P. P. Korovkin-Limits and Continuity

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Textbook: Limits and Continuity
Author(s): P. P. Korovkin

Contents Chapter 1. Functions
1. Variables and Functions. Intervals and Sequences
2. Absolute Values. Neighborhoods
3. Graphs and Tables
4. Some Simple Function Classes
5. Real Numbers and Decimal Expansions Chapter 2. Limits6. Basic Concepts
7. Algebraic Properties of Limits
8. Limits Relative to a Set. One-Sided Limits
9. Infinite Limits. Indeterminate Forms
10. Limits at Infinity
11. Limits of Sequences. The Greatest Lower Bound Property
12. The Bolzano-Weierstrass Theorem. The Cauchy Conver-
gence Criterion
13. Limits of Monotonic Functions. The Function a and the Number e Chapter 3. Continuity
14. Continuous Functions
15. One-Sided Continuity. Classification of Discontinuities
16. The Intermediate Value Theorem. Absolute Extrema
17. Inverse Functions
18. Elementary Functions19. Evaluation of Limits
20. Asymptotes
21. The Modulus of Continuity. Uniform Continuity
Answers to Even-Numbered Problems
Index



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