語系:
繁體中文
English
說明(常見問題)
圖資館首頁
登入
回首頁
切換:
標籤
|
MARC模式
|
ISBD
Real analysisfoundations /
~
Ovchinnikov, Sergei.
Real analysisfoundations /
紀錄類型:
書目-電子資源 : Monograph/item
正題名/作者:
Real analysisby Sergei Ovchinnikov.
其他題名:
foundations /
作者:
Ovchinnikov, Sergei.
出版者:
Cham :Springer International Publishing :2021.
面頁冊數:
xii, 178 p. :ill., digital ;24 cm.
Contained By:
Springer Nature eBook
標題:
Mathematical analysis.
電子資源:
https://doi.org/10.1007/978-3-030-64701-8
ISBN:
9783030647018$q(electronic bk.)
Real analysisfoundations /
Ovchinnikov, Sergei.
Real analysis
foundations /[electronic resource] :by Sergei Ovchinnikov. - Cham :Springer International Publishing :2021. - xii, 178 p. :ill., digital ;24 cm. - Universitext,0172-5939. - Universitext..
1 Rational Numbers -- 2 Real Numbers -- 3 Continuous Functions -- 4 Differentiation -- 5 Integration -- 6 Infinite Series -- A Natural Numbers and Integers -- B Dedekind's Construction of Real Numbers. C A Panorama of Ordered Fields.
This textbook explores the foundations of real analysis using the framework of general ordered fields, demonstrating the multifaceted nature of the area. Focusing on the logical structure of real analysis, the definitions and interrelations between core concepts are illustrated with the use of numerous examples and counterexamples. Readers will learn of the equivalence between various theorems and the completeness property of the underlying ordered field. These equivalences emphasize the fundamental role of real numbers in analysis. Comprising six chapters, the book opens with a rigorous presentation of the theories of rational and real numbers in the framework of ordered fields. This is followed by an accessible exploration of standard topics of elementary real analysis, including continuous functions, differentiation, integration, and infinite series. Readers will find this text conveniently self-contained, with three appendices included after the main text, covering an overview of natural numbers and integers, Dedekind's construction of real numbers, historical notes, and selected topics in algebra. Real Analysis: Foundations is ideal for students at the upper-undergraduate or beginning graduate level who are interested in the logical underpinnings of real analysis. With over 130 exercises, it is suitable for a one-semester course on elementary real analysis, as well as independent study.
ISBN: 9783030647018$q(electronic bk.)
Standard No.: 10.1007/978-3-030-64701-8doiSubjects--Topical Terms:
186133
Mathematical analysis.
LC Class. No.: QA300
Dewey Class. No.: 515.8
Real analysisfoundations /
LDR
:02634nmm a2200337 a 4500
001
600634
003
DE-He213
005
20210616142752.0
006
m d
007
cr nn 008maaau
008
211104s2021 sz s 0 eng d
020
$a
9783030647018$q(electronic bk.)
020
$a
9783030647001$q(paper)
024
7
$a
10.1007/978-3-030-64701-8
$2
doi
035
$a
978-3-030-64701-8
040
$a
GP
$c
GP
041
0
$a
eng
050
4
$a
QA300
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
090
$a
QA300
$b
.O96 2021
100
1
$a
Ovchinnikov, Sergei.
$3
274851
245
1 0
$a
Real analysis
$h
[electronic resource] :
$b
foundations /
$c
by Sergei Ovchinnikov.
260
$a
Cham :
$b
Springer International Publishing :
$b
Imprint: Springer,
$c
2021.
300
$a
xii, 178 p. :
$b
ill., digital ;
$c
24 cm.
490
1
$a
Universitext,
$x
0172-5939
505
0
$a
1 Rational Numbers -- 2 Real Numbers -- 3 Continuous Functions -- 4 Differentiation -- 5 Integration -- 6 Infinite Series -- A Natural Numbers and Integers -- B Dedekind's Construction of Real Numbers. C A Panorama of Ordered Fields.
520
$a
This textbook explores the foundations of real analysis using the framework of general ordered fields, demonstrating the multifaceted nature of the area. Focusing on the logical structure of real analysis, the definitions and interrelations between core concepts are illustrated with the use of numerous examples and counterexamples. Readers will learn of the equivalence between various theorems and the completeness property of the underlying ordered field. These equivalences emphasize the fundamental role of real numbers in analysis. Comprising six chapters, the book opens with a rigorous presentation of the theories of rational and real numbers in the framework of ordered fields. This is followed by an accessible exploration of standard topics of elementary real analysis, including continuous functions, differentiation, integration, and infinite series. Readers will find this text conveniently self-contained, with three appendices included after the main text, covering an overview of natural numbers and integers, Dedekind's construction of real numbers, historical notes, and selected topics in algebra. Real Analysis: Foundations is ideal for students at the upper-undergraduate or beginning graduate level who are interested in the logical underpinnings of real analysis. With over 130 exercises, it is suitable for a one-semester course on elementary real analysis, as well as independent study.
650
0
$a
Mathematical analysis.
$3
186133
650
0
$a
Functions of real variables.
$3
189525
650
0
$a
Ordered fields.
$3
895260
650
1 4
$a
Real Functions.
$3
273779
650
2 4
$a
Measure and Integration.
$3
273777
650
2 4
$a
Sequences, Series, Summability.
$3
275704
650
2 4
$a
Mathematical Logic and Foundations.
$3
274479
650
2 4
$a
Analysis.
$3
273775
710
2
$a
SpringerLink (Online service)
$3
273601
773
0
$t
Springer Nature eBook
830
0
$a
Universitext.
$3
558272
856
4 0
$u
https://doi.org/10.1007/978-3-030-64701-8
950
$a
Mathematics and Statistics (SpringerNature-11649)
筆 0 讀者評論
全部
電子館藏
館藏
1 筆 • 頁數 1 •
1
條碼號
館藏地
館藏流通類別
資料類型
索書號
使用類型
借閱狀態
預約狀態
備註欄
附件
000000199168
電子館藏
1圖書
電子書
EB QA300 .O96 2021 2021
一般使用(Normal)
在架
0
1 筆 • 頁數 1 •
1
多媒體
多媒體檔案
https://doi.org/10.1007/978-3-030-64701-8
評論
新增評論
分享你的心得
Export
取書館別
處理中
...
變更密碼
登入