Transcription of Chapter 2 Complex Analysis - School of Mathematics
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Chapter 2 Complex Analysis - School of Mathematics
Chapter 2. Complex Analysis In this part of the course we will study some basic Complex Analysis . This is an extremely useful and beautiful part of Mathematics and forms the basis of many techniques employed in many branches of Mathematics and physics. We will extend the notions of derivatives and integrals, familiar from calculus, to the case of Complex functions of a Complex variable. In so doing we will come across analytic functions, which form the centerpiece of this part of the course. In fact, to a large extent Complex Analysis is the study of analytic functions. After a brief review of Complex numbers as points in the Complex plane, we will first discuss analyticity and give plenty of examples of analytic functions.
Polar form and the argument function Points in the plane can also be represented using polar coordinates, and ... graphs the function: its graph being the curve y = f(x) in the (x;y)-plane. A complex-valued function of a complex variable f: C! Cmaps complex
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