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Analysis.I

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Analysis.by Terence Tao.
作者:	Tao, Terence.
出版者:	Singapore :Springer Nature Singapore :2022.
面頁冊數:	x, 340 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
標題:	Mathematical analysis.
電子資源:	https://doi.org/10.1007/978-981-19-7261-4
ISBN:	9789811972614$q(electronic bk.)

Analysis.I
Tao, Terence.

Analysis.I[electronic resource] /by Terence Tao. - Fourth edition. - Singapore :Springer Nature Singapore :2022. - x, 340 p. :ill., digital ;24 cm. - Texts and readings in mathematics,372366-8725 ;. - Texts and readings in mathematics ;74..

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.

ISBN: 9789811972614$q(electronic bk.)

Standard No.: 10.1007/978-981-19-7261-4doiSubjects--Topical Terms:

186133
Mathematical analysis.

LC Class. No.: QA300

Dewey Class. No.: 515

Analysis.I
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505 0 $a 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.
520 $a 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.
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