Calculus for the Ambitious 1st Edition by T. W. Körner (PDF)

Description

From the author of The Pleasures of Counting and Naïve Decision Making comes a calculus book perfect for self-study. It will open up the ideas of the calculus for any 16- to 18-year-old, about to begin studies in mathematics, and will be useful for anyone who would like to see a different account of the calculus from that given in the standard texts. In a lively and easy-to-read style, Professor Körner uses approximation and estimates in a way that will easily merge into the standard development of analysis. By using Taylor’s theorem with error bounds he is able to discuss topics that are rarely covered at this introductory level. This book describes important and interesting ideas in a way that will enthuse a new generation of mathematicians.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐nice intro for high school students about to undertake a full course or as an adjunct to one.

⭐Bought it because I liked the author’s wit and style. The first chapter is difficult to get into because it doesn’t seem relevant or useful. The only thing letting this book down is that it is riddled with mistakes! And when I say riddled I mean they’re absolutely everywhere. These could have (and should have) been removed before the book went to print. There is, however, an errata on the author’s website. I went through the book and stuck (literally with glue) corrections into it – it was a bit silly. I like the book, and the author, but I cannot give it any more than 3 stars due to all the mistakes.

⭐This book derives calculus in the style of a Physicist, but with the understanding and clarity of a Mathematician whose job it is to understand exactly how the mechanism works. In the closing stages of the book we begin to learn how the Physicist’s approach eventually fails. It would be great if the author would now write an introductory book in between this one and his “companion to analysis”, which explains which problems are being fixed by rigorous analysis as this new analysis is introduced for the first time. Most books on Quantum Mechanics start by describing how the “old theories” break down – perhaps analysis should be taught in this way too – as a story of enlightenment.

⭐ok but not what i hoped fora greater emphasis on in context questions would better suit me

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