The elements of real analysis | Politeknik Siber dan Sandi Negara

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The elements of real analysis

Bartle, Robert G. - Personal Name;

Chapter Summaries

Introducction: A Glimpse at Set Theory 1
1. The Algebra of Sets
2. Functions
3. Finite and Infinite Sets

I. The Real Numbers
4. The Algebraic Properties of R
5. The Order Properties of R
6. The Completeness Property of R
7. Cuts, Intervals, and the Cantor Set
II. The Topology of Cartesian Spaces
8. Vector and Cartesian Spaces
9. Open and Closed Sets
10. The Nested Cells and Bolzano-Weierstrass Theorems
11. The Heine-Borel Theorem
12. Connected Sets
13. The Complex Number System

III. Convergence
14. Introduction to Sequences
15. Subsequences and Combinations
16. Two Criteria for Convergence
17. Sequences of Functions
18. The Limit Superior
19. Some Extensions

IV. Continuous Functions
20. Local Propertiesof Continuous Functions
21. Linear Functions
22. Global Properties of Continuous Functions
23. Unifrom Continuity and Fixed Points
24. Sequences of Continuous Functions
25. Limits of Functions
26. Some Further Results

V. Functions of One Variable
27. The Mean Value Theorem
28. Further Applications of the Mean Value Theorem
29. The Riemann-Stieltjes Integral
30. Existence of the Integral
31. Further Properties of the Integral
32. Improper and Infinite Integrals
33. Uniform Convergence and Infinite Integrals

VI. Infinite Series
34. Convergence of Infinite Series
35. Tests for Absolute Convergence
36. Further Results for Series
37. Series of Functions
38. Fourier Series

VII. Differentiation in Rᵖ
39. The Derivative in Rᵖ
40. The Chain Rule and Mean Value Theorems
41. Mapping Theorems and Implicit Functions
42. Extremum Problems

VIII. Integration in Rᵖ
43. The integral in Rᵖ
44. Content and the Integral
45. Transformation of Sets and Integral

References
Hints for Selected Exercises
Index

Availability

Perpustakaan Poltek SSN 510 BAR T

500 00081

Available

Perpustakaan Poltek SSN (rak 500) 515 BAR e

b0000510

Available

Detail Information

Series Title: --
Call Number: 515 BAR e
Publisher: Canada : John Wiley & Sons., 1976
Collation: xv, 480 hal.; ilus.; 23 cm
Language: English
ISBN/ISSN: 0471054658
Classification: 515
Content Type: -
Media Type: -
Carrier Type: -
Edition: Second Edition
Subject(s): Analisis Matematis
Mathematical analysis
Specific Detail Info: --
Statement of Responsibility: Robert G. Bartle

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