Complex Variables Study Notes

1. INTRODUCTION

1.1 ANALYTIC FUNCTION

• A function is said to be analytic in a domain D if  is defined and differentiable at all point of D.
• Another term for analytic in D is holomorphic in D.
• A function which is analytic everywhere in the complex plane, is known as an entire function. As derivative of a polynomial exists at every point, a polynomial of any degree is an entire function.

1.2.   CAUCHY RIEMANN EQUATIONS

1.3.   HARMONIC FUNCTION

1.4 CAUCHY’S INTEGRAL FORMULA

1.5 SINGULARITY

1.6 RESIDUES