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Analysis.. II

紀錄類型:	書目-語言資料,印刷品 : 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, 210 p. :ill., digital ; : 24 cm.;
Contained By:	Springer Nature eBook
標題:	Analysis. -
電子資源:	https://doi.org/10.1007/978-981-19-7284-3
ISBN:	9789811972843

Analysis.. II
Tao, Terence.

Analysis.II[electronic resource] /by Terence Tao. - Fourth edition. - Singapore :Springer Nature Singapore :2022. - x, 210 p. :ill., digital ;24 cm. - Texts and readings in mathematics,382366-8725 ;. - Texts and readings in mathematics ;37-38..

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 the second 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 taught in two quarters of twenty-five to thirty lectures each.

ISBN: 9789811972843

Standard No.: 10.1007/978-981-19-7284-3doiSubjects--Topical Terms:

669490
Analysis.

LC Class. No.: QA300

Dewey Class. No.: 515

Analysis.. II
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520 $a This is the second 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 taught in two quarters of twenty-five to thirty lectures each.
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