The Integral Calculus of Finite Differences - Softcover

Fontana, Gregorio

Softcover

ISBN 10: 1545392633 ISBN 13: 9781545392638

Publisher: CreateSpace Independent Publishing Platform, 2017

Synopsis

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 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 reciprocal 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.

Edition details

• Publisher: CreateSpace Independent Publishing Platform
• Publication date: 2017
• Language: English
• ISBN 10: 1545392633
• ISBN 13: 9781545392638
• Binding: Paperback
• Edition number: 1
• Number of pages: 56