國立虎尾科技大學 |

Real Analysis and Applications

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Real Analysis and Applications/ by Fabio Silva Botelho.
作者:	Botelho, Fabio Silva.
面頁冊數:	XIII, 567 p.online resource. :
Contained By:	Springer Nature eBook
標題:	Functions of real variables. -
電子資源:	https://doi.org/10.1007/978-3-319-78631-5
ISBN:	9783319786315

Real Analysis and Applications
Botelho, Fabio Silva.

Real Analysis and Applications[electronic resource] /by Fabio Silva Botelho. - 1st ed. 2018. - XIII, 567 p.online resource.

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

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

792248
Functions of real variables.

LC Class. No.: QA331.5

Dewey Class. No.: 515.8

Real Analysis and Applications
LDR:02581nam a22003975i 4500 001 988457
003 DE-He213
005 20200702224825.0
007 cr nn 008mamaa
008 201225s2018 gw | s |||| 0|eng d
020 $a 9783319786315 $9 978-3-319-78631-5
024 7 $a 10.1007/978-3-319-78631-5 $2 doi
035 $a 978-3-319-78631-5
050 4 $a QA331.5
072 7 $a PBKB $2 bicssc
072 7 $a MAT034000 $2 bisacsh
072 7 $a PBKB $2 thema
082 0 4 $a 515.8 $2 23
100 1 $a Botelho, Fabio Silva. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1205136
245 1 0 $a Real Analysis and Applications $h [electronic resource] / $c by Fabio Silva Botelho.
250 $a 1st ed. 2018.
264 1 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2018.
300 $a XIII, 567 p. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
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 Functions of real variables. $3 792248
650 0 $a Measure theory. $3 527848
650 0 $a Sequences (Mathematics). $3 1253882
650 1 4 $a Real Functions. $3 672094
650 2 4 $a Measure and Integration. $3 672015
650 2 4 $a Sequences, Series, Summability. $3 672022
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9783319786308
776 0 8 $i Printed edition: $z 9783319786322
776 0 8 $i Printed edition: $z 9783030087500
856 4 0 $u https://doi.org/10.1007/978-3-319-78631-5
912 $a ZDB-2-SMA
912 $a ZDB-2-SXMS
950 $a Mathematics and Statistics (SpringerNature-11649)
950 $a Mathematics and Statistics (R0) (SpringerNature-43713)