Functions of a Complex Variable provides all the material for a course on the theory of functions of a complex variable at the senior undergraduate and beginning graduate level Also suitable for self study the book covers every topic essential to training students in complex analysis It also incorporates special topics to enhance students understanding of the subject laying the foundation for future studies in analysis linear algebra numerical analysis geometry number theory physics thermodynamics or electrical engineering After introducing the basic concepts of complex numbers and their geometrical representation the text describes analytic functions power series and elementary functions the conformal representation of an analytic function special transformations and complex integration It next discusses zeros of an analytic function classification of singularities and singularity at the point of infinity residue theory principle of argument Rouche s theorem and the location of zeros of complex polynomial equations and calculus of residues emphasizing the techniques of definite integrals by contour integration The authors then explain uniform convergence of sequences and series involving Parseval Schwarz and Poisson formulas They also present harmonic functions and mappings inverse mappings and univalent functions as well as analytic continuation

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