Infinitesimal Calculus

Rigorous undergraduate treatment introduces calculus at the basic level, using infinitesimals and concentrating on theory rather than applications. Requires only a solid foundation in high school mathematics.Contents: 1. Introduction. 2. Language and Structure. 3. The Hyperreal Numbers. 4. The Hyperreal Line. 5. Continuous Functions. 6. Integral Calculus. 7. Differential Calculus. 8. The Fundamental Theorem. 9. Infinite Sequences and Series. 10. Infinite Polynomials. 11. The Topology of the Real Line. 12. Standard Calculus and Sequences of Functions. Appendixes. Subject Index. Name Index. Unabridged republication of the edition published by The MIT Press, Cambridge, MA, 1979. Numerous figures.

Preface	p. vi
Introduction	p. 3
Language and Structure	p. 13
The Hyperreal Numbers	p. 25
The Hyperreal Line	p. 32
Continuous Functions	p. 42
Integral Calculus	p. 52
Differential Calculus	p. 65
The Fundamental Theorem	p. 77
Infinite Sequences and Series	p. 84
Infinite Polynomials	p. 95
The Topology of the Real Line	p. 106
Standard Calculus and Sequences of Functions	p. 116
Defining Quasi-big Sets	p. 126
The Proof of Theorem 3.1	p. 128
Subject Index	p. 130
Name Index	p. 134
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Infinitesimal Calculus

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