Analysis I, 3rd edition 1 [electronic resource] / Terence Tao.

Call Number	515
Author	Tao, Terence.
Title	Analysis I, 3rd edition Terence Tao.
Edition	3rd ed.
Physical Description	1 online resource (369 pages)
Series	Texts and Readings in Mathematics ; 37
Contents	Analysis I, 3rd edition -- Dediction -- Contents -- Preface to the frst edition -- Preface to the second and third editions -- 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. Infnite sets -- Chapter 9. Continuous functions on R -- Chapter 10. Differentiation of functions -- Chapter 11. The Riemann integral -- Chapter A. Appendix: the basics of mathematical logic -- Chapter B. Appendix: the decimal system -- Index -- Text and Readings in Mathematics.
Summary	This is part one 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.
Subject	MATHEMATICS / Calculus. MATHEMATICS / Mathematical Analysis. Electronic books.
Multimedia	https://portal.igpublish.com/iglibrary/search/HBAB0000084.html

Total Ratings: 0

Copies
MARC Record
Reviews
Details


No records found to display.

03054nam a2200409 i 4500

001

vtls001596314

003

VRT

005

20220902105700.0

006

m eo d

007

cr cn |||m|||a

008

220902s2014 ob 000 0 eng d

020

$a 9789380250649

035

$a HBAB0000084

039

$y 202209021057 $z santha

041

$a eng

050

$a QA300

082

$a 515

100

$a Tao, Terence.

245

$a Analysis I, 3rd edition $n 1 $h [electronic resource] / $c Terence Tao.

250

$a 3rd ed.

264

$a [Place of publication not identified] : $b Hindustan Book Agency, $c 2014.

264

300

$a 1 online resource (369 pages)

336

$a text $b txt $2 rdacontent

337

$a computer $b c $2 rdamedia

338

$a online resource $b cr $2 rdacarrier

490

$a Texts and Readings in Mathematics ; $v 37

504

$a Includes bibliographical references and index.

505

$a Analysis I, 3rd edition -- Dediction -- Contents -- Preface to the frst edition -- Preface to the second and third editions -- 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. Infnite sets -- Chapter 9. Continuous functions on R -- Chapter 10. Differentiation of functions -- Chapter 11. The Riemann integral -- Chapter A. Appendix: the basics of mathematical logic -- Chapter B. Appendix: the decimal system -- Index -- Text and Readings in Mathematics.

506

$a Access restricted to authorized users and institutions.

520

$a This is part one 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.

538

$a Mode of access: World Wide Web.

650

$a MATHEMATICS / Calculus. $2 bisacsh

650

$a MATHEMATICS / Mathematical Analysis. $2 bisacsh

655

$a Electronic books.

856

$u https://portal.igpublish.com/iglibrary/search/HBAB0000084.html

999

$a VIRTUA

No Reviews to Display

Summary	This is part one 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.
Contents	Analysis I, 3rd edition -- Dediction -- Contents -- Preface to the frst edition -- Preface to the second and third editions -- 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. Infnite sets -- Chapter 9. Continuous functions on R -- Chapter 10. Differentiation of functions -- Chapter 11. The Riemann integral -- Chapter A. Appendix: the basics of mathematical logic -- Chapter B. Appendix: the decimal system -- Index -- Text and Readings in Mathematics.
Subject	MATHEMATICS / Calculus. MATHEMATICS / Mathematical Analysis. Electronic books.
Multimedia	https://portal.igpublish.com/iglibrary/search/HBAB0000084.html