Infinite Powers: How Calculus Reveals the Secrets of the Universe

This book is much more than just a history of a branch of mathematics. It's a framework for thinking about calculus. I was mind blown at how Strogatz explains calculus; like I had been blind all those years and now I saw. His 'breaking down and reassembling' analogy may not be the best explanation to the more mathematically inclined, but to me it made perfect sense, at last. This book provided me with a mind model to think about calculus. A gem."To shed light on any continuous shape, object, motion, process, or phenomenon - no matter how wild and complicated it may appear - reimagine it as an infinite series of simpler parts, analyze those, and then add the results back together to make sense of the original whole."

I need to psyche myself up to do some math for work. And I have a math sherpa and I arranged to meet him so he can take me through the paper I must tackle. But I’m old and only really remember my high school math well, so there is a genuine task at hand here.So I duck and dive between the paper and my notes from my MSc thesis from at least fifteen years ago and I work out the answer to lesser problems and I write out my questions for my Sherpa and I also need to be thinking math the whole time; I need to be in a mood, basically.That’s the task.So I did the sensible thing and went on a bit of a binge and bought a whole bunch of popular math books in one go to read in the tube. “Infinite Powers” I read first, because it looked like it would not challenge me at all and it gets good writeups.It’s bloody awesome!It’s more than an anthology of results and it’s more than a series of mini-portraits of mathematicians, it’s almost got a plot. Surprisingly often, even the obligatory corny applications of the math are (somewhat) related to what the author’s talking about.Huge caveat: I knew both the math and even many of the stories upfront, so perhaps it’s not very well explained. I have no way of knowing. But I bet you it is. Perhaps not well enough that you could hope to learn calculus from here, Jordan Ellenberg’s praise on the back cover notwithstanding. (For that I can refer you to “Quick Calculus” by twin gods Kleppner and Ramsey.) But probably well enough to be a companion to anybody taking calculus for the first time.Steven Strogatz had me from “hello,” of course, because he starts with the Greeks, on whom he lavishes immense praise. He could have left it there and I’d still be basking in the warm glow of my ancestors’ work. Needless to say, it does not stop there, he takes you from them to Fermat and Descartes, before introducing you to Newton and Leibniz, a couple words on Fourier and from him straight to Einstein, taking special care to erase all traces of evil men like the unspeakable inventor of delta-epsilon proofs. You won’t find the C-word here.So there’s a massive hole in the nineteenth century, somewhere, but I’m sure you can buy another book to find out about that. Here you’ll discover a decent definition of e, an intuitive explanation of general relativity, the common cause of death of Leibniz and Newton, a fun game to play with your microwave oven, the first and second derivative of the sine wave, the dimension of the three-body problem, a strong defense of infinitesimals, WHAT’S NOT TO LIKE?Enough from me, I’ll now go buy some extra copies for a few boys and girls I know. If one of them likes it, my job is done.Oh, sorry, one more thing. About the plot: it’s a history of how mathematicians throughout time have sliced hard problems into infinite infinitely-thin slices where the problem has a clear answer and then dealt with infinity to sum up the solutions to the easy problem in order to come up with an answer to the hard problem.Whenever you do that, you’re doing calculus, you’re putting together the answer granule by granule.

El autor de este libro te explica cálculo diferencial e integral de una manera mucho más clara que mi profesor de primero de carrera en ingeniería.Te deja claro su historia, de donde vienen los conceptos, su utilidad, todo sin usar muchas fórmulas.Este libro no es para aprobar un examen sino para entender de verdad de que va ésta útil herramienta de las matemáticas.Lo recomiendo para cualquiera que quiera comprender de verdad sus bases y no solo memorizar una serie de fórmulas y gráficas, como pasó en mi curso.

It is a delicious narrative about the origin of calculus and its importance in our daily life. It is a great book for those not familiar with mathematics.

I enjoyed Steven Strogatz's new work, Infinite Powers: How Calculus Reveals the Secrets of the Universe. The book gives an excellent overview of calculus, which permeates all branches of mathematics and so much of life. I should say at the outset that I had the great opportunity of being taught calculus in college by Dr. Strogatz. After reading this book, I feel even more fortunate for this experience because he's such a gifted communicator.What I liked mainly about the book was the intuitive way Strogatz describes differentials and the development of calculus from Newton and Leibniz onwards. He introduces these concepts in several ways. My favorite was the way he demonstrated simply cubing the number 2 and contrasting it with cubing 2.01, where the latter can be expressed as the cube of a sum (2 + .01) and then expanded out with Pascal's triangle. From merely looking at the multiplication of these numbers, one can immediately get a sense of which terms can be neglected in this specific sum and in the whole process of differentiation.Strogatz also clearly explains many classic equations in mathematics and physics, such as the heat and the wave equations. I particularly liked the way he described the development of the Fourier series and how this series converts differentiation of sine and cosine into a simple multiplication by minus one, making it easy to deal with. I also liked how he explained how one can easily express even very angular shapes such as a triangular waveform in terms of Fourier series.I enjoyed many of the practical examples of how we can see calculus in everyday life, ranging from the oscillations of HIV in people, as tracked by Alan Perelson and David Ho, to the development of CT scans by Hounsfield and Cormack. Strogatz gives an especially hands-on understanding of the fundamental theorem of calculus by describing it in terms of a well-known paint roller analogy and how it can link together the disparate ideas of the slope of a function and the area under a curve.Finally, I enjoyed the discussion of many of the personalities in mathematics, such as Descartes and Fermat. I hadn't appreciated the famous feud between these two until I read the book.Overall, a great read. I'd highly recommend it, especially for anyone studying or using calculus.

Me gusta mucho el enfoque del libro donde se tratan los aspectos del cálculo a partir del concepto matemático del infinito, de una manera amena y hasta divertida. Creo que para personas que desean consolidar sus conocimientos en el tema puede ser muy útil, también a los docentes de nivel medio y superior les puede ayudar a dar enfoques más interesantes a sus clases. No soy hablante nativo del inglés, por lo que tuve que recurrir continuamente al diccionario, me parece que al autor le gusta utilizar un inglés elegante con términos no muy frecuentes. Eso puede ser un plus lingüístico, aunque puede hacer perder la continuidad en la lectura. Vale la pena de todas maneras. Muy recomendable

This book is a must for them who find calculus difficult and not interesting. I am teaching Analysis/Calculus for a while now. I will suggest this book to my students. If you belong to that group then you should give it a read too. This book is very well written with motivations coming from Shrek like animations, not joking, it's true. It's a must buy. As for Amazon's end their delivery is wondeful. Thanks Amazon !