The Calculus Story: A Mathematical Adventure

by David Acheson

Calculus is the key to much of modern science and engineering. It is the mathematical method for the analysis of things that change, and since in the natural world we are surrounded by change, the development of calculus was a huge breakthrough in the history of mathematics. But it is also something of a mathematical adventure, largely because of the way infinity enters at virtually every twist and turn...

In The Calculus Story , David Acheson presents a wide-ranging picture of calculus and its applications, from ancient Greece right up to the present day. Drawing on their original writings, he introduces the people who helped to build our understanding of calculus. With a step-by-step treatment, he demonstrates how to start doing calculus, from the very beginning.

Genres: Mathematics, Science, Nonfiction, History, Stem, Historical

208 pages, Hardcover

First published November 1, 2017

Reviews

[Brian Clegg · Rating 3 out of 5]

According to the back cover 'This little book is more ambitious than it looks.' Apart from a distinct feeling of damning with faint praise, there's an element of truth in this, which proves both a negative and a positive, depending on what you're looking for from a book on calculus.

Let's get the negative out of the way first. To make it a mathematical adventure, as the subtitle suggests, it would need rather more story and rather less calculus. Although David Acheson does get some history of maths in, this is much more 'getting your head around calculus for beginners' than it is 'the calculus story.' So, yes, you will discover, for instance, the battle between Newton and Leibniz - and Bishop Berkeley's magnificently titled 'the Analyst, or a discourse addressed to an infidel mathematician' - but only in a few passing lines.

What we get instead is a step by step introduction to calculus from first principles, which builds on Ancient Greek concepts through to limits and far more. Along the way readers will discover why there is such a relationship between calculus and infinite series and how pi and e come into the mix. We even get a spot of calculus using imaginary numbers.

There's frankly far too much grunt work here for this to really qualify as popular maths. But, equally, this little hardback lacks the dull writing style and worked examples of a textbook. It's far too readable to be one of those.

I'd say there are broadly two types of people who may find this book interesting. If you've done some calculus but just crunch the numbers according to the rules without thinking about why it works, the book will be extremely enlightening. And if you have a general interest in mathematics but don't really understand how many apparently unrelated components come together, it should go down very nicely. But don't expect that promised adventure. This book a far too practically minded for that.

[Blair · Rating 2 out of 5]

It starts off as a decent review of elementary calculus, but then degenerates into a sequence of some of the cool things calculus can do, with no explanation. I suppose that is the "adventure" part. I did not find it very satisfying.

[Savir Husain Khan · Rating 4 out of 5]

I found this book, simple and comprehensible, however, there was some part where I had to reread.
This book is about, how the calculus formed, And the story behind various calculus formulas.
As I have a moderate understanding of calculus, so it was not very hard for me to relate to the material, but it could be for the person who's understanding of calculus is not that good.
I Expected this book to be more about the history of calculus, but sometimes it goes into equations only.
However, it was very informative to read, and cleared most of my doubts.

[Alex Linschoten · Rating 4 out of 5]

I wish I understood more of the details of the maths. Aside from that, it was actually a pretty well-written and exciting story, all things considered. Calculus is cool!

[Hashem · Rating 2 out of 5]

The author says it’s a book about the history of calculus and that’s why I bought it but that’s not the case. Yes, some anecdotes are thrown here and there but the author can’t bother to verify them and build a “historical story” behind limits, infinity and imaginary numbers and how they came into life, which is what I thought the book is about.
Not a dull read though and hence the two stars.

[Srikantadatta Tagadur · Rating 5 out of 5]

A short compelling read which takes the reader on a roller coaster ride unravelling many of the lesser known aspects of calculus. The author has kept the mathematics to its bare minimum and has done a fabulous job in narrating it in a story format. I wish I had read this book when I actually started learning calculus, as they say it is better late than never. I highly recommend this book to anyone who wants to know the practical applications of calculus and how it has transformed the way we perceive the real world.

[Petr Vařeka · Rating 4 out of 5]

Calculus, that is limits, derivatives, integrals, differential equations and other interesting things of mathematical analysis. If you are interested in how they came to light, what Newton, Leibniz, Euler and other mathematicians contributed, if you want to know how it works and how it is used in practical applications, you are at the right address.

[Hussain Abbas · Rating 4 out of 5]

The book starts so well but quickly goes into jumping to solutions and assuming knowledge. I enjoyed the book but I am left wishing that I remembered more of my college maths to make sense of some of the things in the last part of the book.

[R. Sharath Kumar · Rating 5 out of 5]

Simply amazing

The book explores calculus from the very beginning to its use now. It isn't very deep but broadly covers every topic sufficiently.

[Rajeev Chugh · Rating 3 out of 5]

It's a fascinating and engaging book that tells the history and development of calculus, one of the most important and influential branches of mathematics. Acheson explains how calculus was born out of the need to solve practical problems, such as finding the area of a circle, the volume of a sphere, or the speed of a falling object. He also shows how calculus helped to create new fields of science and engineering, such as astronomy, physics, and mechanics. Along the way, he introduces some of the greatest minds who contributed to calculus, such as Archimedes, Newton, Leibniz, Euler, and many others.

It is not a textbook, but a storybook. It does not require any prior knowledge of calculus or advanced math. It is written in a clear and lively style, with plenty of examples, illustrations, and anecdotes. It is also full of surprises and insights that will make you appreciate the beauty and power of calculus.

[Danielle Summer · Rating 4 out of 5]

I keep finding great books that would've helped me a lot when I first started learning (in this case) Calculus. (Although the Spivak -like it or hate it- is very well written and clearly motivated.) I believe this book would make a great difference in explaining the historical background, the intrigue, and being all around very clear on why we do some things, why they might seem shaky and how to fix it, how to apply and motivate some of the most common results -the examples given are fairly classic, although I'd confess no one had explained me that the optimization problem explains the refraction of light-. I'm sure I'll use this book as an important resource if I ever get to teach Calculus.

[Olivia · Rating 2 out of 5]

I was expecting a bit more about calculus' interesting history, or at least a bit more mirth. A lot of results were presented without enough detail to really understand where they come from or why they're interesting, and too much focus was placed on complicated real-life connections and applications. I thought it was a bit dry and theory-heavy for beginner readers...it could have been a much more exciting brief romp through calculus and motion. But, if you're looking for a quick sweep through the basic concepts and simple proofs thereof...it might be a good addition to your collection.

[Sean · Rating 4 out of 5]

Too short. The brevity early in the book still fully explained the concepts being discussed, as they were simpler. But with later more complex topics, a very quick equation was shown with very little explanation. Fortunately, I teach Calculus and Physics, so I appreciated the topics being discussed. Once a person is hooked early in a book, on a technical topic, I think you can appeal to their technical side and keep the explanations stronger. Very quick read for me.

[Vaughan · Rating 4 out of 5]

A great little read that brought back plenty of memories of Calculus classes. I admit, this might have been easier to read in print, rather than on a Kindle, as the formulas appeared quite small, and the layout was all over the place.

Fun to get the brain reactivated after the holidays, and a great foundation for more math and science exploration to come!

[Jim · Rating 3 out of 5]

An ok attempt to make calculus easier to understand and to give it context in terms of the types of problems it and differential equations can solve. The author starts well enough, but keeping the explanations clear to non-mathematicians proves a difficulty. I wanted to recommend it to my students, but I think it would frustrate them more than enlighten.

[Jack · Rating 5 out of 5]

This was fun

I really enjoyed the author’s integration of history and mathematical concepts. His explanations don’t require a lot of mathematical background but they do provide some practical insights. I think I’ll pull out my calculus boo from fifty years ago and work some problems. That will be way more fun than reading the news

[Khalil Alfar · Rating 4 out of 5]

This book hit the mark from an expectation perspective as I wanted to reconnect with calculus and it helped stitch some concepts together to help with the roots of the topic. What was missing for me is more the story lines. The book had some good references to the key individuals who shaped calculus but not enough to “package�� it as a book. In some areas maybe a bit repetitive and too deep.

[Gavin Craddock · Rating 3 out of 5]

Interesting discussions about the history of calculus, from Leibniz and Newton to Euler and beyond, but changes depth rapidly and confusingly - from explaining something relatively simple to then assuming much greater understanding in the same paragraph. Useful as a reminder if you already know the content, I imagine it would not be useful as an introduction.

[Duhart Vader · Rating 2 out of 5]

I think it's a first good step to a book to introduce someone who knows nothing about calculus into the subject. However, it's too technical for a 10 to 12 year old and too lenient for a formal introduction. It's not quite a history of calcus either like Eli Maor's books.
In the end, it's not clear to me who the intended audience is.

[Chandra Shekar · Rating 4 out of 5]

It is a very good book that gives you a nice intro to Calculus. The chapters are small and easy to digest. The chapters on differentiation and basic calculus is very good. However the last few chapters are a bit dense and it looks like the author tried to stuff more into the book to complete the subject. But, overall, it is a enjoyable read.

[Deborah Tayler · Rating 4 out of 5]

A little bit short, but did take go through the history of calculus and its applications. I had to stop and work out the height of cone in a cylinder that has the maximum volume for myself, but I enjoyed doing that as it made go back over using the derivative and I got there eventually.

[Everson Luis de Campos Moura · Rating 3 out of 5]

Short book about the calculus

This is a very short book about the calculus history. It is interesting. But, it is very superficial. I had no problem to understand it because I'm an engineer. However, I think it may be hard to understand to someone without any calculus background.

[Paweł Rusin · Rating 4 out of 5]

Very short book. Great storytelling but as the material gets tougher I found it harder and harder to folllow math and felt that some of the material is not explained in necessary depth. First year of university lectures all over again.

[Sean Jude · Rating 5 out of 5]

I’d like to sincerely convey how throughly much I have enjoyed this book. A refreshing sense of clarity, which was written in good spirit. I can already see how my research can improve from The Calculus Story.

[mJ · Rating 3 out of 5]

Very basic read about Calculus

The book is a good introduction to Calculus. It gets little complicated it goes on. He is straight to Calculus without wasting much time on history and other stories

[Monica · Rating 4 out of 5]

This little book tried to teach me calculus!

Well, I showed it! But I'm keeping it around to use while I take a semester of Calculus, because it was very good at distilling down basic concepts even if I still can't wrap my head around some of them.

[Sergio Valverde · Rating 5 out of 5]

Excellent and clear explanation of derivation, integration, differentiation, and infinite series. I had to read slow to make sense of the equations.

[José García Urrutia · Rating 5 out of 5]

A wonderful explanation about the development of the calculus. It helped me to have a better understanding about the reasoning process behind it.

[Rachel · Rating 4 out of 5]

3.5 stars, rounded up.

[Danfan Lin · Rating 3 out of 5]

Not a very good story book as many of the book is stuffed by equation.