Real analysis: foundations and functions of one variable

By: Laczkovich, Miklos
Contributor(s): Sos, Vera T
Series: Undergraduate Texts in MathematicsPublisher: New York Springer 2015Edition: 5th edDescription: x, 483 p.ISBN: 9781493927654Subject(s): Mathematical analysisDDC classification: 515 Summary: Based on courses given at Eotvos Lorand University (Hungary) over the past 30 years, this introductory textbook develops the central concepts of the analysis of functions of one variable — systematically, with many examples and illustrations, and in a manner that builds upon, and sharpens, the student’s mathematical intuition. 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. In the spirit of learning-by-doing, Real Analysis includes more than 500 engaging exercises for the student keen on mastering the basics of analysis. The wealth of material, and modular organization, of the book make it adaptable as a textbook for courses of various levels; the hints and solutions provided for the more challenging exercises make it ideal for independent study. http://www.springer.com/in/book/9781493927654
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Slot 1372 (0 Floor, East Wing) Non-fiction 515 L2R3 (Browse shelf) Available 192900

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

Based on courses given at Eotvos Lorand University (Hungary) over the past 30 years, this introductory textbook develops the central concepts of the analysis of functions of one variable — systematically, with many examples and illustrations, and in a manner that builds upon, and sharpens, the student’s mathematical intuition. 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.
In the spirit of learning-by-doing, Real Analysis includes more than 500 engaging exercises for the student keen on mastering the basics of analysis. The wealth of material, and modular organization, of the book make it adaptable as a textbook for courses of various levels; the hints and solutions provided for the more challenging exercises make it ideal for independent study.

http://www.springer.com/in/book/9781493927654

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