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The book divided in ten chapters deals with Algebra of complex numbers and its various geometrical properties, properties of polar form of complex numbers and regions in the complex plane. Limit, continuity, differentiability. Different kinds of complex valued functions. Different types of transformations. Conformal mappings of different functions. Properties of bilinear and special bilinear transformation. Line integrals, their properties and different theorems. Sequences and series, Power series, Zero’s of functions, residues and residue theorem, meromorphic functions, different kinds of singularities. Evaluation of real integrals. Analytic continuation, construction of harmonic functions, infinite product, their properties and Gamma function. Schwarz-Christoffel transformations, mapping by multi valued functions, entire functions. Jenson’s theorem and Poisson-Jenson theorem.The book is designed as a textbook for UG and PG students of science as well as engineering Table of Contents: Algebra of Complex Numbers Analytic Functions Elementary Functions Conformal Mappings Complex Integration Complex Sequences, Series and Power Series Zeros Singularities and Residue Special Topics Mapping by Multivalued Functions and Schwarz-Christoffel Transformation Growth of Entire Functions IndexAudience: UG and PG students of science and engineering