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Real and complex analysis.Volume 1

Sinha, Rajnikant.

Real and complex analysis.Volume 1

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Real and complex analysis.by Rajnikant Sinha.
作者:	Sinha, Rajnikant.
出版者:	Singapore :Springer Singapore :2018.
面頁冊數:	ix, 637 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
標題:	Mathematical analysis.
電子資源:	https://doi.org/10.1007/978-981-13-0938-0
ISBN:	9789811309380$q(electronic bk.)

Real and complex analysis.Volume 1
Sinha, Rajnikant.

Real and complex analysis.Volume 1[electronic resource] /by Rajnikant Sinha. - Singapore :Springer Singapore :2018. - ix, 637 p. :ill., digital ;24 cm.

Chapter 1. Lebesgue Integration -- Chapter 2. Lp-Spaces -- Chapter 3. Fourier Transforms -- Chapter 4. Holomorphic and Harmonic Functions -- Chapter 5. Conformal Mapping -- Chapter 6. Analytic Continuation -- Chapter 7. Special Functions.

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 and 20th centuries.

ISBN: 9789811309380$q(electronic bk.)

Standard No.: 10.1007/978-981-13-0938-0doiSubjects--Topical Terms:

186133
Mathematical analysis.

LC Class. No.: QA300 / .S564 2018

Dewey Class. No.: 515

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520 $a 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 and 20th centuries.
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