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
More explorations in complex functions
紀錄類型:
書目-語言資料,印刷品 : Monograph/item
正題名/作者:
More explorations in complex functions/ by Richard Beals, Roderick S.C. Wong.
作者:
Beals, Richard.
其他作者:
Wong, Roderick.
出版者:
Cham :Springer Nature Switzerland : : 2023.,
面頁冊數:
xii, 403 p. :ill. (some col.), digital ; : 24 cm.;
Contained By:
Springer Nature eBook
標題:
Number Theory. -
電子資源:
https://doi.org/10.1007/978-3-031-28288-1
ISBN:
9783031282881
More explorations in complex functions
Beals, Richard.
More explorations in complex functions
[electronic resource] /by Richard Beals, Roderick S.C. Wong. - Cham :Springer Nature Switzerland :2023. - xii, 403 p. :ill. (some col.), digital ;24 cm. - Graduate texts in mathematics,2982197-5612 ;. - Graduate texts in mathematics,298..
1. Basics -- 2. Further preliminaries -- 3. Complex dynamics -- 4. Univalent functions and de Brange's theorem -- 5. Harmonic and subharmonic functions; the Dirichlet problem -- 6. General Riemann surfaces -- 7. The uniformization theorem -- 8. Quasiconformal mapping -- 9. Introduction to Teichmüller theory -- 10. The Bergman kernel -- 11. Theta functions -- 12. Padé approximants and continued fractions -- 13. Riemann-Hilbert problems -- 14. Asymptotic and Darboux's method -- References -- Index.
More Explorations in Complex Functions is something of a sequel to GTM 287, Explorations in Complex Functions. Both texts introduce a variety of topics, from core material in the mainstream of complex analysis to tools that are widely used in other areas of mathematics and applications, but there is minimal overlap between the two books. The intended readership is the same, namely graduate students and researchers in complex analysis, independent readers, seminar attendees, or instructors for a second course in complex analysis. Instructors will appreciate the many options for constructing a second course that builds on a standard first course in complex analysis. Exercises complement the results throughout. There is more material in this present text than one could expect to cover in a year's course in complex analysis. A mapping of dependence relations among chapters enables instructors and independent readers a choice of pathway to reading the text. Chapters 2, 4, 5, 7, and 8 contain the function theory background for some stochastic equations of current interest, such as SLE. The text begins with two introductory chapters to be used as a resource. Chapters 3 and 4 are stand-alone introductions to complex dynamics and to univalent function theory, including deBrange's theorem, respectively. Chapters 5-7 may be treated as a unit that leads from harmonic functions to covering surfaces to the uniformization theorem and Fuchsian groups. Chapter 8 is a stand-alone treatment of quasiconformal mapping that paves the way for Chapter 9, an introduction to Teichmüller theory. The final chapters, 10-14, are largely stand-alone introductions to topics of both theoretical and applied interest: the Bergman kernel, theta functions and Jacobi inversion, Padé approximants and continued fractions, the Riemann-Hilbert problem and integral equations, and Darboux's method for computing asymptotics.
ISBN: 9783031282881
Standard No.: 10.1007/978-3-031-28288-1doiSubjects--Topical Terms:
672023
Number Theory.
LC Class. No.: QA331
Dewey Class. No.: 515.9
More explorations in complex functions
LDR
:03471nam a2200337 a 4500
001
1106030
003
DE-He213
005
20230701230141.0
006
m d
007
cr nn 008maaau
008
231013s2023 sz s 0 eng d
020
$a
9783031282881
$q
(electronic bk.)
020
$a
9783031282874
$q
(paper)
024
7
$a
10.1007/978-3-031-28288-1
$2
doi
035
$a
978-3-031-28288-1
040
$a
GP
$c
GP
041
0
$a
eng
050
4
$a
QA331
072
7
$a
PBKD
$2
bicssc
072
7
$a
MAT034000
$2
bisacsh
072
7
$a
PBKD
$2
thema
082
0 4
$a
515.9
$2
23
090
$a
QA331
$b
.B366 2023
100
1
$a
Beals, Richard.
$3
686507
245
1 0
$a
More explorations in complex functions
$h
[electronic resource] /
$c
by Richard Beals, Roderick S.C. Wong.
260
$a
Cham :
$c
2023.
$b
Springer Nature Switzerland :
$b
Imprint: Springer,
300
$a
xii, 403 p. :
$b
ill. (some col.), digital ;
$c
24 cm.
490
1
$a
Graduate texts in mathematics,
$x
2197-5612 ;
$v
298
505
0
$a
1. Basics -- 2. Further preliminaries -- 3. Complex dynamics -- 4. Univalent functions and de Brange's theorem -- 5. Harmonic and subharmonic functions; the Dirichlet problem -- 6. General Riemann surfaces -- 7. The uniformization theorem -- 8. Quasiconformal mapping -- 9. Introduction to Teichmüller theory -- 10. The Bergman kernel -- 11. Theta functions -- 12. Padé approximants and continued fractions -- 13. Riemann-Hilbert problems -- 14. Asymptotic and Darboux's method -- References -- Index.
520
$a
More Explorations in Complex Functions is something of a sequel to GTM 287, Explorations in Complex Functions. Both texts introduce a variety of topics, from core material in the mainstream of complex analysis to tools that are widely used in other areas of mathematics and applications, but there is minimal overlap between the two books. The intended readership is the same, namely graduate students and researchers in complex analysis, independent readers, seminar attendees, or instructors for a second course in complex analysis. Instructors will appreciate the many options for constructing a second course that builds on a standard first course in complex analysis. Exercises complement the results throughout. There is more material in this present text than one could expect to cover in a year's course in complex analysis. A mapping of dependence relations among chapters enables instructors and independent readers a choice of pathway to reading the text. Chapters 2, 4, 5, 7, and 8 contain the function theory background for some stochastic equations of current interest, such as SLE. The text begins with two introductory chapters to be used as a resource. Chapters 3 and 4 are stand-alone introductions to complex dynamics and to univalent function theory, including deBrange's theorem, respectively. Chapters 5-7 may be treated as a unit that leads from harmonic functions to covering surfaces to the uniformization theorem and Fuchsian groups. Chapter 8 is a stand-alone treatment of quasiconformal mapping that paves the way for Chapter 9, an introduction to Teichmüller theory. The final chapters, 10-14, are largely stand-alone introductions to topics of both theoretical and applied interest: the Bergman kernel, theta functions and Jacobi inversion, Padé approximants and continued fractions, the Riemann-Hilbert problem and integral equations, and Darboux's method for computing asymptotics.
650
2 4
$a
Number Theory.
$3
672023
650
2 4
$a
Special Functions.
$3
672152
650
1 4
$a
Functions of a Complex Variable.
$3
672126
650
0
$a
Functions of complex variables.
$3
528649
700
1
$a
Wong, Roderick.
$3
684444
710
2
$a
SpringerLink (Online service)
$3
593884
773
0
$t
Springer Nature eBook
830
0
$a
Graduate texts in mathematics,
$v
298.
$3
1415402
856
4 0
$u
https://doi.org/10.1007/978-3-031-28288-1
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