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＜電子ブック＞
Analysis II : Third Edition / by Terence Tao
(Texts and Readings in Mathematics. ISSN:23668725 ; 38)

版	1st ed. 2016.
出版者	(Singapore : Springer Nature Singapore : Imprint: Springer)
出版年	2016
大きさ	XVII, 220 p : online resource
著者標目	*Tao, Terence author SpringerLink (Online service)
件　名	LCSH:Mathematical analysis FREE:Analysis
一般注記	Chapter 1. Metric Spaces -- Chapter 2. Continuous functions on metric spaces -- Chapter 3. Uniform convergence -- Chapter 4. Power series -- Chapter 5. Fourier series -- Chapter 6. Several variable differential calculus -- Chapter 7. Lebesgue measure -- Chapter 8. Lebesgue integration 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. HTTP:URL=https://doi.org/10.1007/978-981-10-1804-6

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