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1.

図書

図書
Tobin A. Driscoll, Lloyd N. Trefethen
出版情報: Cambridge : Cambridge University Press, 2002  xvi, 132 p. ; 24 cm.
シリーズ名: Cambridge monographs on applied and computational mathematics ; 8
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Preface
Introduction / 1:
Essentials / 2:
Numerical methods / 3:
Variations / 4:
Applications / 5:
Using the SC toolbox
Preface
Introduction / 1:
Essentials / 2:
2.

図書

図書
C. Carathéodory
出版情報: Mineola, N.Y. : Dover Publications, 1998  ix, 115 p. ; 22 cm
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目次情報: 続きを見る
Preface
Introduction
Historical Summary
Mwbius Transformation / I:
Conformal representation in general
Invariance of the cross-ratio
Pencils of circles
Bundles of circles
Inversion with respect to a circle
Geometry of Mwbius Transformations
Non-Euclidean Geometry / II:
Inversion with respect to the circles of a bundle
Representation of a circular area on itself
Angle and distance
The triangle theorem
Non-Euclidean length of a curve
Geodesic curvature:45-47
Non-Euclidean motions
Parallel curves
Elementary Transformations:49-51 / III:
The exponential function
Representation of a rectilinear strip on a circle:
Representation of a circular crescent
Representation of Riemann surfaces
Representation of the exterior of an ellipse
Representation of an arbitrary simply-connected domain on a bounded domain
Schwarz's Lemma: / IV:
Schwarz's Theorem:
Theorem of uniqueness for the conformal representation of simply-connected domains:
Liouville's Theorem
Invariant enunciation of Schwarz's Lemma:
Functions with positive real parts:
Harnack's Theorem:
Functions with bounded real parts
Surfaces with algebraic and logarithmic branch-points
Representation of simple domains
Representation upon one another of domains containing circular areas:
Problem
Extensions of Schwarz's Lemma
Julia's Theorem
The Fundamental Theorems of Conformal Representation / V:
Continuous convergence
Limiting oscillation
Normal families of bounded functions
Existence of the solution in certain problems of the calculus of variations
Normal families of regular analytic functions
Application to conformal representation
The main theorem of conformal representation:
Normal families composed of functions which transform simple domains into circles
The kernel of a sequence of domains:
Examples
Simultaneous conformal transformation of domains lying each within another
Transformation of the Frontier / VI:
An inequality due to Lindelwf
Lemma 1, on representation of the frontier
Lemma 2
Transformation of one Jordan domain into another
Inversion with respect to an analytic curve
The inversion principle
Transformation of corners
Conformal transformation on the frontier
Transformation of Closed Surfaces / VII:
Blending of domains
Conformal transformation of a three-dimensional surface
Conformal representation of a closed surface on a sphere
The General Theorem of Uniformisation / VIII:
Abstract surfaces
The universal covering surface: 167
Domains and their boundaries: 168
The Theorem of van der Waerden: 169
Riemann surfaces
The Uniformisation Theorem: 172
Conformal representation of a torus
Bibliographical
Notes
Preface
Introduction
Historical Summary
3.

図書

図書
Gregory F. Lawler
出版情報: Providence, R.I. : American Mathematical Society, c2005  xi, 242 p. ; 27 cm
シリーズ名: Mathematical surveys and monographs ; v. 114
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4.

図書

図書
by M. Tsuji
出版情報: New York : Chelsea Pub. Co, c1975  x, 590 p ; 21 cm
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5.

図書

図書
Carl Ludwig Siegel
出版情報: New York ; London : Academic Press, 1964  86 p. ; 24 cm
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6.

図書

図書
by M. Tsuji
出版情報: Tokyo : Maruzen, 1959  8, 590 p. ; 21 cm
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7.

図書

図書
A. I. Markushevich
出版情報: Delhi : Hindustan Publishing Corpn., 1961  62 p ; 23 cm
シリーズ名: International monographs on advanced mathematics and physics
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8.

図書

図書
von Hans Wittich
出版情報: Berlin : Springer, 1955  viii, 163 p ; 24 cm
シリーズ名: Ergebnisse der Mathematik und ihrer Grenzgebiete ; n.F., Heft 8
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9.

図書

図書
by Boris N. Apanasov
出版情報: Dordrecht : Boston : Kluwer Academic Publishers, c1991  xvii, 482 p. ; 25 cm
シリーズ名: Mathematics and its applications ; . Soviet series ; 40
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10.

図書

図書
Leo Lewent ; herausgegeben von Eugen Jahnke ; mit einem beitrag von Wilhelm Blaschke
出版情報: Leipzig : B.G. Teubner, 1912  vi, 118 p. ; 21 cm
シリーズ名: Mathematisch-physikalische Schriften für Ingenieure und Studierende ; 14
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