期刊全称 | Analysis II | 期刊简称 | Third Edition | 影响因子2023 | Terence 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 |  | 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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