國立高雄大學圖資館 |

Language: English

Back

A second course in analysis

Record Type:	Electronic resources : Monograph/item
Title/Author:	A second course in analysisby M. Ram Murty.
Author:	Murty, Maruti Ram.
Published:	Singapore :Springer Singapore :2022.
Description:	xi, 334 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Mathematical analysis.
Online resource:	https://doi.org/10.1007/978-981-16-7246-0
ISBN:	9789811672460$q(electronic bk.)

A second course in analysis
Murty, Maruti Ram.

A second course in analysis[electronic resource] /by M. Ram Murty. - Singapore :Springer Singapore :2022. - xi, 334 p. :ill., digital ;24 cm. - IMSc lecture notes in mathematics,2509-8098. - IMSc lecture notes in mathematics..

1. Background -- 2. Measure Theory -- 3. Fourier Transforms -- 4. Complex Analysis -- 5. Introduction to Algebraic Topology -- Index.

This book discusses major topics in measure theory, Fourier transforms, complex analysis and algebraic topology. It presents material from a mature mathematical perspective. The text is suitable for a two-semester graduate course in analysis and will help students prepare for a research career in mathematics. After a short survey of undergraduate analysis and measure theory, the book highlights the essential theorems that have now become ubiquitous in mathematics. It studies Fourier transforms, derives the inversion theorem and gives diverse applications ranging from probability theory to mathematical physics. It reviews topics in complex analysis and gives a synthetic, rigorous development of the calculus of residues as well as applications to a wide array of problems. It also introduces algebraic topology and shows the symbiosis between algebra and analysis. Indeed, algebraic archetypes were providing foundational support from the start. Multivariable calculus is comprehended in a single glance through the algebra of differential forms. Advanced complex analysis inevitably leads one to the study of Riemann surfaces, and so the final chapter gives the student a hint of these motifs and underlying algebraic patterns.

ISBN: 9789811672460$q(electronic bk.)

Standard No.: 10.1007/978-981-16-7246-0doiSubjects--Topical Terms:

186133
Mathematical analysis.

LC Class. No.: QA300

Dewey Class. No.: 515

A second course in analysis
LDR:02373nmm a2200337 a 4500 001 621436
003 DE-He213
005 20220503205248.0
006 m d
007 cr nn 008maaau
008 221121s2022 si s 0 eng d
020 $a 9789811672460$q(electronic bk.)
020 $a 9789811672477$q(paper)
024 7 $a 10.1007/978-981-16-7246-0 $2 doi
035 $a 978-981-16-7246-0
040 $a GP $c GP
041 0 $a eng
050 4 $a QA300
072 7 $a PBKB $2 bicssc
072 7 $a MAT034000 $2 bisacsh
072 7 $a PBKB $2 thema
082 0 4 $a 515 $2 23
090 $a QA300 $b .M984 2022
100 1 $a Murty, Maruti Ram. $3 277740
245 1 2 $a A second course in analysis $h [electronic resource] / $c by M. Ram Murty.
260 $a Singapore : $b Springer Singapore : $b Imprint: Springer, $c 2022.
300 $a xi, 334 p. : $b ill., digital ; $c 24 cm.
490 1 $a IMSc lecture notes in mathematics, $x 2509-8098
505 0 $a 1. Background -- 2. Measure Theory -- 3. Fourier Transforms -- 4. Complex Analysis -- 5. Introduction to Algebraic Topology -- Index.
520 $a This book discusses major topics in measure theory, Fourier transforms, complex analysis and algebraic topology. It presents material from a mature mathematical perspective. The text is suitable for a two-semester graduate course in analysis and will help students prepare for a research career in mathematics. After a short survey of undergraduate analysis and measure theory, the book highlights the essential theorems that have now become ubiquitous in mathematics. It studies Fourier transforms, derives the inversion theorem and gives diverse applications ranging from probability theory to mathematical physics. It reviews topics in complex analysis and gives a synthetic, rigorous development of the calculus of residues as well as applications to a wide array of problems. It also introduces algebraic topology and shows the symbiosis between algebra and analysis. Indeed, algebraic archetypes were providing foundational support from the start. Multivariable calculus is comprehended in a single glance through the algebra of differential forms. Advanced complex analysis inevitably leads one to the study of Riemann surfaces, and so the final chapter gives the student a hint of these motifs and underlying algebraic patterns.
650 0 $a Mathematical analysis. $3 186133
650 0 $a Algebra. $3 188312
650 1 4 $a Real Functions. $3 273779
650 2 4 $a Functions of a Complex Variable. $3 275780
650 2 4 $a Abstract Harmonic Analysis. $3 274074
650 2 4 $a Measure and Integration. $3 273777
650 2 4 $a Fourier Analysis. $3 273776
650 2 4 $a Algebraic Topology. $3 273784
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer Nature eBook
830 0 $a IMSc lecture notes in mathematics. $3 922632
856 4 0 $u https://doi.org/10.1007/978-981-16-7246-0
950 $a Mathematics and Statistics (SpringerNature-11649)