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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
Description
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.
