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Real analysis : foundations and functions of one variable / Miklos Laczkovich and Vera T. Sos.

By: Contributor(s): Series: Undergraduate texts in mathematicsPublication details: New York : Springer, 2015.Edition: 5th edDescription: x, 483 p. : illustrations ; 24 cmISBN:
  • 9781493927654
Subject(s): DDC classification:
  • 515 23 L152
Contents:
1. A Short Historical Introduction.- 2. Basic Concepts.- 3. Real Numbers.- 4. Infinite Sequences I.- 5. Infinite Sequences II.- 6. Infinite Sequences III.- 7. Rudiments of Infinite Series.- 8. Countable Sets.- 9. Real Valued Functions of One Variable.- 10. Continuity and Limits of Functions.- 11. Various Important Classes of Functions (Elementary Functions).- 12. Differentiation.- 13. Applications of Differentiation.- 14. The Definite Integral.- 15. Integration.- 16. Applications of Integration.- 17. Functions of Bounded Variation.- 18. The Stieltjes Integral.- 19. The Improper Integral.- Hints, solutions.- Notation.- References.- Index.
Summary: The book provides a solid grounding in the basics of logic and proofs, sets, and real numbers, in preparation for a study of the main topics: limits, continuity, rational functions and transcendental functions, differentiation, and integration. Numerous applications to other areas of mathematics, and to physics, are given, thereby demonstrating the practical scope and power of the theoretical concepts treated.
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Holdings
Item type Current library Call number Status Date due Barcode Item holds
Books ISI Library, Kolkata 515 L152 (Browse shelf(Opens below)) Available 136481
Total holds: 0

Includes bibliographical references and index.

1. A Short Historical Introduction.-
2. Basic Concepts.-
3. Real Numbers.-
4. Infinite Sequences I.-
5. Infinite Sequences II.-
6. Infinite Sequences III.-
7. Rudiments of Infinite Series.-
8. Countable Sets.-
9. Real Valued Functions of One Variable.-
10. Continuity and Limits of Functions.-
11. Various Important Classes of Functions (Elementary Functions).-
12. Differentiation.-
13. Applications of Differentiation.-
14. The Definite Integral.-
15. Integration.-
16. Applications of Integration.-
17. Functions of Bounded Variation.-
18. The Stieltjes Integral.-
19. The Improper Integral.-
Hints, solutions.-
Notation.-
References.-
Index.

The book provides a solid grounding in the basics of logic and proofs, sets, and real numbers, in preparation for a study of the main topics: limits, continuity, rational functions and transcendental functions, differentiation, and integration. Numerous applications to other areas of mathematics, and to physics, are given, thereby demonstrating the practical scope and power of the theoretical concepts treated.

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