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Real analysis = foundations and functions of one variable /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Real analysis/ by Miklos Laczkovich, Vera T. Sos.
其他題名:	foundations and functions of one variable /
作者:	Laczkovich, Miklos.
其他作者:	Sos, Vera T.
出版者:	New York, NY :Springer New York : : 2015.,
面頁冊數:	x, 483 p. :ill., digital ; : 24 cm.;
Contained By:	Springer eBooks
標題:	Analysis. -
電子資源:	http://dx.doi.org/10.1007/978-1-4939-2766-1
ISBN:	9781493927661

Real analysis = foundations and functions of one variable /
Laczkovich, Miklos.

Real analysisfoundations and functions of one variable /[electronic resource] :by Miklos Laczkovich, Vera T. Sos. - New York, NY :Springer New York :2015. - x, 483 p. :ill., digital ;24 cm. - Undergraduate texts in mathematics,0172-6056. - Undergraduate texts in mathematics..

A Short Historical Introduction -- Basic Concepts -- Real Numbers -- Infinite Sequences I -- Infinite Sequences II -- Infinite Sequences III -- Rudiments of Infinite Series -- Countable Sets -- Real Valued Functions of One Variable -- Continuity and Limits of Functions -- Various Important Classes of Functions (Elementary Functions) -- Differentiation -- Applications of Differentiation -- The Definite Integral -- Integration -- Applications of Integration -- Functions of Bounded Variation -- The Stieltjes Integral -- The Improper Integral.

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 students' mathematical intuition. The modular organization of the book makes it adaptable for either semester or year-long introductory courses, while the wealth of material allows for it to be used at various levels of student sophistication in all programs where analysis is a part of the curriculum, including teachers' education. 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. There are frequent hints and occasional complete solutions provided for the more challenging exercises making it an ideal choice for independent study. The book includes a solid grounding in the basics of logic and proofs, sets, and real numbers, in preparation for a rigorous study of the main topics: limits, continuity, rational functions and transcendental functions, differentiation, and integration. Numerous historical notes and applications to other areas of mathematics, and to physics, are given, thereby demonstrating the practical scope and power of mathematical analysis.

ISBN: 9781493927661

Standard No.: 10.1007/978-1-4939-2766-1doiSubjects--Topical Terms:

669490
Analysis.

LC Class. No.: QA300

Dewey Class. No.: 515

Real analysis = foundations and functions of one variable /
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520 $a 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 students' mathematical intuition. The modular organization of the book makes it adaptable for either semester or year-long introductory courses, while the wealth of material allows for it to be used at various levels of student sophistication in all programs where analysis is a part of the curriculum, including teachers' education. 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. There are frequent hints and occasional complete solutions provided for the more challenging exercises making it an ideal choice for independent study. The book includes a solid grounding in the basics of logic and proofs, sets, and real numbers, in preparation for a rigorous study of the main topics: limits, continuity, rational functions and transcendental functions, differentiation, and integration. Numerous historical notes and applications to other areas of mathematics, and to physics, are given, thereby demonstrating the practical scope and power of mathematical analysis.
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