A Treatise on the Calculus of Finite Differences

by George Boole

Overview

Written by a great English mathematician, this classic text begins with the differences of elementary functions and explores interpolation, mechanical quadrature, finite integration, and the summation of series. Several useful tests for the convergence and divergence of series are developed, as is a method for finding the limits of error in series expansions. The latter half of the book discusses difference-equations, including linear, mixed, and partial difference-equations, and concludes with applications to problems in geometry and optics. The text pays particular attention to the connection of the calculus of finite differences with the differential calculus, and more than 200 problems appear in the text (some with solutions). Unabridged republication of the classic 1872 edition.

Product Details

ISBN-13:	9780486158525
Publisher:	Dover Publications
Publication date:	03/05/2014
Series:	Dover Books on Mathematics
Sold by:	Barnes & Noble
Format:	eBook
Pages:	352
File size:	32 MB
Note:	This product may take a few minutes to download.

Table of Contents

Preface to the first edition; Preface to the second edition; 1. Nature of the calculus of finite differences; 2. Direct theorems of finite differences; 3. On interpolation, and mechanical quadrature; 4. Finite integration, and the summation of series; 5. The approximate summation of series; 6. Bernoulli's numbers, and factorial coefficients; 7. Convergency and divergency of series; 8. Exact theorems; 9. Difference-equations of the first order; 10. General theory of the solutions of difference- and differential equations of the first order; 11. Linear difference-equations with constant coefficients; 12. Miscellaneous propositions and equations. Simultaneous equations; 13. Linear equations with variable coefficients. Symbolical and general methods; 14. Mixed and partial difference-equations; 15. Of the calculus of functions; 16. Geometrical applications; Answers to the exercises.