Complex Analysis: An Introduction to The Theory of Analytic Functions of One Complex VariableA standard source of information of functions of one complex variable, this text has retained its wide popularity in this field by being consistently rigorous without becoming needlessly concerned with advanced or overspecialized material. Difficult points have been clarified, the book has been reviewed for accuracy, and notations and terminology have been modernized. Chapter 2, Complex Functions, features a brief section on the change of length and area under conformal mapping, and much of Chapter 8, Global-Analytic Functions, has been rewritten in order to introduce readers to the terminology of germs and sheaves while still emphasizing that classical concepts are the backbone of the theory. Chapter 4, Complex Integration, now includes a new and simpler proof of the general form of Cauchy's theorem. There is a short section on the Riemann zeta function, showing the use of residues in a more exciting situation than in the computation of definite integrals. |
Contents
The Geometric Representation of Complex Numbers | 12 |
COMPLEX FUNCTIONS | 21 |
Elementary Theory of Power Series | 33 |
Copyright | |
27 other sections not shown
Common terms and phrases
a₁ algebraic analytic continuation analytic function assume boundary bounded C₁ Cauchy's theorem Chap choose closed curve coefficients compact set complex numbers condition conformal mapping consider constant contained convergence corresponding defined definition denote derivative end points entire function equal exists finite number follows formula function elements function f(z ƒ dz global analytic function harmonic function hence homologous homotopic imaginary inequality infinite initial germ integral lemma linear transformation maximum principle meromorphic function metric space multiple neighborhood notation obtain open set poles polynomial power series proof prove R₁ radius radius of convergence real axis rectangle removable singularity residue Riemann satisfies sequence simple simply connected simply connected region single-valued singularity solution subharmonic subset Suppose tion topological u₁ uniform convergence uniformly upper half plane vanishes w₁ w₂ whole plane y₁ ди მყ