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The Calculus Story


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Table of Contents

1: Introduction 2: The spirit of mathematics 3: Infinity 4: How steep is a curve? 5: Differentiation 6: Greatest and least 7: Playing with infinity 8: Area and volume 9: Infinite series 10: 'Too much delight' 11: Dynamics 12: Newton and planetary motion 13: Leibniz's paper of 1684 14: 'An enigma' 15: Who invented calculus? 16: Round in circles 17: Pi and the odd numbers 18: Calculus under attack 19: Differential equations 20: Calculus and the electric guitar 21: The best of all possible worlds? 22: The mysterious number e 23: How to make a series 24: Calculus with imaginary numbers 25: Infinity bites back 26: What is a limit, exactly? 27: The equations of nature 28: From calculus to chaos References Further Reading Index

About the Author

David Acheson is a British applied mathematician, best known for his popular maths book 1089 and All That (OUP, 2010), which has been translated into 11 languages. He is an Emeritus Fellow of Jesus College, Oxford, and was Oxford University's first winner of a National Teaching Fellowship, in 2004. He was President of the Mathematical Association for 2010-11, and now lectures widely on mathematics to young people and the general public. In 2013, David Acheson was awarded an Honorary D.Sc by the University of East Anglia for his outstanding work in the popularisation of mathematics.


A masterpiece... Packed with insights, both historical and mathematical. * Steven Strogatz, professor of mathematics, Cornell University, and author of The Joy of X and Infinite Powers *
This is the book on calculus I wish I'd written. It's a beautifully simple, friendly guide that's bursting at the seams with glorious, persuasive explanations as to why calculus is one of the most powerful ideas ever conceived by mankind. * Hannah Fry, Broadcaster, lecturer, and author of The Mathematics of Love *
A splendid little book ... accessible to a very wide audience ... The book is highly recommended. * Adam McBride, Mathematical Gazette *
A remarkably expansive and frictionless tour of mathematical history and theory... The calculus story is no textbook... It is the antithesis of the dreary way calculus is too often taught at schools and universities... a supplement for a high school student, the parents of such a student, or an adult wishing to reacquaint herself painlessly with material long forgotten. * Henrik Latter, Plus *
This is a very readable book... It offers an illuminating perspective on calculus... A very enjoyable book for the layperson or the user of calculus. * Alex Chaplin, School Science Review *
Wish I'd had it as a maths student! * Tim Harford, Undercover Economist *
Another wonderful book. * Mark McCartney, LMS Newsletter *
A very clear explanation of calculus ([I] wish I'd had it as a maths student!) along with some history of the subject. * Tim Harford, The Undercover Economist *
Superb introduction to calculus that should be in every young mathematician's bookcase. * Peter Ransom, Symmetry Plus *
Don't panic if your mathematical muscles appear to have withered away (or you never truly cracked differentiation), David Acheson's The Calculus Story could be just the thing... A roller-coaster read, constantly climbing and diving through the wonderful world of calculus... There's something for everyone, from the inexperienced integrator to the seasoned solver of equations... His enthusiasm for calculus is almost palpable. * Timothy Revell, New Scientist *
Dazzling. * Matthew Reisz, Times Higher Education *
I would have killed for this book when I was 13 ... he [David Acheson] belongs in the league of great authors of popular works on mathematics. * George Matthews, Mathematics Today *
A worthy successor to 1089 and All That. * Adhemar Bult heel, European Mathematical Society *
A simple guide to calculus - where it came from, how it works, what it's good for, and where it went. Brief, informative, charming, and a model of clarity. Ideal motivation for beginners, and recommended to anyone who wonders what the subject is about. * Ian Stewart, author of Seventeen Equations that Changed the World *
This wide-ranging picture of calculus and its applications, from antiquity to the present, reveals the method as both the key to much of modern science and engineering, and something of a mathematical adventure. * Science *
Acheson offers a much-needed short account of the big picture of calculus as a whole, illustrated with examples and reproductions from historic publications [...] Short pages, many illustrations, and a sense of telling a big story contribute to the success of the book. * Paul J. Campbell, Mathematical Magazine *

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