MA 304

Complex numbers. Functions of a complex variable, limits and continuity, complex differentiation, analytic functions, Cauchy Riemann equations, elementary complex functions(exponential, trigonometric, power, and logarithmic functions). Contour integration, Cauchy-Goursat theorem, Cauchy’s integral theorem and formula. Liouville’s theorem and the fundamental theorem of algebra, the maximum modulus theorem. Taylor and Laurent series, definition and classification of isolated singularities (poles, removable, essential), the residue theorem, and applications to evaluating improper real integrals. <br> <br><font color="crimson">