Dr. Euler's Fabulous Formula

Paul Nahin

Published by Princeton University Press 2011

Dr. Euler's Fabulous Formula

Cures Many Mathematical Ills

Paul Nahin

Volume 83 in the series Princeton Science Library

https://doi.org/10.1515/9781400838479

Overview
Contents

About this book

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. In some ways a sequel to Nahin's An Imaginary Tale, this book examines the many applications of complex numbers alongside intriguing stories from the history of mathematics. Dr. Euler's Fabulous Formula is accessible to any reader familiar with calculus and differential equations, and promises to inspire mathematicians for years to come.

Author information

Paul J. Nahin is the author of many bestselling popular math books, including Mrs. Perkins's Electric Quilt, In Praise of Simple Physics, and An Imaginary Tale (all Princeton). He is professor emeritus of electrical engineering at the University of New Hampshire.

Reviews

What a treasure of a book this is! This is the fourth enthusiastic, informative, and delightful book Paul Nahin has written about the beauties of various areas of mathematics. . . . This book is a marvelous tribute to Euler's genius and those who built upon it and would make a great present for students of mathematics, physics, and engineering and their professors.---Henry Ricardo, , MAA Reviews

It is very difficult to sum up the greatness of Euler. . . . This excellent book goes a long way to explaining the kind of mathematician he really was.---Steve Humble, Mathematics Today

"The range and variety of topics covered here is impressive. I found many little gems that I have never seen before in books of this type. Moreover, the writing is lively and enthusiastic and the book is highly readable."—Des Higham, University of Strathclyde, Glasgow

The heart and soul of the book are the final three chapters on Fourier series, Fourier integrals, and related engineering. One can recommend them to all applied math students for their historical development and sensible content.---Robert E. O'Malley, Jr., SIAM Review

"If you ever wondered about the beauties and powers of mathematics, this book is a treasure trove. Paul Nahin uses Euler's formula as the magic key to unlock a wealth of surprising consequences, ranging from number theory to electronics, presented clearly, carefully, and with verve."—Peter Pesic, St. John's College

Professional, Scholarly Cover/Jacket Award, New York Book Show

Nahin's tale of the formula e[pi] i+1=0, which links five of the most important numbers in mathematics, is remarkable. With a plethora of historical and anecdotal material and a knack for linking events and facts, he gives the reader a strong sense of what drove mathematicians like Euler.---Matthew Killeya, , New Scientist

Nahin includes gems from all over mathematics, ranging from engineering applications to beautiful pure-mathematical identities. . . . It would be good to have more books like this.---Timothy Gowers, Nature

It is a 'popular' book, written for a general reader with some mathematical background equivalent to a first-year undergraduate course in the UK.---Robin Wilson, London Mathematical Society Newsletter

This is a book for mathematicians who enjoy historically motivated mathematical explanations on a high mathematical level.---Eberhard Knobloch, Mathematical Reviews

Topics

Frontmatter Publicly Available Download PDF	i
Contents Publicly Available Download PDF	ix
Preface to the Paperback Edition Requires Authentication Unlicensed Licensed Download PDF	xiii
Preface Requires Authentication Unlicensed Licensed Download PDF	xxix
Introduction Requires Authentication Unlicensed Licensed Download PDF	1
Chapter 1. Complex Numbers Requires Authentication Unlicensed Licensed Download PDF	13
Chapter 2. Vector Trips Requires Authentication Unlicensed Licensed Download PDF	68
Chapter 3. The Irrationality of π² Requires Authentication Unlicensed Licensed Download PDF	92
Chapter 4. Fourier Series Requires Authentication Unlicensed Licensed Download PDF	114
Chapter 5. Fourier Integrals Requires Authentication Unlicensed Licensed Download PDF	188
Chapter 6. Electronics and √ −1 Requires Authentication Unlicensed Licensed Download PDF	275
Euler: The Man and the Mathematical Physicist Requires Authentication Unlicensed Licensed Download PDF	324
Notes Requires Authentication Unlicensed Licensed Download PDF	347
Acknowledgments Requires Authentication Unlicensed Licensed Download PDF	375
Index Requires Authentication Unlicensed Licensed Download PDF	377

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