Complex analysis is the branch of mathematics that investigates functions of complex numbers, that is, functions whose independent and dependent variables are both complex numbers. The course extends concepts from the analysis of real valued functions to complex functions. Complex Analysis is of enormous practical use in applied mathematics and in Physics.
By the end of the course, the student should be able to: · Extend concepts of analysis of real variables to complex numbers likes sequences and series.· Differentiate and Integrate Complex functions.· Carry out contour Integration.· State and prove the Fundamental Theorem of Calculus.· State and provide various proofs of the Fundamental Theorem of Algebra.· Compute integrals using residues.· Apply techniques of Complex analysis to summation of series· Apply conformal mappings to problems from physical sciences.
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