Infinitesimal Calculus

By James M. Henle and Eugene M. Kleinberg

$15.95

Publication Date: 22nd July 2003

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... Read More
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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... Read More
Description
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.
Details
  • Price: $15.95
  • Pages: 144
  • Publisher: Dover Publications
  • Imprint: Dover Publications
  • Series: Dover Books on Mathematics
  • Publication Date: 22nd July 2003
  • Trim Size: 6.14 x 9.21 in
  • Illustration Note: Figs. throughout
  • ISBN: 9780486428864
  • Format: Paperback
  • BISACs:
    MATHEMATICS / Calculus
Table of Contents
Preface
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
Appendix A Defining Quasi-big Sets
Appendix B The Proof of Theorem 3.1
Subject Index
Name Index
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.
  • Price: $15.95
  • Pages: 144
  • Publisher: Dover Publications
  • Imprint: Dover Publications
  • Series: Dover Books on Mathematics
  • Publication Date: 22nd July 2003
  • Trim Size: 6.14 x 9.21 in
  • Illustrations Note: Figs. throughout
  • ISBN: 9780486428864
  • Format: Paperback
  • BISACs:
    MATHEMATICS / Calculus
Preface
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
Appendix A Defining Quasi-big Sets
Appendix B The Proof of Theorem 3.1
Subject Index
Name Index