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 1

• Functions of Complex variables, Analytic Function, Cauchy Riemann Equations

• Some examples of Cauchy Riemann Equations

• Milne Thomson Method to construct Analytic function

• Simply and Multiply Connected Domains, Cauchy's theorem and its proof, extension of Cauchy's theorem for multiply connected domain

• Some examples of Cauchy's theorem

• Cauchy's Integral Formula with its proof

• Some examples of Cauchy's integral formula

• Morera's Theorem

• Power series and Radius of Convergence

Part 2

• Taylor's series and Laurent's series and some examples based on these

• Residues and Cauchy's Residue Theorem

• Some applications of Cauchy's residue theorem

• Poles and Singularities

• Contour Integration

• Bi linear or Mobius Transformation

Complex 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.