The Resource Complex Analysis in One Variable, by Raghavan Narasimhan, Yves Nievergelt, (electronic resource)

Complex Analysis in One Variable, by Raghavan Narasimhan, Yves Nievergelt, (electronic resource)

Label
Complex Analysis in One Variable
Title
Complex Analysis in One Variable
Statement of responsibility
by Raghavan Narasimhan, Yves Nievergelt
Creator
Contributor
Author
Author
Subject
Language
  • eng
  • eng
Summary
This book presents complex analysis in one variable in the context of modern mathematics, with clear connections to several complex variables, de Rham theory, real analysis, and other branches of mathematics. Thus, covering spaces are used explicitly in dealing with Cauchy's theorem, real variable methods are illustrated in the Loman-Menchoff theorem and in the corona theorem, and the algebraic structure of the ring of holomorphic functions is studied. Using the unique position of complex analysis, a field drawing on many disciplines, the book also illustrates powerful mathematical ideas and tools, and requires minimal background material. Cohomological methods are introduced, both in connection with the existence of primitives and in the study of meromorphic functionas on a compact Riemann surface. The proof of Picard's theorem given here illustrates the strong restrictions on holomorphic mappings imposed by curvature conditions. New to this second edition, a collection of over 100 pages worth of exercises, problems, and examples gives students an opportunity to consolidate their command of complex analysis and its relations to other branches of mathematics, including advanced calculus, topology, and real applications
http://library.link/vocab/creatorName
Narasimhan, Raghavan
Dewey number
515/.9
http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
  • fel_qlvikxc
  • IbBJZ4s6RKY
Image bit depth
0
Language note
English
LC call number
QA331.5
Literary form
non fiction
http://library.link/vocab/relatedWorkOrContributorName
Nievergelt, Yves.
http://library.link/vocab/subjectName
  • Mathematics
  • Functions of complex variables
  • Geometry, algebraic
  • Global analysis (Mathematics)
  • Differential equations, partial
  • Real Functions
  • Functions of a Complex Variable
  • Algebraic Geometry
  • Analysis
  • Several Complex Variables and Analytic Spaces
Label
Complex Analysis in One Variable, by Raghavan Narasimhan, Yves Nievergelt, (electronic resource)
Instantiates
Publication
Note
Bibliographic Level Mode of Issuance: Monograph
Antecedent source
mixed
Carrier category
online resource
Carrier category code
  • cr
Color
not applicable
Content category
text
Content type code
  • txt
Contents
I Complex Analysis in One Variable -- 1 Elementary Theory of Holomorphic Functions -- 2 Covering Spaces and the Monodromy Theorem -- 3 The Winding Number and the Residue Theorem -- 4 Picard’s Theorem -- 5 Inhomogeneous Cauchy-Riemann Equation and Runge’s Theorem -- 6 Applications of Runge’s Theorem -- 7 Riemann Mapping Theorem and Simple Connectedness in the Plane -- 8 Functions of Several Complex Variables -- 9 Compact Riemann Surfaces -- 10 The Corona Theorem -- 11 Subharmonic Functions and the Dirichlet Problem -- II Exercises -- 0 Review of Complex Numbers -- 1 Elementary Theory of Holomorphic Functions -- 2 Covering Spaces and the Monodromy Theorem -- 3 The Winding Number and the Residue Theorem -- 4 Picard’s Theorem -- 5 The Inhomogeneous Cauchy—Riemann Equation and Runge’s Theorem -- 6 Applications of Runge’s Theorem -- 7 The Riemann Mapping Theorem and Simple Connectedness in the Plane -- 8 Functions of Several Complex Variables -- 9 Compact Riemann Surfaces -- 10 The Corona Theorem -- 11 Subharmonic Functions and the Dirichlet Problem -- Notes for the exercises -- References for the exercises
Dimensions
unknown
Edition
Second Edition.
Extent
1 online resource (XIV, 381 p.)
File format
multiple file formats
Form of item
online
Isbn
9781461201755
Level of compression
uncompressed
Media category
computer
Media type code
  • c
Other control number
10.1007/978-1-4612-0175-5
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
  • (CKB)3400000000089022
  • (SSID)ssj0001296191
  • (PQKBManifestationID)11857674
  • (PQKBTitleCode)TC0001296191
  • (PQKBWorkID)11348119
  • (PQKB)10868457
  • (SSID)ssj0000805570
  • (PQKBManifestationID)12406118
  • (PQKBTitleCode)TC0000805570
  • (PQKBWorkID)10835899
  • (PQKB)11522861
  • (DE-He213)978-1-4612-0175-5
  • (EXLCZ)993400000000089022
Label
Complex Analysis in One Variable, by Raghavan Narasimhan, Yves Nievergelt, (electronic resource)
Publication
Note
Bibliographic Level Mode of Issuance: Monograph
Antecedent source
mixed
Carrier category
online resource
Carrier category code
  • cr
Color
not applicable
Content category
text
Content type code
  • txt
Contents
I Complex Analysis in One Variable -- 1 Elementary Theory of Holomorphic Functions -- 2 Covering Spaces and the Monodromy Theorem -- 3 The Winding Number and the Residue Theorem -- 4 Picard’s Theorem -- 5 Inhomogeneous Cauchy-Riemann Equation and Runge’s Theorem -- 6 Applications of Runge’s Theorem -- 7 Riemann Mapping Theorem and Simple Connectedness in the Plane -- 8 Functions of Several Complex Variables -- 9 Compact Riemann Surfaces -- 10 The Corona Theorem -- 11 Subharmonic Functions and the Dirichlet Problem -- II Exercises -- 0 Review of Complex Numbers -- 1 Elementary Theory of Holomorphic Functions -- 2 Covering Spaces and the Monodromy Theorem -- 3 The Winding Number and the Residue Theorem -- 4 Picard’s Theorem -- 5 The Inhomogeneous Cauchy—Riemann Equation and Runge’s Theorem -- 6 Applications of Runge’s Theorem -- 7 The Riemann Mapping Theorem and Simple Connectedness in the Plane -- 8 Functions of Several Complex Variables -- 9 Compact Riemann Surfaces -- 10 The Corona Theorem -- 11 Subharmonic Functions and the Dirichlet Problem -- Notes for the exercises -- References for the exercises
Dimensions
unknown
Edition
Second Edition.
Extent
1 online resource (XIV, 381 p.)
File format
multiple file formats
Form of item
online
Isbn
9781461201755
Level of compression
uncompressed
Media category
computer
Media type code
  • c
Other control number
10.1007/978-1-4612-0175-5
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
  • (CKB)3400000000089022
  • (SSID)ssj0001296191
  • (PQKBManifestationID)11857674
  • (PQKBTitleCode)TC0001296191
  • (PQKBWorkID)11348119
  • (PQKB)10868457
  • (SSID)ssj0000805570
  • (PQKBManifestationID)12406118
  • (PQKBTitleCode)TC0000805570
  • (PQKBWorkID)10835899
  • (PQKB)11522861
  • (DE-He213)978-1-4612-0175-5
  • (EXLCZ)993400000000089022

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