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Analysis II = Third Edition /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Analysis II/ by Terence Tao.
其他題名:	Third Edition /
作者:	Tao, Terence.
面頁冊數:	XVII, 220 p.online resource. :
Contained By:	Springer Nature eBook
標題:	Mathematical analysis. -
電子資源:	https://doi.org/10.1007/978-981-10-1804-6
ISBN:	9789811018046

Analysis II = Third Edition /
Tao, Terence.

Analysis IIThird Edition /[electronic resource] :by Terence Tao. - 1st ed. 2016. - XVII, 220 p.online resource. - Texts and Readings in Mathematics,382366-8717 ;. - Texts and Readings in Mathematics,71.

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. .

ISBN: 9789811018046

Standard No.: 10.1007/978-981-10-1804-6doiSubjects--Topical Terms:

527926
Mathematical analysis.

LC Class. No.: QA299.6-433

Dewey Class. No.: 515

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