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Real analysis: foundations and functions of one variable Laczkovich, Miklos

By: Contributor(s): Series: Undergraduate Texts in MathematicsPublication details: Springer 2015 New YorkEdition: 5th edDescription: x, 483 pISBN:
  • 9781493927654
Subject(s): DDC classification:
  • 515 L2R3
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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Holdings
Item type Current library Collection Call number Status Date due Barcode Item holds
Book Book Ahmedabad Non-fiction 515 L2R3 (Browse shelf(Opens below)) Available 192900
Total holds: 0

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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