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Titlebook: Real Analysis; Foundations and Func Miklós Laczkovich,Vera T. Sós Textbook 2015 Springer New York 2015 Fourier series.Stieltjes integral.co

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書目名稱Real Analysis
副標(biāo)題Foundations and Func
編輯Miklós Laczkovich,Vera T. Sós
視頻videohttp://file.papertrans.cn/823/822121/822121.mp4
概述Includes insightful historical remarks regarding real analysis.Presents core ideas of analysis “as a way of thinking” as opposed to “a body of facts”.Explains how and why ideas arise, then how they ev
叢書名稱Undergraduate Texts in Mathematics
圖書封面Titlebook: Real Analysis; Foundations and Func Miklós Laczkovich,Vera T. Sós Textbook 2015 Springer New York 2015 Fourier series.Stieltjes integral.co
描述.Based on courses given at E?tv?s Loránd 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..
出版日期Textbook 2015
關(guān)鍵詞Fourier series; Stieltjes integral; continuous functions; differentiation; infinite sequences; infinite s
版次1
doihttps://doi.org/10.1007/978-1-4939-2766-1
isbn_softcover978-1-4939-4222-0
isbn_ebook978-1-4939-2766-1Series ISSN 0172-6056 Series E-ISSN 2197-5604
issn_series 0172-6056
copyrightSpringer New York 2015
The information of publication is updating

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Basic Concepts,s Rademacher and Otto Toeplitz, ., literally . [6].) Nowadays, however, such a definition will not do, for modern algebra deals with abstract structures instead of numbers, and some branches of geometry study objects that barely resemble any figure in the plane or in space. Other branches of mathema
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Infinite Sequences II,nce (18) in Example ., that is, let .. be the .th digit in the decimal expansion of .. We know that (..) does not have a limit. But does the sequence . have a limit? First of all, let us note that ..?≥?1, and thus ..?≥?1 for infinitely many .. Now if there are infinitely many zeros among the terms .
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The Definite Integral,called the indefinite integral of .. Now we introduce a very different kind of concept that we also call integrals—definite integrals, to be precise. This concept, in contrast to that of the indefinite integral, assigns numbers to functions (and not a family of functions). In the next chapter, we wi
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Applications of Integration,d volume). We have already spent time computing arc lengths, but only for graphs of functions. We saw examples of computing the area of certain shapes (mostly regions under graphs), and at the same time, we got a taste of computing volumes when we determined the volume of a sphere (see item 2 in Exa
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