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A second course in analysis

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	A second course in analysisby M. Ram Murty.
作者:	Murty, Maruti Ram.
出版者:	Singapore :Springer Singapore :2022.
面頁冊數:	xi, 334 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
標題:	Mathematical analysis.
電子資源:	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
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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.
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