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Real analysis and applications

Botelho, Fabio Silva.

Real analysis and applications

Record Type:	Electronic resources : Monograph/item
Title/Author:	Real analysis and applicationsby Fabio Silva Botelho.
Author:	Botelho, Fabio Silva.
Published:	Cham :Springer International Publishing :2018.
Description:	xiii, 567 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Mathematical analysis.
Online resource:	http://dx.doi.org/10.1007/978-3-319-78631-5
ISBN:	9783319786315$q(electronic bk.)

Real analysis and applications
Botelho, Fabio Silva.

Real analysis and applications[electronic resource] /by Fabio Silva Botelho. - Cham :Springer International Publishing :2018. - xiii, 567 p. :ill., digital ;24 cm.

Chapter 01- Real Numbers -- Chapter 02- Metric Spaces -- Chapter 03- Real Sequences and Series -- Chapter 04- Real Function Limits -- Chapter 05- Continuous Functions -- Chapter 06- Derivatives -- Chapter 07- The Riemann Integral -- Chapter 08- Differential Analysis in Rn -- Chapter 09- Integration in Rn -- Chapter 10- Topics on Vector Calculus and Vector Analysis.

This textbook introduces readers to real analysis in one and n dimensions. It is divided into two parts: Part I explores real analysis in one variable, starting with key concepts such as the construction of the real number system, metric spaces, and real sequences and series. In turn, Part II addresses the multi-variable aspects of real analysis. Further, the book presents detailed, rigorous proofs of the implicit theorem for the vectorial case by applying the Banach fixed-point theorem and the differential forms concept to surfaces in Rn. It also provides a brief introduction to Riemannian geometry. With its rigorous, elegant proofs, this self-contained work is easy to read, making it suitable for undergraduate and beginning graduate students seeking a deeper understanding of real analysis and applications, and for all those looking for a well-founded, detailed approach to real analysis.

ISBN: 9783319786315$q(electronic bk.)

Standard No.: 10.1007/978-3-319-78631-5doiSubjects--Topical Terms:

186133
Mathematical analysis.

LC Class. No.: QA300 / .B684 2018

Dewey Class. No.: 515

Real analysis and applications
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100 1 $a Botelho, Fabio Silva. $3 816288
245 1 0 $a Real analysis and applications $h [electronic resource] / $c by Fabio Silva Botelho.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2018.
300 $a xiii, 567 p. : $b ill., digital ; $c 24 cm.
505 0 $a Chapter 01- Real Numbers -- Chapter 02- Metric Spaces -- Chapter 03- Real Sequences and Series -- Chapter 04- Real Function Limits -- Chapter 05- Continuous Functions -- Chapter 06- Derivatives -- Chapter 07- The Riemann Integral -- Chapter 08- Differential Analysis in Rn -- Chapter 09- Integration in Rn -- Chapter 10- Topics on Vector Calculus and Vector Analysis.
520 $a This textbook introduces readers to real analysis in one and n dimensions. It is divided into two parts: Part I explores real analysis in one variable, starting with key concepts such as the construction of the real number system, metric spaces, and real sequences and series. In turn, Part II addresses the multi-variable aspects of real analysis. Further, the book presents detailed, rigorous proofs of the implicit theorem for the vectorial case by applying the Banach fixed-point theorem and the differential forms concept to surfaces in Rn. It also provides a brief introduction to Riemannian geometry. With its rigorous, elegant proofs, this self-contained work is easy to read, making it suitable for undergraduate and beginning graduate students seeking a deeper understanding of real analysis and applications, and for all those looking for a well-founded, detailed approach to real analysis.
650 0 $a Mathematical analysis. $3 186133
650 0 $a Numbers, Real. $3 189607
650 1 4 $a Mathematics. $3 184409
650 2 4 $a Real Functions. $3 273779
650 2 4 $a Measure and Integration. $3 273777
650 2 4 $a Sequences, Series, Summability. $3 275704
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer eBooks
856 4 0 $u http://dx.doi.org/10.1007/978-3-319-78631-5
950 $a Mathematics and Statistics (Springer-11649)