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**About this book :- **
**Calculus (3E Solution) ** written by
** Michael Spivak **

This is soluton manual book. Every aspect of this book was influenced by the desire to present calculus not merely as a prelude to but as the first real encounter with mathematics. Since the foundations of analysis provided the arena in which modern modes of mathematical thinking developed, calculus ought to be the place in which to expect, rather than avoid, the strengthening of insight with logic. In addition to developing the students' intuition about the beautiful concepts of analysis, it is surely equally important to persuade them that precision and rigor are neither deterrents to intuition, nor ends in themselves, but the natural medium in which to formulate and think about mathematical questions.

This goal implies a view of mathematics which, in a sense, the entire book attempts to defend. No matter how well particular topics may be developed, the goals of this book will be realized only if it succeeds as a whole. For this reason, it would be of little value merely to list the topics covered, or to mention pedagogical practices and other innovations. Even the cursory glance customarily bestowed on new calculus texts will probably tell more than any such extended advertisement, and teachers with strong feelingsabout particular aspects of calculus will knowjust where to look to see if this book fulfillstheir requirements.

**Book Detail :- **
** Title: ** Calculus (Solution)
** Edition: ** 3rd
** Author(s): ** Michael Spivak
** Publisher: ** Publish or Perish
** Series: **
** Year: ** 1994
** Pages: ** 422
** Type: ** PDF
** Language: ** English
** ISBN: ** 091409890X,9780914098904
** Country: ** US

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**About Author :- **

Author ** Michael David Spivak ** was born in May 25, 1940 at Queens, New York. He is an American mathematician specializing in differential geometry, an expositor of mathematics.

In 1964 Spivak received a Ph.D. from Princeton University under the supervision of John Milnor. In 1985 Spivak received the Leroy P. Steele Prize. Spivak is the author of the five-volume A Comprehensive Introduction to Differential Geometry.

Spivak has also lectured on elementary physics. Spivak's most recent book, Physics for Mathematicians: Mechanics I, which contains the material that these lectures stemmed from and more, was published on December 6, 2010. Spivak is also the designer of the MathTime Professional 2 fonts (which are widely used in academic publishing) and the creator of Science International.

Spivak has also authored several well-known undergraduate textbooks. Among them, his text Calculus (W. A. Benjamin Inc., 1967; Publish or Perish, 4th ed., 2008) takes a rigorous and theoretical approach to introductory calculus and includes proofs of many theorems taken on faith in most other introductory textbooks.[8] Spivak acknowledges in the preface that others might consider this textbook to be an introduction to mathematical analysis rather than a calculus book. Another of his well-known textbooks is Calculus on Manifolds (W. A. Benjamin Inc., 1965; Addison-Wesley, revised edition, 1968), a concise (146 pp.) but rigorous and modern treatment of multivariable calculus accessible to advanced undergraduates. Spivak has also written The Joy of TeX: A Gourmet Guide to Typesetting With the AMS-TeX Macro Package and The Hitchhiker's Guide to Calculus. The book Morse Theory, by John Milnor, was based on lecture notes by Spivak and Robert Wells (as mentioned on the cover page of the booklet).

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**Book Contents :- **
**Calculus (3E Solution) ** written by
** Michael Spivak **
cover the following topics.
**PART-I Prologne**

l. Basic Properties of Numbers

2. Numbers of Various Sorts
**PART-II Foundations**

3. Functions

Appendix.OrderedPairs

4. Graphs

Aþþendix1.Vectors

Appendix2. The Cone Sections

Appendix3.Polar Coordinates

5. Limits

6. Continuous Functions

7. Three Hard Theorems

8. Least Upper Bounds

Appendix.UnformContinuity
**PART-III Derivatives and Integrals**

9. Derivatives

10. Differentiation

11. Significance of the Derivative

Appendix.Convexipand Concavig

12. Inverse Functions

Appendir.ParametricRepresentationof Curves

13. Integrals

Appendix.RiemannSums

14. The Fundamental Theorem of Calculus

15. The Trigonometric Functions

16. x is Irrational

17. Planetary Motion

18. The Logarithm and Exponential Functions

19. Integration in Elementary Terms

Appenda. The Cosmopolitan Integral
**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

SuggestedReading

Answers (toselectedproblems)

Glossaryof Symbols

Index

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