Online-Ressource
Verfasst von:	Murty, Maruti Ram [VerfasserIn]
Titel:	A second course in analysis
Verf.angabe:	M. Ram Murty
Verlagsort:	Singapore
	New Delhi
Verlag:	Springer
	Hindustan Book Agency
E-Jahr:	2022
Jahr:	[2022]
	[2022]
Umfang:	1 Online-Ressource (xiii, 337 Seiten)
Illustrationen:	Illustrationen, Diagramme
Gesamttitel/Reihe:	IMSc lecture notes in mathematics
	HBA lecture notes in mathematics
ISBN:	978-981-16-7246-0
Abstract:	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.
DOI:	doi:10.1007/978-981-16-7246-0
URL:	Resolving-System: https://doi.org/10.1007/978-981-16-7246-0
	DOI: https://doi.org/10.1007/978-981-16-7246-0
Datenträger:	Online-Ressource
Sprache:	eng
Bibliogr. Hinweis:	Erscheint auch als : Druck-Ausgabe
K10plus-PPN:	1801277133
	Universitätsbibliothek
Lokale URL UB:	Zum Volltext