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.
1. The concept of the limit: Acheson explores the notion of limits, which is fundamental to calculus. He discusses how mathematicians like Newton and Leibniz developed the concept to understand rates of change and infinitesimal quantities.
2. The discovery of derivatives: The book delves into the work of Isaac Newton and Gottfried Leibniz, who independently developed the concept of derivatives to analyze rates of change and solve problems involving curves and motion.
3. The integral as an area under a curve: Acheson explains how mathematicians extended their understanding of derivatives to develop the concept of integrals, which are used to find areas under curves and solve problems of accumulation and measurement.
4. The fundamental theorem of calculus: The book introduces the fundamental theorem of calculus, which establishes the fundamental relationship between derivatives and integrals. Acheson illustrates its significance and its role in connecting two seemingly separate aspects of calculus.
5. The power of mathematical notation: Acheson emphasizes the importance of mathematical notation, highlighting how the development of symbols and notation significantly aided the progress and understanding of calculus.
6. The concept of infinity: The book explores the concept of infinity and how calculus deals with infinite quantities and processes. Acheson explains how mathematicians grappled with the paradoxes and challenges of infinity while developing calculus.
7. The connection between calculus and motion: Acheson explores the connection between calculus and motion, showcasing how calculus allows us to understand and model the behavior of moving objects through concepts such as position, velocity, and acceleration.
8. Applications in physics: The book discusses the profound impact of calculus on the field of physics. Acheson illustrates how calculus is used to describe and analyze physical phenomena, including motion, forces, and natural laws.
9. Calculus as a problem-solving tool: Acheson highlights how calculus provides powerful problem-solving techniques across various disciplines. The book presents examples of how calculus can be applied to solve practical problems in fields such as economics, biology, and engineering.
10. The beauty and elegance of calculus: Throughout the book, Acheson conveys the beauty and elegance of calculus as a mathematical discipline. He showcases its versatility, its ability to explain complex phenomena, and the elegance of its concepts and techniques.
A straightforward summary of calculus, made interesting. And a tennis match date!
I enjoyed reading it, felt that I have learnt from it and will happily read it again some day. My old head had to think about some of the maths, which is a good thing.
I majored in math as an undergraduate and am pretty opinionated on math education at secondary schools. I found this book very entertaining and introduces calculus (and Newton mechanics) in a very intuitive way from a historical perspective. I read the book together with my son, who is a 10th grader in high school, and he really enjoys it without knowing that some of the stuff is beyond AP Physics I.
Obviously written by an excellent and experienced teacher. No matter where you are on the learning spectrum, this book has some gems for you.
While I have not yet completed the book, I have found the portion of the book I’ve read to be very informative.