Analysis. I / Terence Tao.

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Analysis. I / Terence Tao.

Fourth edition.

9789811972614 (electronic bk.)
9811972613 (electronic bk.)
9789811972621

Singapore : Springer, 2022.

English

1 online resource (x, 340 pages).

10.1007/978-981-19-7261-4 doi

QA300 .T36 2022

515

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.

Includes index.

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Online resource; title from PDF title page (SpringerLink, viewed February 28, 2023).

Texts and readings in mathematics.

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