This course gives students an introduction to the theory of functions of complex variables. A function of a complex variable has some remarkable properties which do not hold true necessarily for a function of a real variable. In this course, we discuss many such properties. We do so by studying complex numbers and their properties; analytic functions and their derivatives, integrals and power series expansions; singularities and zeros of a complex function. The course also covers applications to physics and engineering.
Understanding of geometry of complex plane and complex numbers.
Understanding of functions of a complex variable, the meaning of their derivative and integral.
Understanding of singularities and zeroes of a function of a complex variable.
Evaluation of complicated real integrals using residue calculus.
Some applications of the theory to problems of interest in physics and engineering.