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Dr. Euler's Fabulous Formula: Cures Many Mathematical Ills
Binding: Hardcover
Author: Paul J. Nahin
Manufacturer: Princeton University Press
Availability: Usually ships in 24 hours
Features:
Average Rating: 4.5
Total Customer Reviews: 17
List Price: $29.95
Our Price: $19.77
Sales Rank: 184733
Product Description
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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Users Product Reviews: |
Product Review Summary: eipye +1=0 Notwithstanding that E=mc2 is a famous equation in physics, eipye+1=0 is the most famous and interesting relationship in mathematics. It has a fundamental information base second to no other. The author delves into many applications of the relationship in various branches of mathematics and engineering, as well as noting the ancient thinkers who recognized some aspects of it. I found this book fascinating, challenging, and even daunting. But try it, as it is also very entertaining.
Product Review Summary: Not one of the best books of Professor Nahin Well this time I don't agree with reviewers above in the sense that if we liked An Imaginary Tale, then this book would like us too.
Certainly I enjoyed a great deal An Imaginary Tale, but I hoped I would find much more in Dr Euler's Formula, as I was really very impressed the first time I met -in my second year of electrical engineering- the most beautiful equation in mathematics, as professor Nahin has pointed out, but I really was very dissapointed, that in this new book I did not find anything about the fact that Dr. Euler's Fabulous Formula is most remarkable because even with differentiation and integration the mathematical operations that represent change, Euler's Identity remains with the same form, except for being affected by the square root of minus one, i.e., by a process of rotation.
It is this remarkable property the one that permits
"to reduce steady-state sinusoidal problems to forms which are identical to those for resistive networks."
and that made that Charles Steinmetz was called
"the wizard who generated electricity from the square root of minus one"
when the great historical struggle between AC and DC current was solved by that famous paper of Steinmetz.
Yes, it was this remarkable property that made me think that Dr. Euler's Formula could cure not only many mathematical ills, but physical ones such as those of deducing both the pendulum formula and the Complex Schrodinger's wave equation, based in a complex metrics in which Euler's identity plays the fundamental role, an exercise that I did many years ago and put somewhere at LANL.
Of course, I highly recommend this book by professor Nahin, as you will find in it a real complement to Fourier series and Integrals and to the study of Dirac's impulse function in chapters 4 and 5 and an important application to electronics in chapter 6.
Product Review Summary: Great stuff, but what's the point? I came to this book because I enjoyed The Story of the Square Root of Minus One, another book by Paul Nahin. This book is of a very different nature: unlike that other book, this one is light on concepts and heavy on calculations.
I enjoyed it quite a bit, however, hence the 4 stars, because I like complicated-looking integrals, but let me be frank I could not help thinking throughout: what's the point? (and do I deserve to be treated to so many typos?)
What's the point? It shows many uses of Euler's formula, but without explaining why we should care. A couple of chapters are devoted to Fourier series and transforms: again, what's the point? Towards the end, Nahin writes something to the effect that he has "avoided giving physical interpretations to the mathematical calculations" and that's precisely the problem: until the end of the book where there are clear references to things like electricity and other waves, we are never told (or reminded) why these clever manipulations are important.
It was shocking not to see any reference to the Riemann hypothesis and zeta function, which are perhaps the most beautiful example of the use of Euler's formula.
To Nahin's credit, he goes through the calculations step by step, so that if you do care (for some reason) then you can follow pretty much the whole thing without breaking a sweat (Nahin did the hard work). But I will confess that I did skip a few pages here and there: my eyes and brains got tired and the nagging thought came, well, what's the point?
Thoroughly recommended, however.
Product Review Summary: Warning Don't buy this book without buying the companion i book by Paul Nahin. This is clearly meant as a supplement to the i book. Does not stand alone except maybe in the applications of the formula.
I gave this book 5 stars because I had no basis for judgment. The author clearly states in the beginning of the book that this book has many interesting things he couldn't fit in the first one.
Product Review Summary: Dr Euler's Fabulous Formula A very interesting book. I am a retired Electrical Engineer and hence find this book particularly interesting. Not for the faint hearted as it contains a very large amount of complex mathematics. Overall, very good.
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Similar Products with reviews:
An Imaginary Tale: The Story of "i" [the square root of minus one]
"e": The Story of a Number (Princeton Science Library)
When Least Is Best: How Mathematicians Discovered Many Clever Ways to Make Things as Small (or as Large) as Possible
Gamma: Exploring Euler's Constant (Princeton Science Library)
Zero: The Biography of a Dangerous Idea
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