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.
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.
Table of Contents
FrontMatter, pg. i
Contents, pg. ix
Preface to the Paperback Edition, pg. xiii
Preface, pg. xxix
Introduction, pg. 1
Chapter 1. Complex Numbers, pg. 13
Chapter 2. Vector Trips, pg. 68
Chapter 3. The Irrationality of π2, pg. 92
Chapter 4. Fourier Series, pg. 114
Chapter 5. Fourier Integrals, pg. 188
Chapter 6. Electronics and √ −1, pg. 275
Euler: The Man and the Mathematical Physicist, pg. 324
Notes, pg. 347
Acknowledgments, pg. 375
Index, pg. 377
What People are Saying About This
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
From the Publisher
"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
"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
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
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