Theory of functions of a complex variable / by C. Carathéodory ; translated by F. Steinhardt.

; Steinhardt, F
2d English ed.. New York : Chelsea Pub. Company, 1954.

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Standard Title Funktionentheorie. English
Other Authors Steinhardt, F.
Subjects Analise Complexa (Matematica)
Fonctions d'une variable complexe.
Funciones de variable compleja.
Funcoes (Matematica)
Functions of complex variables.
Description 2 volumes : illustrations ; 24 cm
Copyright Date 1954.
Notes Includes index.
Contents v. 1. part I. Complex numbers. 1. The complex numbers from the algebraic point of view -- 2. The geometry of the complex numbers -- 3. Euclidean, spherical, and non-euclidean geometry -- part II. Some results from point set theory and from topology. 1. Convergent sequences of numbers and continuous complex functions -- 2. Curves and regions -- 3. Contour integration -- part III. Analytic functions. 1. Foundations of the theory -- 2. The maximum-modulus principle -- 3. The Poisson integral and harmonic functions -- 4. Meromorphic functions -- part IV. Analytic functions defined by limiting processes. 1. Continuous convergence -- 2. Normal families of meromorphic functions -- 3. Power series -- 4. Partial-fraction decomposition and the calculus of residues -- part V. Special functions. 1. The exponential and trigonometric functions -- 2. The logarithmic function and the general power function -- 3. The Bernoulli numbers and the gamma function -- volume 2. part VI. Foundations of geometric function theory. 1. Bounded functions -- 2. Conformal mapping -- 3. The mapping of the boundary -- part VII. The triangle functions and Picard's theorem. 1. Functions of several complex variables -- 2. Conformal mapping of circular-arc triangles -- 3. The Schwarz triangle functions and the modular functions -- 4. The essential singularities and Picard's theorems.
Network Numbers (OCoLC)1058293
(OCoLC)ocm01058293
WorldCat Search OCLC WorldCat
WorldCat Identities Carathéodory, Constantin, 1873-1950.
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