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Titlebook: Mathematical Analysis II; Vladimir A. Zorich Textbook 2016Latest edition Springer-Verlag Berlin Heidelberg 2016 calculus.differential equa

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發(fā)表于 2025-3-21 20:03:08 | 只看該作者 |倒序?yàn)g覽 |閱讀模式
書(shū)目名稱(chēng)Mathematical Analysis II
編輯Vladimir A. Zorich
視頻videohttp://file.papertrans.cn/626/625972/625972.mp4
概述Thoroughness of coverage, from elementary to very advanced.Clarity of exposition.Originality and variety of exercises and examples.Complete logical rigor of discussion.Various new appendices.Useful no
叢書(shū)名稱(chēng)Universitext
圖書(shū)封面Titlebook: Mathematical Analysis II; Vladimir A. Zorich Textbook 2016Latest edition Springer-Verlag Berlin Heidelberg 2016 calculus.differential equa
描述.This secondEnglish edition of a very popular two-volume work presents a thorough firstcourse in analysis, leading from real numbers to such advanced topics asdifferential forms on manifolds; asymptotic methods; Fourier, Laplace, andLegendre transforms; elliptic functions; and distributions. Especially notablein this course are the clearly expressed orientation toward the naturalsciences and the informal exploration of the essence and the roots of the basicconcepts and theorems of calculus. Clarity of exposition is matched by a wealthof instructive exercises, problems, and fresh applications to areas seldomtouched on in textbooks on real analysis..The maindifference between the second and first English editions is the addition of aseries of appendices to each volume. There are six of them in the first volumeand five in the second. The subjects of these appendices are diverse. They aremeant to be useful to both students (in mathematics and physics) and teachers,who may be motivated by different goals. Some of the appendices are surveys,both prospective and retrospective. The final survey establishes importantconceptual connections between analysis and other parts of mathematics...Th
出版日期Textbook 2016Latest edition
關(guān)鍵詞calculus; differential equations; functions; integral calculus; limits; real numbers
版次2
doihttps://doi.org/10.1007/978-3-662-48993-2
isbn_softcover978-3-662-56966-5
isbn_ebook978-3-662-48993-2Series ISSN 0172-5939 Series E-ISSN 2191-6675
issn_series 0172-5939
copyrightSpringer-Verlag Berlin Heidelberg 2016
The information of publication is updating

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沙發(fā)
發(fā)表于 2025-3-21 23:52:24 | 只看該作者
板凳
發(fā)表于 2025-3-22 03:58:51 | 只看該作者
https://doi.org/10.1007/978-3-662-48993-2calculus; differential equations; functions; integral calculus; limits; real numbers
地板
發(fā)表于 2025-3-22 07:53:00 | 只看該作者
Vladimir A. ZorichThoroughness of coverage, from elementary to very advanced.Clarity of exposition.Originality and variety of exercises and examples.Complete logical rigor of discussion.Various new appendices.Useful no
5#
發(fā)表于 2025-3-22 11:06:00 | 只看該作者
6#
發(fā)表于 2025-3-22 16:48:49 | 只看該作者
*Differential Calculus from a More General Point of View,l tool far beyond real-valued functions, discussed in the first part of the textbook. Formally speaking, this chapter is independent of the material presented earlier, but without the background acquired by reading the first volume, the reader, most likely, would not recognize the rich content of the beautiful abstractions appearing here.
7#
發(fā)表于 2025-3-22 20:26:43 | 只看該作者
Surfaces and Differential Forms in ,,ve a formula for calculating the area of a surface, and we give an initial idea of the concept of a differential form. All these concepts are essential when working with curvilinear and surface integrals, which will be the main subject of the next chapter.
8#
發(fā)表于 2025-3-22 22:58:56 | 只看該作者
*Integration of Differential Forms on Manifolds, derive the contemporary version of the Newton–Leibniz formula, called the general Stokes formula. It incorporates all fundamental classical integral formulas of analysis (Newton–Leibniz, Green, Gauss–Ostrogradskii, and Stokes formulas).
9#
發(fā)表于 2025-3-23 02:06:47 | 只看該作者
Uniform Convergence and the Basic Operations of Analysis on Series and Families of Functions,series, one of the most important technical tools of analysis. We consider different types of convergence of sequences and series of functions, and discuss conditions under which certain useful properties of functions persist after passing to a limit.
10#
發(fā)表于 2025-3-23 08:28:44 | 只看該作者
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