Real and Complex Analysis
Volume 1
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Beschreibung
This is the first volume of the two-volume book on real and complex analysis. This volume is an introduction to measure theory and Lebesgue measure where the Riesz representation theorem is used to construct Lebesgue measure. Intended for undergraduate students of mathematics and engineering, it covers the essential analysis that is needed for the study of functional analysis, developing the concepts rigorously with sufficient detail and with minimum prior knowledge of the fundamentals of advanced calculus required. Divided into three chapters, it discusses exponential and measurable functions, Riesz representation theorem, Borel and Lebesgue measure, -spaces, Riesz–Fischer theorem, Vitali–Caratheodory theorem, the Fubini theorem, and Fourier transforms. Further, it includes extensive exercises and their solutions with each concept. The book examines several useful theorems in the realm of real and complex analysis, most of which are the work of great mathematicians of the 19th and20th centuries.
This is the first volume of the two-volume book on real and complex analysis. This volume is an introduction to measure theory and Lebesgue measure where the Riesz representation theorem is used to construct Lebesgue measure. Intended for undergraduate students of mathematics and engineering, it covers the essential analysis that is needed for the study of functional analysis, developing the concepts rigorously with sufficient detail and with minimum prior knowledge of the fundamentals of advanced calculus required. Divided into three chapters, it discusses exponential and measurable functions, Riesz representation theorem, Borel and Lebesgue measure, -spaces, Riesz–Fischer theorem, Vitali–Caratheodory theorem, the Fubini theorem, and Fourier transforms. Further, it includes extensive exercises and their solutions with each concept. The book examines several useful theorems in the realm of real and complex analysis, most of which arethe work of great mathematicians of the 19th and 20th centuries.
Discusses major topics in real and complex analysis Includes the essential analysis that is needed for the study of functional analysis Presents applications of complex analysis to analytic number theory Features over 800 step-by-step, fully solved examples Is useful to undergraduate students of mathematics and engineering
Autor*in
Rajnikant Sinha
Themen in »Real and Complex Analysis«
Conformal Mapping Harmonic Functions Holomorphic Functions Fourier Transforms Lebesgue Integration
Stimmen zu »Real and Complex Analysis«
“This introductory book should be useful to undergraduate students in mathematics and engineering. … The approach to each topic appears to have been carefully thought out, both as to the mathematical treatment and to the pedagogical presentation. The end result is a quite satisfactory book for undergraduate classroom use or even self-study.” (Christian Lavault, Mathematical Reviews, July, 2019)
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