Съдържание: Theory of functions of a complex variable /

Книга

Основен автор:	Carathéodory, Constantin, 1873-1950.
Други автори:	Steinhardt, F.
Формат:	Книга
Език:	English Undetermined
Публикувано:	New York : Chelsea Pub. Co., 1954.
Издание:	2nd English ed.
Предмети:	Functions of complex variables.
Подобни документи:	Online version:: Theory of functions of a complex variable.

Съдържание:

v. 1. pt. 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
pt. 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
pt. III. Analytic functions. 1. Foundations of the theory
2. The maximum-modulus principle
3. The Poisson integral and harmonic functions
4. Meromorphic functions
pt. 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
pt. 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
v. 2. pt. VI. Foundations of geometric function theory. 1. Bounded functions
2. Conformal mapping
3. The mapping of the boundary
pt. 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.