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Titlebook: Analysis II; Third Edition Terence Tao Textbook 20161st edition The Editor(s) (if applicable) and The Author(s), under exclusive license to

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发表于 2025-3-21 18:36:34 | 显示全部楼层 |阅读模式
期刊全称Analysis II
期刊简称Third Edition
影响因子2023Terence Tao
视频video
发行地址Discusses all major topics of analysis in a simple, lucid manner.Highlights the concrete setting of the real line and Euclidean spaces.Provides examples, and step-by-step instructions.Evolves from the
学科分类Texts and Readings in Mathematics
图书封面Titlebook: Analysis II; Third Edition Terence Tao Textbook 20161st edition The Editor(s) (if applicable) and The Author(s), under exclusive license to
影响因子.This is part two of a two-volume book on real analysis and is intended for senior undergraduate students of mathematics who have already been exposed to calculus. The emphasis is on rigour and foundations of analysis. Beginning with the construction of the number systems and set theory, the book discusses the basics of analysis (limits, series, continuity, differentiation, Riemann integration), through to power series, several variable calculus and Fourier analysis, and then finally the Lebesgue integral. These are almost entirely set in the concrete setting of the real line and Euclidean spaces, although there is some material on abstract metric and topological spaces. The book also has appendices on mathematical logic and the decimal system. The entire text (omitting some less central topics) can be taught in two quarters of 25–30 lectures each. The course material is deeply intertwined with the exercises, as it is intended that the student actively learn the material (and practice thinking and writing rigorously) by proving several of the key results in the theory.   .
Pindex Textbook 20161st edition
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发表于 2025-3-21 23:39:11 | 显示全部楼层
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发表于 2025-3-22 07:48:41 | 显示全部楼层
Lebesgue integration,hings, piecewise constant functions only attain a finite number of values (as opposed to most functions in real life, which can take an infinite number of values). Once one learns how to integrate piecewise constant functions, one can then integrate other Riemann integrable functions by a similar procedure.
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发表于 2025-3-22 15:49:27 | 显示全部楼层
Sumer S. Vaid,Gabriella M. Hararia rich subject, the theory of metric spaces becomes even richer, and of more importance to analysis, when one considers not just a single metric space, but rather . (..) and (..) of metric spaces, as well as . : . between such spaces.
发表于 2025-3-22 17:41:20 | 显示全部楼层
Davide Marengo,Michele Settanniimated by polynomials. Later, we showed how a different class of functions (real analytic functions) could be written exactly (not approximately) as an infinite polynomial, or more precisely a power series.
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发表于 2025-3-23 03:16:33 | 显示全部楼层
Sumer S. Vaid,Gabriella M. Hararia rich subject, the theory of metric spaces becomes even richer, and of more importance to analysis, when one considers not just a single metric space, but rather . (..) and (..) of metric spaces, as well as . : . between such spaces.
发表于 2025-3-23 08:50:32 | 显示全部楼层
Davide Marengo,Michele Settanniimated by polynomials. Later, we showed how a different class of functions (real analytic functions) could be written exactly (not approximately) as an infinite polynomial, or more precisely a power series.
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