Synopsis
( 4 ) CHAPTER II. direct theorems of finite differences. 1. The operation denoted by A is capable of repetition. For the difference of a function of x, being itself a function of x, is subject to operations of the same kind. In accordance with the algebraic notation of indices, the difference of the difference of a function of x, usually called the second difference, is expressed by attaching the index 2 to the symbol A. Thus AAws= AX- In like manner AAX = AX, and generally AA"~X = AX (1), the last member being termed the nth difference of the function ux. If we suppose ux = »3, the successive values of ux with their successive differences of the first, second, and third orders will be represented in the following scheme: Values of X 1 2 3 4 5 6 . 1 8 27 64 125 216 At*. 7 19 37 61 91 ... AX 12 18 24 30... AX 6 6 6... It may be observed that each set of differences may either be formed from the preceding set by successive subtractions in accordance with the Table of Contents
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Paperback. Condition: New. Print on Demand. This book delves into the fascinating world of the Calculus of Finite Differences, a mathematical system that explores the relationships between changing quantities. The author meticulously explains how this calculus is closely intertwined with the Differential Calculus, a more familiar concept, and how the two systems often mirror each other in surprising ways. The book explores the fundamentals of this calculus, including its central operations, and delves into the core theorems that govern how differences are calculated and expressed. This exploration leads the reader to understand how the Calculus of Finite Differences can be used to solve problems in a variety of fields, including physics, engineering, and economics. By providing clear explanations and insightful examples, the author reveals the rich history of this branch of mathematics, showcasing the connections between the work of earlier mathematicians, such as Lagrange and Euler, and its continuing relevance in modern times. This book offers a comprehensive and accessible guide to the Calculus of Finite Differences, making it an invaluable resource for students and mathematicians alike. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. print-on-demand item. Seller Inventory # 9781440059001_0
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Calculus of Finite Differences: Fourth Edition (Classic Reprint)
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TREATISE ON THE CALCULUS OF FI
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Condition: New. KlappentextrnrnExcerpt from A Treatise on the Calculus of Finite DifferencesAs such Treatises as the present are in close connexion with the course of Mathematical Study at the University Of Cambridge, there is considerable difficulty in. Seller Inventory # 2148536323
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