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
Smooth Functions and Maps
~
Makarov, Boris M.
Smooth Functions and Maps
紀錄類型:
書目-語言資料,印刷品 : Monograph/item
正題名/作者:
Smooth Functions and Maps/ by Boris M. Makarov, Anatolii N. Podkorytov.
作者:
Makarov, Boris M.
其他作者:
Podkorytov, Anatolii N.
面頁冊數:
XL, 244 p. 19 illus.online resource. :
Contained By:
Springer Nature eBook
標題:
Mathematical analysis. -
電子資源:
https://doi.org/10.1007/978-3-030-79438-5
ISBN:
9783030794385
Smooth Functions and Maps
Makarov, Boris M.
Smooth Functions and Maps
[electronic resource] /by Boris M. Makarov, Anatolii N. Podkorytov. - 1st ed. 2021. - XL, 244 p. 19 illus.online resource. - Moscow Lectures,72522-0322 ;. - Moscow Lectures,2.
Introduction -- Differentiable functions -- Smooth maps -- Implicit function theorem and some its applications -- Critical values of smooth maps -- Appendix -- References -- Names Index -- Subject Index. .
The book contains a consistent and sufficiently comprehensive theory of smooth functions and maps insofar as it is connected with differential calculus. The scope of notions includes, among others, Lagrange inequality, Taylor’s formula, finding absolute and relative extrema, theorems on smoothness of the inverse map and on conditions of local invertibility, implicit function theorem, dependence and independence of functions, classification of smooth functions up to diffeomorphism. The concluding chapter deals with a more specific issue of critical values of smooth mappings. In several chapters, a relatively new technical approach is used that allows the authors to clarify and simplify some of the technically difficult proofs while maintaining full integrity. Besides, the book includes complete proofs of some important results which until now have only been published in scholarly literature or scientific journals (remainder estimates of Taylor’s formula in a nonconvex area (Chapter I, §8), Whitney's extension theorem for smooth function (Chapter I, §11) and some of its corollaries, global diffeomorphism theorem (Chapter II, §5), results on sets of critical values of smooth mappings and the related Whitney example (Chapter IV). The text features multiple examples illustrating the results obtained and demonstrating their accuracy. Moreover, the book contains over 150 problems and 19 illustrations. Perusal of the book equips the reader to further explore any literature basing upon multivariable calculus.
ISBN: 9783030794385
Standard No.: 10.1007/978-3-030-79438-5doiSubjects--Topical Terms:
527926
Mathematical analysis.
LC Class. No.: QA299.6-433
Dewey Class. No.: 515
Smooth Functions and Maps
LDR
:03123nam a22004095i 4500
001
1049431
003
DE-He213
005
20211211011025.0
007
cr nn 008mamaa
008
220103s2021 sz | s |||| 0|eng d
020
$a
9783030794385
$9
978-3-030-79438-5
024
7
$a
10.1007/978-3-030-79438-5
$2
doi
035
$a
978-3-030-79438-5
050
4
$a
QA299.6-433
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
100
1
$a
Makarov, Boris M.
$e
author.
$4
aut
$4
http://id.loc.gov/vocabulary/relators/aut
$3
1353554
245
1 0
$a
Smooth Functions and Maps
$h
[electronic resource] /
$c
by Boris M. Makarov, Anatolii N. Podkorytov.
250
$a
1st ed. 2021.
264
1
$a
Cham :
$b
Springer International Publishing :
$b
Imprint: Springer,
$c
2021.
300
$a
XL, 244 p. 19 illus.
$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
490
1
$a
Moscow Lectures,
$x
2522-0322 ;
$v
7
505
0
$a
Introduction -- Differentiable functions -- Smooth maps -- Implicit function theorem and some its applications -- Critical values of smooth maps -- Appendix -- References -- Names Index -- Subject Index. .
520
$a
The book contains a consistent and sufficiently comprehensive theory of smooth functions and maps insofar as it is connected with differential calculus. The scope of notions includes, among others, Lagrange inequality, Taylor’s formula, finding absolute and relative extrema, theorems on smoothness of the inverse map and on conditions of local invertibility, implicit function theorem, dependence and independence of functions, classification of smooth functions up to diffeomorphism. The concluding chapter deals with a more specific issue of critical values of smooth mappings. In several chapters, a relatively new technical approach is used that allows the authors to clarify and simplify some of the technically difficult proofs while maintaining full integrity. Besides, the book includes complete proofs of some important results which until now have only been published in scholarly literature or scientific journals (remainder estimates of Taylor’s formula in a nonconvex area (Chapter I, §8), Whitney's extension theorem for smooth function (Chapter I, §11) and some of its corollaries, global diffeomorphism theorem (Chapter II, §5), results on sets of critical values of smooth mappings and the related Whitney example (Chapter IV). The text features multiple examples illustrating the results obtained and demonstrating their accuracy. Moreover, the book contains over 150 problems and 19 illustrations. Perusal of the book equips the reader to further explore any literature basing upon multivariable calculus.
650
0
$a
Mathematical analysis.
$3
527926
650
0
$a
Analysis (Mathematics).
$3
1253570
650
0
$a
Global analysis (Mathematics).
$3
1255807
650
0
$a
Manifolds (Mathematics).
$3
1051266
650
1 4
$a
Analysis.
$3
669490
650
2 4
$a
Global Analysis and Analysis on Manifolds.
$3
672519
700
1
$a
Podkorytov, Anatolii N.
$e
author.
$4
aut
$4
http://id.loc.gov/vocabulary/relators/aut
$3
1353555
710
2
$a
SpringerLink (Online service)
$3
593884
773
0
$t
Springer Nature eBook
776
0 8
$i
Printed edition:
$z
9783030794378
776
0 8
$i
Printed edition:
$z
9783030794392
776
0 8
$i
Printed edition:
$z
9783030794408
830
0
$a
Moscow Lectures,
$x
2522-0314 ;
$v
2
$3
1279725
856
4 0
$u
https://doi.org/10.1007/978-3-030-79438-5
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)
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