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＜電子ブック＞
Analysis I : Fourth Edition / by Terence Tao
(Texts and Readings in Mathematics. ISSN:23668725 ; 37)

版	2nd ed. 2022.
出版者	(Singapore : Springer Nature Singapore : Imprint: Springer)
出版年	2022
大きさ	X, 340 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. Introduction -- Chapter 2. Starting at the beginning: the natural numbers -- Chapter 3. Set theory -- Chapter 4. Integers and rationals -- Chapter 5. The real numbers -- Chapter 6. Limits of sequences -- Chapter 7. Series -- Chapter 8. Infinite sets -- Chapter 9. Continuous functions on R -- Chapter 10. Differentiation of functions -- Chapter 11. The Riemann integral. This is the first book of a two-volume textbook on real analysis. Both the volumes—Analysis I and Analysis II—are intended for honors undergraduates who have already been exposed to calculus. The emphasis is on rigor and foundations. The material starts at the very beginning—the construction of number systems and set theory (Analysis I, Chaps. 1–5), then on to the basics of analysis such as limits, series, continuity, differentiation, and Riemann integration (Analysis I, Chaps. 6–11 on Euclidean spaces, and Analysis II, Chaps. 1–3 on metric spaces), through power series, several variable calculus, and Fourier analysis (Analysis II, Chaps. 4–6), and finally to the Lebesgue integral (Analysis II, Chaps. 7–8). There are appendices on mathematical logic and the decimal system. The entire text (omitting some less central topics) is in two quarters of twenty-five to thirty lectures each HTTP:URL=https://doi.org/10.1007/978-981-19-7261-4

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