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Calculus for the Ambitious

Book 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.

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Further reading
[1] J. C., Burkill. A First Course in Mathematical Analysis. Cambridge University Press, Cambridge, 1962.
[2] R., Courant and H., Robbins. What is Mathematics?Oxford University Press, Oxford, 1941. OUP has issued this book in various forms including a second edition with an extra chapter by Ian Stewart discussing later developments.
[3] P. R., Halmos. Naive Set Theory. Van Nostrand, Princeton, 1960. The later publishing history is complicated, but the book is available in many libraries and is usually in print.
[4] F., Klein. Elementary Mathematics from an Advanced Standpoint (Part 1). Macmillan, New York, 1932. Third edition. Translated by E. R. Hedrick and C. A. Hedrick. There is a Dover reprint.
[5] A. E., Maxwell. An Analytical Calculus, volume 1. Cambridge University Press, Cambridge, 1957. There are three further volumes covering successively more advanced topics.
[6] M., Spivak. Calculus. Cambridge University Press, Cambridge, third edition, 1994.
[7] S. P., Thompson. Calculus Made Easy. Macmillan, London, second edition, 1914. There are several editions revised by various hands. The revisions are not always happy. The 1914 edition is available from Project Gutenberg.

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