Transcription of Chapter 2 Complex Analysis - School of Mathematics
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Chapter 2 Complex Analysis - School of Mathematics
Chapter 2 Complex AnalysisIn this part of the course we will study some basic Complex Analysis . This isan extremely useful and beautiful part of Mathematics and forms the basisof many techniques employed in many branches of Mathematics and 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 willcome across analytic functions, which form the centerpiece of this part of thecourse. In fact, to a large extent Complex Analysis is the study of analyticfunctions. After a brief review of Complex numbers as points in the complexplane, we will first discuss analyticity and give plenty of examples of analyticfunctions. We will then discuss Complex integration, culminating with thegeneralised Cauchy Integral Formula, and some of its applications. We thengo on to discuss the power series representations of analytic functions andthe residue calculus, which will allow us to compute many real integrals andinfinite sums very easily via Complex Analytic functionsIn this section we will study Complex functions of a Complex variable.
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
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