Second course in analysis

By:

Murty, M. Ram

Series: Institute of Mathematical Sciences Lecture NotesPublication details: Hindustan Book Agency, 2020 New Delhi:Description: xiv, 336p. ; pb, 24cmISBN:

9789386279842

Subject(s):

DDC classification:

515 MUR

Summary: This book represents material suitable for a two-semester graduate course in analysis. Based on courses given by the author since 2007, it is targeted towards graduate students preparing for a research career in mathematics. After reviewing what a typical student would have learned in single variable and multivariable calculus courses, the first chapter presents familiar material from a mature mathematical perspective. The second chapter surveys measure theory and highlights the essential theorems that have now become ubiquitous in mathematics. The third chapter on Fourier transforms derives the inversion theorem and gives diverse applications ranging from probability theory to mathematical physics. The fourth chapter reviews complex analysis giving a synthetic, rigorous development of the calculus of residues and its applications to a wide array of problems. The final chapter is an introduction to algebraic topology and is included to show the symbiosis between algebra and analysis

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Holdings
Item type	Current library	Collection	Call number	Copy number	Status	Date due	Barcode
Books	IIT Gandhinagar General Stacks	General	515 MUR (Browse shelf(Opens below))	1	Available		030805

Includes references and index

This book represents material suitable for a two-semester graduate course in analysis. Based on courses given by the author since 2007, it is targeted towards graduate students preparing for a research career in mathematics. After reviewing what a typical student would have learned in single variable and multivariable calculus courses, the first chapter presents familiar material from a mature mathematical perspective. The second chapter surveys measure theory and highlights the essential theorems that have now become ubiquitous in mathematics. The third chapter on Fourier transforms derives the inversion theorem and gives diverse applications ranging from probability theory to mathematical physics. The fourth chapter reviews complex analysis giving a synthetic, rigorous development of the calculus of residues and its applications to a wide array of problems. The final chapter is an introduction to algebraic topology and is included to show the symbiosis between algebra and analysis

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