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Calculus: 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

Front Cover
30 Reviews
Cambridge University Press, Jun 8, 2006 - Mathematics - 670 pages
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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Review: Calculus

User Review  - Alex - Goodreads

A solid text and reference on the topic. Were I to want to re-learn calculus, I'd start here. Read full review

Review: Calculus

User Review  - Phoenix - Goodreads

Simply the best of its kind. Single variable differential and integral calculus, presented with rigor and style. Many calculus texts motivate the study of the material with physics problems. Spivak ... Read full review

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Common terms and phrases

ˇnd ˇnding ˇrst algebraic Appendix arcsin arctan calculus Cauchy Cauchy sequence Chapter choose complex numbers compute Consequently consider continuous function converges uniformly convex cosx deˇned deˇnition defined denoted derivative difˇcult easy equation example exist expression f and g f is continuous f is differentiable f(x+ fact Find fn(x formula function deˇned function f geometric graph of f Hint inˇnite induction inequality interval irrational least upper bound lemma lim f(x lim x→a limit logx mathematical maximum Mean Value Theorem minimum point natural numbers notation Notice obtain one-one pairs partition polar coordinates polynomial function power series Problem properties Prove that lim radius radius of convergence rational numbers real numbers root satisˇes satisfying sequence simple sin2 sinx sufˇciently Suppose that f tangent line Taylor polynomial Taylor's Theorem true

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References from web pages

Calculus - Wikipedia, the free encyclopedia
Calculus (Latin, calculus, a small stone used for counting) is a branch of mathematics that includes the study of limits, derivatives, integrals, ...
en.wikipedia.org/ wiki/ Calculus

Long Sunday: calculus: a plea
Calculus My formal study of Mathematics, such as it was, ended at the age of thirteen. Even before then, however, it had been rather discontinuous: it was ...
www.long-sunday.net/ long_sunday/ 2006/ 02/ calculus_a_plea.html

Textbook for Calculus [Self-Learn] Text - Physics Forums Library
[Archive] Textbook for Calculus [Self-Learn] Academic & Career Guidance.
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The most enlightening Calculus books | Math-Blog
In other words, no matter how easy a Calculus course is, there will always be a majority of C students. Making the courses dumber has only resulted in the ...
math-blog.com/ 2007/ 05/ 13/ the-most-enlightening-calculus-books/

Ovablastic: The most enlightening Calculus books
In other words, no matter how easy a Calculus course is, there will always be a majority of C students. Making the courses dumber has only resulted in the ...
ovablastic.blogspot.com/ 2008/ 04/ most-enlightening-calculus-books.html

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The Calculus on Line project has been. under development since Summer 1998, ... the students enrolled in first-year calculus. are engineering majors. ...
www.calonline.msstate.edu/ hearin-news-899.pdf

Lee Lady: Topics in Calculus
Lee Lady: Lectures on various top;ics such as applications of integration, convergence of infinite series, curvature, discontinuities for functions of ...
www.math.hawaii.edu/ ~lee/ calculus/

Honors Multivariable Calculus and Linear Algebra
Honors Multivariable Calculus and Linear Algebra. ... Calculus on Manifolds by Michael Spivak, published by Westview Press These are available from Harvard ...
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JSTOR: Convexity in Elementary Calculus: Some Geometric Equivalences
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Calculus - Cambridge University Press
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 ...
www.cambridge.org/ catalogue/ catalogue.asp?isbn=9780521867443

Bibliographic information

QR code for Calculus: 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
TitleCalculus: 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, Michael Spivak
AuthorMichael Spivak
Edition3, illustrated, revised
PublisherCambridge University Press, 2006
ISBN0521867444, 9780521867443
Length670 pages
Subjects ›  › 

Mathematics / Calculus
Mathematics / Geometry / General
Mathematics / Mathematical Analysis
  
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