A rigorous route through calculus and mathematical reasoning
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A rigorous route through calculus and mathematical reasoning
Nicolaescu’s text develops calculus from foundational principles, pairing its core material with complete rigorous arguments. The coverage moves across one-variable and multivariable calculus, then adds a basic introduction to the topology of Euclidean space. Mathematical reasoning is an explicit part of the book’s aim, so the scope extends beyond learning calculus results to engaging with the arguments behind them. At 690 pages, it offers substantial coverage of these subjects within a single volume.
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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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