Calculus

基本信息

Format:Hardback 681 pages, 700 Line drawings, unspecified

Publisher:Cambridge University Press

Imprint:Cambridge University Press

Edition:3 Revised edition

ISBN:9780521867443

Published:8 Jun 2006

Weight:1788g

Dimensions:230 x 256 x 39 (mm)

页面参数仅供参考，具体以实物为准

书籍简介

斯皮瓦克著名的教科书被广泛认为是数学分析的最好介绍之一。他的目标是将微积分作为第一次真正接触数学的机会:在这里学习如何将逻辑推理与基本概念结合起来，发展成严格的数学理论，而不是死记硬背地学习一堆工具和技术。由于分析是一个学生传统上很难掌握的科目，Spivak提供了悠闲的解释，大量的例子，广泛的练习和大量的插图在一个容易的方法，启发困难的概念和奖励努力。微积分将继续被视为现代经典，为优等生和数学专业的理想，他们寻求一个替代教科书的微积分，以及更令人生畏的实际分析介绍。

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.

目录

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.

作者简介

Michael Spivak, Publish or Perish Inc., Houston, Texas