Shelves: science , mathematics For me the best introduction to calculus in one variable, yet absolutely rigurous it is more focussed in explain fundamental concepts in deep that in long full of calculations demostrations;also has some touchs of subtle humour ,some uncommon in a textbook and a lot of remarkable exercises. Has a lot of explainig clear graphics,give examples of bizarre functions for clearing concepts,give a original introduction to complex variable by convergent complex power series,makes a formal costruction of For me the best introduction to calculus in one variable, yet absolutely rigurous it is more focussed in explain fundamental concepts in deep that in long full of calculations demostrations;also has some touchs of subtle humour ,some uncommon in a textbook and a lot of remarkable exercises. Has a lot of explainig clear graphics,give examples of bizarre functions for clearing concepts,give a original introduction to complex variable by convergent complex power series,makes a formal costruction of the real numbers field, and make at this level unusual excursions in more advanced results as the demostration of the irracionality of pi or the demostration of the trancendence of e. Is a pure mathematics text and has no mention of physical or tecnological use

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Shelves: science , mathematics For me the best introduction to calculus in one variable, yet absolutely rigurous it is more focussed in explain fundamental concepts in deep that in long full of calculations demostrations;also has some touchs of subtle humour ,some uncommon in a textbook and a lot of remarkable exercises. Has a lot of explainig clear graphics,give examples of bizarre functions for clearing concepts,give a original introduction to complex variable by convergent complex power series,makes a formal costruction of For me the best introduction to calculus in one variable, yet absolutely rigurous it is more focussed in explain fundamental concepts in deep that in long full of calculations demostrations;also has some touchs of subtle humour ,some uncommon in a textbook and a lot of remarkable exercises.

Has a lot of explainig clear graphics,give examples of bizarre functions for clearing concepts,give a original introduction to complex variable by convergent complex power series,makes a formal costruction of the real numbers field, and make at this level unusual excursions in more advanced results as the demostration of the irracionality of pi or the demostration of the trancendence of e.

Is a pure mathematics text and has no mention of physical or tecnological use Seriously, just get your head around what deductions are and what the principle of mathematical induction is.

I recommend a Fitch-style natural deductive system. Calculus was the product of many hard years of trying to make progress on problems concerning finding tangents and areas to curves, and trying to mathematically analyse bodies in motion. A lot of mathematics was developed this way, so understanding the motivation is of ultimate importance.

The epsilon-delta approach to analysis is what you will find in this book. Infinitesimals should not be omitted entirely from mathematical education. It is how the calculus was developed and is a great tool for intuitively understanding lots of problems. There is a modern framework for infinitesimals called non-standard analysis. Check it out if you are interested.

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## CALCULUS. CALCUL INFINITESIMAL (2ยช ED.)

Todos los hechos conocidos acerca de desigualdades, por elementales que parezcan, son consecuencias de PP En este capitulo hemos supuesto que los mimeros nos son familiares y que P1-P12 son meramente enunciados explicitos de algunas de sus propiedades evidentes y bien sabidas. Pero ser4 necesario trabajar con numeros a lo largo de todo el libro. Por lo tanto sera razonable admitir franca- mente que todavia no entendemos bien lo que son; podemos, con todo, afirmar que, de cualquier manera que se definan, han de satisfacer las propiedades P1-P En este capitulo hemos intentado poner en evidencia que P1-P12 son de verdad propiedades bdsicas que deben admitirse para deducir de ellas otras propiedades corrientes de los ntimeros. Queda todavia la cuestin crucial de si de P1-P12 se derivan en realidad todas las propiedades de los mimeros. Pronto veremos que no.

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## CALCULUS: CALCULO INFINITESIMAL

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