Introduction to Analysis of the Infinite: Book I

by Leonhard Euler, J.D. Blanton (translator)

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..."

Genres: Mathematics, Science, Nonfiction

Kindle Edition

First published December 31, 1921

About the author

Noted Swiss mathematician Leonhard Euler worked in analysis and algebra, including complex numbers and logarithms, and he introduced much of the basic notation in mathematics.

This pioneering physicist made important discoveries in fields as diverse as infinitesimal calculus and graph theory. He also introduced much of the modern terminology, particularly for analysis, such as the notion of a function. He is also renowned for his work in mechanics, fluid dynamics, optics, astronomy, and music theory.

People considered Euler the preeminent mathematician of the 18th century and one of the greatest who ever lived. He is also one of the most prolific mathematicians; his collected works fill sixty to eighty quarto volumes. He spent most of his adult life in Saint Petersburg, Russia, and in Berlin, Prussia.

A statement, attributed to Pierre Simon de Laplace, expresses influence of Euler on mathematics: "Read Euler, read Euler, he is the master of us all."

Reviews

[Connor McDonnell · Rating 5 out of 5]

An absolute masterpiece, this text should be the standard precalculus text book as it explains functions, infinite series and eulers formula so well. Euler isnt just a genius , he is a great teacher , he explains exactly how to prove his famous formula , though it should be noted that his proofs may not be acceptable by todays rigor ( as cauchy disproved the generality of algebra , something that virtually every proof in the book hinges on) .Still nevertheless it may not be formal proofs, it EXPLAINS THE PROCESS OF DERIVING such ideas from what appears to be thin air.

So to reiterate .If you want a perfect precalculus textbook for those in secondary school , this is the book for you. If you want to know where Eulers formula comes from , this o the book for you . If you want to know where euler/napiars constant comes from , this is the book , if you want to see first hand where the trig functions are represented in their modern form. .....etc. I could go on forever , and to quote Laplace "read euler , he is the master of us all".

[Michael Walker · Rating 5 out of 5]

The most gifted mathematician in the history of the human race. In book 1, Leonhard with ultimate clarity writes the conceptual maths that begin to touch on and then grasp at the infinite. Although no exact place exists anywhere in the history of mathematics where Euler's Identity is written where it is set to zero, Analysis of the Infinite describes the Identity using for instance the square root of negative one representing the same thing, so there is no guessing here - Leonhard is the discoverer of the Identity. That is to say, Euler does not set the Identity to zero in Analaysis of the Infinite, but it is expressed there. Lots of other fabulous surprises are in this book. He is the apples-to-oranges equivalent of a Shakespeare within the field of mathematics.