Isolated singularities of complex functions (removable, poles, and essential), Laurent series and its annulus of convergence, relationship with Fourier series, meromorphic functions, the residues theorem, the Jordan lemma and applications to real functions improper integrals, the Argument Principle, Rouché theorem, Jensen formula. Exercises, including on the Gamma function, Mittag–Leffler theorem, infinite products, Weierstrass factorization theorem, holomorphic functions factorization theorem, Riemann Zeta function, asymptotic expansions, and with applications to fluid dynamics, aerodynamics, and linear systems analysis and control including root locus, Nyquist contour and stability criterion, polar and Nichols diagrams, Proportional–Integral–Derivative and Proportional–Derivative controllers.