A second course in analysis [electronic resource] / M. Ram Murty.

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A second course in analysis [electronic resource] / M. Ram Murty.

9789811672460 (electronic bk.)
9811672466 (electronic bk.)

Singapore : Springer, 2022.

English

1 online resource.

10.1007/978-981-16-7246-0 doi

QA300

515

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.

Includes bibliographical references and index.

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Online resource; title from PDF title page (SpringerLink, viewed May 16, 2022).

IMSc lecture notes in mathematics.

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