TY  - BOOK
AU  - Moreno,Luis F.
TI  - Invitation to real analysis
T2  - MAA textbooks
SN  - 9781939512055 (hbk)
U1  - 515.8 23
PY  - 2015///
CY  - Washington, DC
PB  - The Mathematical Association of America
KW  - Mathematical analysis
KW  - Functions of real variables
N1  - Includes bibliographical references and index;  0. Paradoxes!; 
1. Logical foundations; 
2. Proof, and the natural numbers; 
3. The integers, and the ordered field of rational numbers; 
4. Induction, and well-ordering; 
5. Sets; 
6. Functions; 
7. Inverse functions; 
8. Some subsets of the real numbers; 
9. The rational numbers are denumerable; 
10. The uncountability of the real numbers; 
11. The infinite; 
12. The complete, ordered field of real numbers; 
13. Further properties of real numbers; 
14. Cluster points and related concepts; 
15. The triangle inequality; 
16. Infinite sequences; 
17. Limits of sequences; 
18. Divergence: the non-existence of a limit; 
19. Four great theorems in real analysis; 
20. Limit theorems for sequences; 
21. Cauchy sequences and the Cauchy convergence criterion; 22. The limit superior and limit inferior of a sequence; 
23. Limits of functions; 
24. Continuity and discontinuity; 
25. The sequential criterion for continuity; 
26. Theorems about continuous functions; 
27. Uniform continuity; 
28. Infinite series of constants; 
29. Series with positive terms; 
30. Further tests for series with positive terms; 
31. Series with negative terms; 
32. Rearrangements of series; 
33. Products of series; 
34. The numbers e and Y 
35. The functions exp x and ln x; 
36. The derivative; 
37. Theorems for derivatives; 
38. Other derivatives; 
39. The mean value theorem; 
40. Taylor's theorem; 
41. Infinite sequences of functions; 
42. Infinite series of functions; 
43. Power series; 
44. Operations with power series; 
45. Taylor series; 
46. Taylor series,part II; 
47. The Riemann integral; 
48. The Riemann integral, part II; 
49. The fundamental theorem of integral calculus; 
50. Improper integrals; 
51. The Cauchy-Schwartz and Minkowski inequalities; 
52. Metric spaces; 
53. Functions and limits in metric spaces; 
54. Some topology of the real number line; 
55. The Cantor ternary set; 
Appendix A. Farey sequences; 
Appendix B. Proving that; 
Appendix C. The ruler function is Riemann integrable; 
Appendix D. Continued fractions; 
Appendix E. L'Hospital's Rule; 
Appendix F. Symbols, and the Greek alphabet
N2  - Investigation of the theorems and methods that establish calculus. It is a textbook for an analysis course following Calculus II. It emphasizes the writing of proofs, and extends the development of limits, sequences, and infinite series. Riemann integration is discussed in depth. The axiomatic structures presented here build upward from those for natural numbers to those for real numbers. Related topics will interest those who need a theoretical background for secondary school teaching, the sciences, and the technologies. Historical material is included throughout the text ... . Many diagrams and hints support students as they navigate through the topics. Detailed solutions to odd-numbered exercises are included
ER  -