語系:
繁體中文
English
說明(常見問題)
登入
回首頁
切換:
標籤
|
MARC模式
|
ISBD
A circle-line study of mathematical analysis
紀錄類型:
書目-語言資料,印刷品 : Monograph/item
正題名/作者:
A circle-line study of mathematical analysis/ by Simone Secchi.
作者:
Secchi, Simone.
出版者:
Cham :Springer International Publishing : : 2022.,
面頁冊數:
xix, 469 p. :ill., digital ; : 24 cm.;
Contained By:
Springer Nature eBook
標題:
Analysis. -
電子資源:
https://doi.org/10.1007/978-3-031-19738-3
ISBN:
9783031197383
A circle-line study of mathematical analysis
Secchi, Simone.
A circle-line study of mathematical analysis
[electronic resource] /by Simone Secchi. - Cham :Springer International Publishing :2022. - xix, 469 p. :ill., digital ;24 cm. - UNITEXT. La matematica per il 3+2,v. 1412038-5757 ;. - UNITEXT.La matematica per il 3+2 ;v. 139..
Part I First half of the journey -- 1 An appetizer of propositional logic -- 2 Sets, relations, functions in a naïve way -- 3 Numbers -- 4 Elementary cardinality -- 5 Distance, topology and sequences on the set of real numbers -- 6 Series -- 7 Limits: from sequences to functions of a real variable -- 8 Continuous functions of a real variable -- 9 Derivatives and differentiability- 10 Riemann's integral -- 11 Elementary functions -- Part II Second half of the journey -- 12 Return to Set Theory -- 13 Neighbors again: topological spaces -- 14 Differentiating again: linearization in normed spaces -- 15 A functional approach to Lebesgue integration theory -- 16 Measures before integrals.
The book addresses the rigorous foundations of mathematical analysis. The first part presents a complete discussion of the fundamental topics: a review of naive set theory, the structure of real numbers, the topology of R, sequences, series, limits, differentiation and integration according to Riemann. The second part provides a more mature return to these topics: a possible axiomatization of set theory, an introduction to general topology with a particular attention to convergence in abstract spaces, a construction of the abstract Lebesgue integral in the spirit of Daniell, and the discussion of differentiation in normed linear spaces. The book can be used for graduate courses in real and abstract analysis and can also be useful as a self-study for students who begin a Ph.D. program in Analysis. The first part of the book may also be suggested as a second reading for undergraduate students with a strong interest in mathematical analysis.
ISBN: 9783031197383
Standard No.: 10.1007/978-3-031-19738-3doiSubjects--Topical Terms:
669490
Analysis.
LC Class. No.: QA300
Dewey Class. No.: 515
A circle-line study of mathematical analysis
LDR
:02671nam a2200337 a 4500
001
1105492
003
DE-He213
005
20230315140655.0
006
m d
007
cr nn 008maaau
008
231013s2022 sz s 0 eng d
020
$a
9783031197383
$q
(electronic bk.)
020
$a
9783031197376
$q
(paper)
024
7
$a
10.1007/978-3-031-19738-3
$2
doi
035
$a
978-3-031-19738-3
040
$a
GP
$c
GP
041
0
$a
eng
050
4
$a
QA300
072
7
$a
PBK
$2
bicssc
072
7
$a
MAT034000
$2
bisacsh
072
7
$a
PBK
$2
thema
082
0 4
$a
515
$2
23
090
$a
QA300
$b
.S444 2022
100
1
$a
Secchi, Simone.
$3
1414530
245
1 2
$a
A circle-line study of mathematical analysis
$h
[electronic resource] /
$c
by Simone Secchi.
260
$a
Cham :
$c
2022.
$b
Springer International Publishing :
$b
Imprint: Springer,
300
$a
xix, 469 p. :
$b
ill., digital ;
$c
24 cm.
490
1
$a
UNITEXT. La matematica per il 3+2,
$x
2038-5757 ;
$v
v. 141
505
0
$a
Part I First half of the journey -- 1 An appetizer of propositional logic -- 2 Sets, relations, functions in a naïve way -- 3 Numbers -- 4 Elementary cardinality -- 5 Distance, topology and sequences on the set of real numbers -- 6 Series -- 7 Limits: from sequences to functions of a real variable -- 8 Continuous functions of a real variable -- 9 Derivatives and differentiability- 10 Riemann's integral -- 11 Elementary functions -- Part II Second half of the journey -- 12 Return to Set Theory -- 13 Neighbors again: topological spaces -- 14 Differentiating again: linearization in normed spaces -- 15 A functional approach to Lebesgue integration theory -- 16 Measures before integrals.
520
$a
The book addresses the rigorous foundations of mathematical analysis. The first part presents a complete discussion of the fundamental topics: a review of naive set theory, the structure of real numbers, the topology of R, sequences, series, limits, differentiation and integration according to Riemann. The second part provides a more mature return to these topics: a possible axiomatization of set theory, an introduction to general topology with a particular attention to convergence in abstract spaces, a construction of the abstract Lebesgue integral in the spirit of Daniell, and the discussion of differentiation in normed linear spaces. The book can be used for graduate courses in real and abstract analysis and can also be useful as a self-study for students who begin a Ph.D. program in Analysis. The first part of the book may also be suggested as a second reading for undergraduate students with a strong interest in mathematical analysis.
650
1 4
$a
Analysis.
$3
669490
650
0
$a
Set theory.
$3
579942
650
0
$a
Mathematical analysis.
$3
527926
710
2
$a
SpringerLink (Online service)
$3
593884
773
0
$t
Springer Nature eBook
830
0
$a
UNITEXT.
$p
La matematica per il 3+2 ;
$v
v. 139.
$3
1408214
856
4 0
$u
https://doi.org/10.1007/978-3-031-19738-3
950
$a
Mathematics and Statistics (SpringerNature-11649)
筆 0 讀者評論
多媒體
評論
新增評論
分享你的心得
Export
取書館別
處理中
...
變更密碼[密碼必須為2種組合(英文和數字)及長度為10碼以上]
登入