TY - BOOK AU - Narayan, Shanthi AU - Mittal, P.K. TI - Theory of functions of a complex variable SN - 9788121906395 U1 - 515.9 PY - 2017/// CY - New Delhi PB - S. Chand KW - Functions of complex variables KW - Flounces (Matematica) View all subjects KW - Functions dune variable complex. N1 - 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 ER -