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A second course in analysis

Murty, Maruti Ram.

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A second course in analysis

Record Type:	Electronic resources : Monograph/item
Title/Author:	A second course in analysis/ by M. Ram Murty.
Author:	Murty, Maruti Ram.
Published:	Singapore :Springer Singapore : : 2022.,
Description:	xi, 334 p. :ill., digital ;24 cm.
[NT 15003449]:	1. Background -- 2. Measure Theory -- 3. Fourier Transforms -- 4. Complex Analysis -- 5. Introduction to Algebraic Topology -- Index.
Contained By:	Springer Nature eBook
Subject:	Mathematical analysis. -
Online resource:	https://doi.org/10.1007/978-981-16-7246-0
ISBN:	9789811672460

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

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

516833
Mathematical analysis.

LC Class. No.: QA300

Dewey Class. No.: 515

A second course in analysis
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100 1 $a Murty, Maruti Ram. $3 708340
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 516833
650 0 $a Algebra. $3 516203
650 1 4 $a Real Functions. $3 891265
650 2 4 $a Functions of a Complex Variable. $3 897310
650 2 4 $a Abstract Harmonic Analysis. $3 891093
650 2 4 $a Measure and Integration. $3 891263
650 2 4 $a Fourier Analysis. $3 891095
650 2 4 $a Algebraic Topology. $3 891269
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer Nature eBook
830 0 $a IMSc lecture notes in mathematics. $3 3599447
856 4 0 $u https://doi.org/10.1007/978-981-16-7246-0
950 $a Mathematics and Statistics (SpringerNature-11649)