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Infinitesimal Calculus

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. Numerous figures. 1979 edition.

Reprint of The MIT Press, Cambridge, MA, 1979 edition.
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Infinitesimal Calculus—
$15.95

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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. Numerous figures. 1979 edition.

Reprint of The MIT Press, Cambridge, MA, 1979 edition.
graph theory;pure mathematics;differential equations;math competition;algebraic geometry;theory stands;theory applied;maximum information;signal processing;mathematical content;integral calculus;math majors;projective geometry;differential calculus;school texts;non-standard analysis;missing concepts;modern texts;self study;nonstandard analysis;school mathematics;mathematical reasoning;communication theory;accessible introductions;mathematical notation;mathematical rigor;pure math;mathematical proofs;left-hand column;linear algebra;mathematical theory;claude shannon;information theory;classic text;coddington;stoll;trigonometry;pugh;coburn;berge;greenberg;fourier;krantz;dover;yeh;topology;chartrand;multidimensional;bartle;polynomials;epsilon-delta;coxeter;matrix;infinitesimals;probability;hartog;hamiltonian;edwards;statics;logarithms;hyperreal;trig;self-study;partial;euclid;stewart;wylie;manual;statistics;wilson;theorems;trudeau;leibniz;solutions;taylor;arithmetic;entropy;graphs;textbook;newton;applications;rigorous;intuitive;approachable;engineering;suggestion;introductory;pierce;exercises;books on self studies;books on school texts;books on theory stands;books on integral calculus;books on signal processings;books on differential calculus;books on graph theories;books on school mathematics;books on pure mathematics;books on modern texts;books on algebraic geometries;books on communication theories;books on mathematical contents;books on differential equations
Infinitesimal Calculus | Dover Publications