by Pierre Schapira
Publisher: Université Paris VI 2011
Number of pages: 60
The aim of these Notes is to provide a short and self-contained presentation of the main concepts of differential calculus. Our point of view is to work in the abstract setting of a real normed space, and when necessary to specialize to the case of a finite dimensional space endowed with a basis.
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This book provides an introductory chapter containing background material as well as a mini-overview of much of the course, making the book accessible to readers with varied backgrounds. It uses a wealth of examples to illustrate important concepts.
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This text surveys the recent results that concern real functions whose statements involve the use of set theory. The choice of the topics follows the author's personal interest in the subject. Most of the results are left without the proofs.
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This classic book has inspired successive generations of budding mathematicians at the beginning of their undergraduate courses. Hardy explains the fundamental ideas of the differential and integral calculus, and the properties of infinite series.