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Titlebook: Elementary Analysis; The Theory of Calcul Kenneth A. Ross Textbook 19801st edition Springer-Verlag New York 1980 Differentialrechnung.Eleme

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发表于 2025-3-21 19:22:12 | 显示全部楼层 |阅读模式
书目名称Elementary Analysis
副标题The Theory of Calcul
编辑Kenneth A. Ross
视频video
丛书名称Undergraduate Texts in Mathematics
图书封面Titlebook: Elementary Analysis; The Theory of Calcul Kenneth A. Ross Textbook 19801st edition Springer-Verlag New York 1980 Differentialrechnung.Eleme
描述Designed for students having no previous experience with rigorous proofs, this text on analysis can be used immediately following standard calculus courses. It is highly recommended for anyone planning to study advanced analysis, e.g., complex variables, differential equations, Fourier analysis, numerical analysis, several variable calculus, and statistics. It is also recommended for future secondary school teachers. A limited number of concepts involving the real line and functions on the real line are studied. Many abstract ideas, such as metric spaces and ordered systems, are avoided. The least upper bound property is taken as an axiom and the order properties of the real line are exploited throughout. A thorough treatment of sequences of numbers is used as a basis for studying standard calculus topics. Optional sections invite students to study such topics as metric spaces and Riemann-Stieltjes integrals.
出版日期Textbook 19801st edition
关键词Differentialrechnung; Elementary Analysis; Integralrechnung; calculus; differential equation
版次1
doihttps://doi.org/10.1007/978-1-4757-3971-8
isbn_ebook978-1-4757-3971-8Series ISSN 0172-6056 Series E-ISSN 2197-5604
issn_series 0172-6056
copyrightSpringer-Verlag New York 1980
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发表于 2025-3-21 23:07:23 | 显示全部楼层
Aihua Huang,Ken Wijekoon,Fazleena BadurdeenMost of the calculus involves the study of continuous functions. In this chapter we study continuous and uniformly continuous functions.
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L. van Keimpema,D.B. de Koning,J.P.H. DrenthIn this chapter we give a theoretical treatment of differentiation and related concepts, most or all of which will be familiar from the standard calculus course. Three of the most useful results are the Mean Value Theorem, which is treated in §29, L’ Hospital’s Rule, which is treated in §30, and Taylor’s Theorem, which is given in §31.
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Sequences and Series of Functions,In this chapter we develop some of the basic properties of power series. In doing so, we will introduce uniform convergence and illustrate its impor tance. In §26 we prove that power series can be differentiated and integrated term-by-term.
发表于 2025-3-22 17:55:55 | 显示全部楼层
Differentiation,In this chapter we give a theoretical treatment of differentiation and related concepts, most or all of which will be familiar from the standard calculus course. Three of the most useful results are the Mean Value Theorem, which is treated in §29, L’ Hospital’s Rule, which is treated in §30, and Taylor’s Theorem, which is given in §31.
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