The calculus story : a mathematical adventure / David Acheson

Includes bibliographical references (pages 183-186) and index

Introduction -- The spirit of mathematics -- Infinity -- How steep is a curve? -- Differentiation -- Greatest and least -- Playing with infinity -- Area and volume -- Infinite series -- 'Too much delight' -- Dynamics -- Newton and planetary motion -- Leibniz's paper of 1684 -- 'An enigma' -- Who invented calculus? -- Round in circles -- Pi and the odd numbers -- Calculus under attack -- Differential equations -- Calculus and the electric guitar -- The best of all possible worlds? -- The mysterious number e -- How to make a series -- Calculus with imaginary numbers -- Infinity bites back -- What is a limit, exactly? -- The equations of nature -- From calculus to chaos

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