A rigorous route into calculus and analysis
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A rigorous route into calculus and analysis
Nicolaescu’s 690-page text treats calculus as both a body of results and a way to learn mathematical reasoning. It builds the subject from foundational arguments, with detailed coverage of one-variable and multivariable calculus, then adds an introduction to the topology of Euclidean space. That combination places the book between a calculus text and a first step toward more abstract analysis, with proofs central to its approach.
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This is a text that develops calculus "from scratch", with complete rigorous arguments. Its aim is to introduce the reader not only to the basic facts about calculus but, as importantly, to mathematical reasoning. It covers in great detail calculus of one variable and multivariable calculus. Additionally it offers a basic introduction to the topology of Euclidean space. It is intended to more advanced or highly motivated undergraduates.
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