Complex Analysis

4

Complex Integration

4.1 INTRODUCTION

Integration of complex functions plays a significant role in various areas of science and engineering. In this chapter, we will deal with the notion of integral of a complex function along a curve in the complex plane. We start with the definition of integration of a complex-valued function of a real variable and extend this idea to the integration of a complex-valued function of a complex variable. Using integration, we will prove an important result on analytic functions. This chapter also includes the Cauchy–Goursat theorem, Cauchy’s integral formula, some related theorems, maximum modulus principle and their applications.

4.2 DERIVATIVE OF FUNCTION w(t)

Before introducing the integrals for complex-valued ...