Dr. Euler's Fabulous Formula: Cures Many Mathematical Ills

Dr. Euler's Fabulous Formula: Cures Many Mathematical Ills

by Paul J. Nahin
     
 

ISBN-10: 0691118221

ISBN-13: 9780691118222

Pub. Date: 04/10/2006

Publisher: Princeton University Press

I used to think math was no fun

'Cause I couldn't see how it was done

Now Euler's my hero

For I now see why zero

Equals e[pi] i+1

—Paul Nahin, electrical engineer

In the mid-eighteenth century, Swiss-born mathematician Leonhard Euler developed a formula so innovative and complex that it continues to inspire research,

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Overview

I used to think math was no fun

'Cause I couldn't see how it was done

Now Euler's my hero

For I now see why zero

Equals e[pi] i+1

—Paul Nahin, electrical engineer

In the mid-eighteenth century, Swiss-born mathematician Leonhard Euler developed a formula so innovative and complex that it continues to inspire research, discussion, and even the occasional limerick. Dr. Euler's Fabulous Formula shares the fascinating story of this groundbreaking formula—long regarded as the gold standard for mathematical beauty—and shows why it still lies at the heart of complex number theory.

This book is the sequel to Paul Nahin's An Imaginary Tale: The Story of I [the square root of -1], which chronicled the events leading up to the discovery of one of mathematics' most elusive numbers, the square root of minus one. Unlike the earlier book, which devoted a significant amount of space to the historical development of complex numbers, Dr. Euler begins with discussions of many sophisticated applications of complex numbers in pure and applied mathematics, and to electronic technology. The topics covered span a huge range, from a never-before-told tale of an encounter between the famous mathematician G. H. Hardy and the physicist Arthur Schuster, to a discussion of the theoretical basis for single-sideband AM radio, to the design of chase-and-escape problems.

The book is accessible to any reader with the equivalent of the first two years of college mathematics (calculus and differential equations), and it promises to inspire new applications for years to come. Or as Nahin writes in the book's preface: To mathematicians ten thousand years hence, "Euler's formula will still be beautiful and stunning and untarnished by time."

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Product Details

ISBN-13:
9780691118222
Publisher:
Princeton University Press
Publication date:
04/10/2006
Edition description:
New Edition
Pages:
404
Product dimensions:
6.40(w) x 9.30(h) x 1.50(d)

Table of Contents

Preface : "when did math become sexy?"
1Complex numbers (an assortment of essays beyond the elementary involving complex numbers)
2Vector trips (some complex plane problems in which direction matters)
3The irrationality of [pi][superscript 2] ("higher" math at the sophomore level)
4Fourier series (named after Fourier but Euler was there first - but he was, alas, partially wrong!)
5Fourier integrals (what happens as the period of a periodic function becomes infinite, and other neat stuff)
6Electronics and [actual symbol not reproducible] (technological applications of complex numbers that Euler, who was a practical fellow himself, would have loved)
Euler : the man and the mathematical physicist

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