Calculus

Michael Spivak

Spivak's celebrated textbook is widely held as one of the finest introductions to mathematical analysis. His aim is to present calculus as the first real encounter with mathematics: it is the place to learn how logical reasoning combined with fundamental concepts can be developed into a rigorous mathematical theory rather than a bunch of tools and techniques learned by rote. Since analysis is a subject students traditionally find difficult to grasp, Spivak provides leisurely explanations, a profusion of examples, a wide range of exercises and plenty of illustrations in an easy-going approach that enlightens difficult concepts and rewards effort. Calculus will continue to be regarded as a modern classic, ideal for honours students and mathematics majors, who seek an alternative to doorstop textbooks on calculus, and the more formidable introductions to real analysis.

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[目次]

  • Preface
  • Part I. Prologue: 1. Basic properties of mumbers
  • 2. Numbers of various sorts
  • Part II. Foundations: 3. Functions
  • 4. Graphs
  • 5. Limits
  • 6. Continuous functions
  • 7. Three hard theorems
  • 8. Least upper bounds
  • Part III. Derivatives and Integrals: 9. Derivatives
  • 10. Differentiation
  • 11. Significance of the derivative
  • 12. Inverse functions
  • 13. Integrals
  • 14. The fundamental theorem of calculus
  • 15. The trigonometric functions
  • 16. Pi is irrational
  • 17. Planetary motion
  • 18. The logarithm and exponential functions
  • 19. Integration in elementary terms
  • Part IV. Infinite Sequences and Infinite Series: 20. Approximation by polynomial functions
  • 21. e is transcendental
  • 22. Infinite sequences
  • 23. Infinite series
  • 24. Uniform convergence and power series
  • 25. Complex numbers
  • 26. Complex functions
  • 27. Complex power series
  • Part V. Epilogue: 28. Fields
  • 29. Construction of the real numbers
  • 30. Uniqueness of the real numbers
  • Suggested reading
  • Answers (to selected problems)
  • Glossary of symbols
  • Index.

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この本の情報

書名 Calculus
著作者等 Spivak, Michael David
Spivak Michael
出版元 Cambridge University Press
刊行年月 2006
版表示 Corr. 3rd ed
ページ数 xii, 670 p.
大きさ 26 cm
ISBN 9780521867443
NCID BA77750925
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言語 英語
出版国 イギリス
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