What Is Calculus About?

Anneli Lax New Mathematical Library

by W.W. Sawyer

A must for calculus teachers and students.

This book gives students the big picture about calculus. It should be read by prospective and current calculus students and by their teachers. Even someone who has completely mastered the technical side of the subject can benefit from being reminded of the essentially simple ideas and the calculational needs that led mathematicians to develop the rather complex machinery of calculus. Sawyer deals with it all, from what background a student needs to begin, to the study of speed and acceleration, to graphing (slope and curvature), to areas, volumes, and the integral.

Calculus, invented by Newton and Leibniz in the seventeenth century, has played a decisive role in the development of mathematics and the growth of our present technological society. It is an indispensable tool of both the pure and applied sciences and is one of the cornerstones of modern mathematics. It has provided ways of understanding such phenomena as the velocity of a moving object at any moment, the rate at which moving objects change their speeds and, more generally, the way in which quantities vary as factors affecting them change. In this book, the author tells what calculus is about in simple nontechnical language, understandable to any interested reader.

W.W. Sawyer was born in St Ives, Hunts, England in 1911. He attended Highgate School and St. John's College, Cambridge, where he specialized in the mathematics of quantum theory and relativity. He has taught at Leicester College of Technology and has lectured in mathematics at universities in Dundee, Manchester, Ghana, New Zealand, Illinois and Connecticut. In 1965 he became a professor jointly to the departments of mathematics and education at the University of Toronto, retiring in July 1976. His books include Mathematician's Delight, Prelude to Mathematics, A Concrete Approach to Abstract Algebra and An Engineering Approach to Linear Algebra.

Content:
What must you know to learn about calculus?
The study of speed
The simplest case of varying speed
The higher powers
Extending our results
Calculus and graphs
Acceleration and curvature
The reverse problem
Circles and spheres, squares and cubes
Intuition and logic.

Genres: Mathematics, Calculus, Science

118 pages, Paperback

First published January 1, 1961

About the author

Walter Warwick Sawyer (or W.W. Sawyer) was a mathematician, mathematics educator and author, who taught on several continents.
https://en.wikipedia.org/wiki/Walter_...

Reviews

[Kyle · Rating 5 out of 5]

Another great Sawyer book from my perspective. It would again be nice to know the perspective from someone who is the target audience for the book (pre-calculus). I thought the presentation was excellent, with the usual amount of Sawyer wit. The explanations of derivatives is especially good for those wanting concrete examples. Using both distance, velocity, and acceleration with the curve, slope of a curve, slope of a slope of a curve, is a great way of explaining the basics of calculus.

This is also a very short book, but covers its subject and puts in the caveats about what more advanced treatments will teach (and why they need to be taught). I remain impressed by Sawyer's explanatory abilities, even for simple mathematical concepts.

[Charles · Rating 4 out of 5]

To his credit, Sawyer uses the example that is the easiest to understand when he is describing derivatives and how they represent a rate of change. That example is the position of a moving particle over time, how the velocity changes over time, how it is derived and the rate at which velocity changes over time. In other words, start with the formula for position, the first derivative is velocity and the second derivative the acceleration. The underlying algebra is as easy as it can be.
This is a physical principle that nearly everyone can understand, which makes it an excellent introduction to the basics of differential calculus. The problem is that this example is used to the point of overuse. The reader beginning their study of calculus will not understand how powerful it is, as there is little in the way of other examples where calculus is used to solve problems in the world.
The principles that are explained are handled very well, there is just not enough of them covered.

[Alex Furst · Rating 3 out of 5]

Book #24 of 2022. "What is Calculus About?" by W. W. Sawyer. 3/5 rating.

If there were any questions left on whether I'm a complete nerd, those have all been put to bed by my reading this book in my spare time...

"The mathematician has the instincts of the explorer; at all costs, go forward, if things are different, so much the better; that will make it more interesting." I absolutely loved this quote! One, because it's true, and behind the drive for new knowledge that is fostered in engineering. And two, because it just cracked me up having mathematicians call themselves explorers and adventurers.

This book is an inquiry-based introduction to calculus. I think it does a great job of basing all calculus in the exploration of finding speeds. Using this basic idea, Sawyer very plainly goes through how you can use a known position at different times in order to calculate velocities. Between the discussed math, his pointed questions, and the exercises, I think this is a great guide to understanding what calculus can do.

This being said, this is a textbook. I don't expect anyone to pick this up for some light reading. But, if you are taking a calc class (or any engineering, physics, or related higher-level math class), this could be a really helpful grounding in the topic. So often, students just memorize formulas and don't actually understand the basis behind them. I think this book could really help fix that.

[ِAhmed AboELkheir · Rating 3 out of 5]

Okay.
It is a good book to well know what is really calculus ? and How we can see it is effect in something that we are daily deal with it "Das Auto".
Really in some points I enjoyed a lot and gain a new information about calculus although I read about and studied a lot about but Sawyer not only his perspective is remarkable, but also the way he talk about information and the way to deliver it. The way is very important in mathematics and in calculus especial as there were teachers that complicated everything with no purpose!.
There were a thing that I was not prefer well, there were in some points that he repeated what he talked about, repeated the thing sometimes not in a new but in the same circle. That is the only thing that I do not prefer.
At the end of the book you will read a good , fascinating list that talk about calculus.

[Diana · Rating 3 out of 5]

This book aims to explain the basic concepts of calculus to someone unfamiliar with the subject, but I think it's much more helpful to someone who hasn't used calculus in years and wants a refresher. It's even more helpful to someone who is reviewing calculus in order to explain the basics to someone else, like I am.

[Lynn Speegle · Rating 5 out of 5]

This is a great book for students to read as well as those who love mathematics and/or teach Calculus!

[Maurizio Codogno · Rating 3 out of 5]

Quando ero ragazzo avevo comprato alcuni libri della collana Matematica Moderna di Zanichelli, scegliendo accuratamente temi che non insegnavano a scuola. Poi è capitato che il mio amico Matteo si dovesse disfare di alcuni libri, e mi ha lasciato tra gli altri questo. Che dire? Walter Warwick Sawyer è stato un insegnante britannico morto quasi centenario, e del quale avevo letto - sempre in questa collana - Preludio alla matematica. Ho il sospetto che abbia avuto a che fare con studenti molto testoni, perché continua a rispiegare le cose e mostrare possibili errori piuttosto improbabili, spiegando cosa ha probabilmente in testa chi li fa. L'approccio all'analisi matematica è quasi newtoniano, nel senso che parte dalla fisica e dal concetto di velocità: anche se verso il fondo mostra come lo stesso approccio valga in altri casi, il lettore digiuno della materia rischia di non farsi un'idea del motivo per cui la materia è così importante, cosa che sarebbe dovuta a mio parere essere lo scopo di un libro come questo che non è certo un manuale scolastico. Gli accenni nell'ultimo capitolo alle cose che non funzionano così bene come sembrava fino ad adesso lo fanno davvero diventare «il più interessante dell'intero volume», come ammette Sawyer nell'introduzione.
La traduzione di Maria Spoglianti è corretta ma risente del mezzo secolo di età; non capita certo più di leggere «il corpo in istudio» (pagina 27) o «Abbiamo visto dianzi» (pagina 64)...

[Siraaj Khandkar · Rating 5 out of 5]

Amazing! Sawyer does not disappoint - a very intuitive explanation of differentiation and some of its uses, followed by a sneaky preview of integration (without calling it so), then guidance to further study. Besides the topic being explained, what is really worthy to pay careful attention to is the explanation itself - the way Sawyer builds up an idea, priming you for independent eureka moments, is the pedagogy at its finest - I hope to be half as good of a teacher to my kids.

[Brandon · Rating 4 out of 5]

great introduction to calculus
including an answer key and key terms in the back, it is great for calc new-comers or those wishing to re-learn the elementary components

[Sharif Ahmad · Rating 4 out of 5]

I should have read this book long ago. Calculus is explained in a simple way. I have not seen anyone else explaining this hard subject like him before.