An Introduction to Mathematical Analysis
- 1st Edition - September 12, 2014
- Latest edition
- Author: Robert A. Rankin
- Language: English
International Series of Monographs on Pure and Applied Mathematics, Volume 43: An Introduction to Mathematical Analysis discusses the various topics involved in the analysis of… Read more
International Series of Monographs on Pure and Applied Mathematics, Volume 43: An Introduction to Mathematical Analysis discusses the various topics involved in the analysis of functions of a single real variable. The title first covers the fundamental idea and assumptions in analysis, and then proceeds to tackling the various areas in analysis, such as limits, continuity, differentiability, integration, convergence of infinite series, double series, and infinite products. The book will be most useful to undergraduate students of mathematical analysis.
Preface
List of Symbols and Notations
I. Fundamental Ideas and Assumptions
1. Introduction
2. Assumptions Relating to the Field Operations
3. Assumptions Relating to the Ordering of the Real Numbers
4. Mathematical Induction
5. Upper and Lower Bounds of Sets of Real Numbers
6. Functions
II. Limits and Continuity
7. Limits of Real Functions on the Positive Integers
8. Limits of Real Functions of a Real Variable x as x Tends to Infinity
9. Elementary Topological Ideas
10. Limits of Real Functions at Finite Points
11. Continuity
12. Inverse Functions and Fractional Indices
III. Differentiability
13. Derivatives
14. General Theorems Concerning Real Functions
15. Maxima, Minima and Convexity
16. Complex Numbers and Functions
IV. Infinite Series
17. Elementary Properties of Infinite Series
18. Series with Non-Negative Terms
19. Absolute and Conditional Convergence
20. The Decimal Notation for Real Numbers
V. Functions Defined by Power Series
21. General Theory of Power Series
22. Real Power Series
23. The Exponential and Logarithmic Functions
24. The Trigonometric Functions
25. The Hyperbolic Functions
26. Complex Indices
VI. Integration
27. The Indefinite Integral
28. Interval Functions and Functions of Bounded Variation
29. The Riemann-Stieltjes Integral
30. The Riemann Integral
31. Curves
32. Area
VII. Convergence and Uniformity
33. Upper and Lower Limits and Their Applications
34. Further Convergence Tests for Infinite Series
35. Uniform Convergence
36. Improper Integrals
37. Double Series
38. Infinite Products
Hints for Solutions of Exercises
Index
- Edition: 1
- Latest edition
- Published: September 12, 2014
- Language: English
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