#### deepa08

##### Well-Known Member

**An Introduction To Analysis Of The Infinite Book I &11 Euler**

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..."

This is a seminal text by one of history's greatest mathematicians. Unique to his great mathematical peers, Euler was also an extraordinary teacher and expositor. His enthusiasm and genius pour through the pages of this book, with Euler making his characteristically bold and ingenious symbolic arguments to come up with many of the well known formulas that were probably mentioned in your math class. For example, Euler brilliantly uses basic algebra (plus infinitesimals) to come up with some very deep and beautiful formulas, such as Sine's infinite product, e's continued fraction expansion and much more. In fact, if you have ever wondered how all of Euler's beautiful formulas that you saw in class were actually derived; here is your chance to get it straight from the genius who discovered them!

As with any book by a mathematician of the highest rank, this is wholly different from any modern "textbook" and should NOT be considered as such. The should be used for self study or as a compliment to a calculus course, or perhaps most of all (like it was intended in those days believe it or not), be read for the pure enjoyment of the subject. Its format is much more flowing and intuitive than a modern textbook; Euler presents clearly stated mathematical arguments (numbered in order), which he then uses and cites later on to produce more mathematical arguments. He also seems to subtly encourage the reader to pursue various ideas for themselves, lending a certain adventurous quality that in NEVER encountered in the "modern" crap texts.

Be forewarned though; it is NOT for the symbolically weak. If you lack skills in basic algebra its best to brush up before you read this book. Just because it is a "pre-calculus" text does not at all mean that this is elementary. This IS however a relatively easy read IMO due to Euler's intuitive style. Euler is the by far the most accessible compared to his modern peers; Newton and Gauss.

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