This is a complete course on complex analysis in which all the topics are explained in detailed but simple and easy manner. This course is designed for university and college level students of science and engineering stream as well as for the students who are preparing for various competitive exams. The whole curriculum is divided into two parts. Part 1Functions of Complex variables, Analytic Function, Cauchy Riemann EquationsSome examples of Cauchy Riemann EquationsMilne Thomson Method to construct Analytic functionSimply and Multiply Connected Domains, Cauchy’s theorem and its proof, extension of Cauchy’s theorem for multiply connected domainSome examples of Cauchy’s theoremCauchy’s Integral Formula with its proofSome examples of Cauchy’s integral formulaMorera’s TheoremPower series and Radius of ConvergencePart 2Taylor’s series and Laurent’s series and some examples based on theseResidues and Cauchy’s Residue TheoremSome applications of Cauchy’s residue theoremPoles and SingularitiesContour IntegrationBi linear or Mobius TransformationComplex numbers are just extension of real numbers. In complex Analysis mostly we discuss about complex variables. This course on Complex Analysis is taught to the students of science and engineering with the task of meeting two objectives: one, it must create a sound foundation based on the understanding of fundamental concepts and development of manipulative skills, and second it must reach far enough so that the student who completes such a course will be prepared to tackle relatively advanced applications of the subject in subsequent courses that utilize complex variables.
