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Course Discription |
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*Complex numbers, geometric, polar representation of complex numbers, exponentials and roots, regions in the complex plane, analytic functions, continuity, elementary functions, logarithmic functions and their branches, contour integrals, integrals on closed contours, Cauchy theorem, derivatives of analytic functions, Morera’s theorem, Liouville’s theorem, convergence of sequences and series, Taylor’s series, Laurent’s series, uniform convergence, integrals, residues and poles, residue theorem, improper real integrals. |