An interactive introduction to mathematical analysis
著者
書誌事項
An interactive introduction to mathematical analysis
Cambridge University Press, 2003
- : hard
- : pbk
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注記
Includes bibliographical references (p. 480-481) and index
内容説明・目次
内容説明
This book provides a rigorous course in the calculus of functions of a real variable. Its gentle approach, particularly in its early chapters, makes it especially suitable for students who are not headed for graduate school but, for those who are, this book also provides the opportunity to engage in a penetrating study of real analysis. The companion on-screen version of this text contains hundreds of links to alternative approaches, more complete explanations and solutions to exercises; links that make it more friendly than any printed book could be. In addition, there are links to a wealth of optional material that an instructor can select for a more advanced course, and that students can use as a reference long after their first course has ended. The on-screen version also provides exercises that can be worked interactively with the help of the computer algebra systems that are bundled with Scientific Notebook.
目次
- 1. The emergence of rigorous calculus
- 2. Mathematical grammar
- 3. Strategies for writing proofs
- 4. Elements of set theory
- 5. The real number system
- 6. Elementary topology of the real line
- 7. Limits of sequences
- 8. Limits and continuity of functions
- 9. Differentiation
- 10. The exponential and logarithmic functions
- 11. The Riemann integral
- 12. Infinite series
- 13. Improper integrals
- 14. Sequences and series of functions
- 15. Calculus of a complex variable
- 16. Integration of functions of two variables
- 17. Sets of measure zero
- 18. Calculus of several variables.
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