Introduction to Analysis of the Infinite: Book I / Edition 1

by Leonhard Euler, J.D. Blanton

Overview

From the preface of the author: "...I have divided this work into two books; in the first of these I have confined myself to those matters concerning pure analysis. In the second book I have explained those thing which must be known from geometry, since analysis is ordinarily developed in such a way that its application to geometry is shown. In the first book, since all of analysis is concerned with variable quantities and functions of such variables, I have given full treatment to functions. I have also treated the transformation of functions and functions as the sum of infinite series. In addition I have developed functions in infinite series..."

Product Details

ISBN-13:	9780387968247
Publisher:	Springer New York
Publication date:	09/21/1988
Edition description:	1988
Pages:	327
Product dimensions:	6.40(w) x 9.30(h) x 1.00(d)

Table of Contents

I. On Functions in General.- II. On the Transformation of Functions.- III. On the Transformation of Functions by Substitution.- IV. On the Development of Functions in Infinite Series.- V. Concerning Functions of Two or More Variables.- VI. On Exponentials and Logarithms.- VII. Exponentials and Logarithms Expressed through Series.- VIII. On Transcendental Quantities Which Arise from the Circle.- IX. On Trinomial Factors.- X. On the Use of the Discovered Factors to Sum Infinite Series.- XI. On Other Infinite Expressions for Arcs and Sines.- XII. On the Development of Real Rational Functions.- XIII. On Recurrent Series.- XIV. On the Multiplication and Division of Angles.- XV. On Series Which Arise from Products.- XVI. On the Partition of Numbers.- XVII. Using Recurrent Series to Find Roots of Equations.- XVIII. On Continued Fractions.

Editorial Reviews

A classic mathematical monograph by L. Euler (1748), which has previously been available to readers of French, German, and Russian, but is here (at the suggestion of Andre Weil) being made available to readers of English for the first time. To peruse these pages is to be introduced to the mental processes of a master, and to experience a pleasure as ever-fresh as Mozart. In the present instance even the typography adds to the pleasure. A treasure, which will be of enduring value on the shelves of mathematical libraries. (NW) Annotation c. Book News, Inc., Portland, OR (booknews.com)

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