Ordinary differential equations: definitions, examples. Differential equations of first order: integrating factors, applications. Linear differential equations of order n, with constant coefficients. Systems of linear differential equations. Applications. Partial differential equations with separated variables. Complex numbers and their representation. Applications to electric circuits. Functions of complex variables. The theorem of Cauchy. Cauchy's formula. Singularities. Poles. Residua. Integration around branching points. Applications. Conformal mapping.