrency relation.A Chess problem: given a starting and a finishing square, in how many ways may a castle pass from start to finish in just x moves? The solution requires the simultaneous solving of three first-order linear finite difference equations with constant coefficients.Basic notions of finite differences of more than one variable.The fitting of regular observed data to a describing equation.+Comment on the composition of two Newtonian forces into a single force.

• Format: Paperback
• Language: English
• ISBN: 1545392633
• ISBN13: 9781545392638
• Release Date: May 2017
• Publisher: CreateSpace Independent Publishing Platform
• Length: 56 Pages
• Weight: 0.30 lbs.
• Dimensions: 9.0" x 0.1" x 6.0"