RESUMEN

A systematic investigation of basic boundary value problems for complex partial differential equations of arbitrary order is started in these lectures restricted to model equations. In the first part [3] the Schwarz, the Dirichlet, and the Neumann problems are treated for the inhomogeneous Cauchy-Riemann equation. The fundamental tools are the Gauss theorem and the Cauchy-Pompeiu representation. The principle of iterating these representation formulas is introduced which will enable treating higher

order equations. Those are studied in a second part of these lectures. The whole course was delivered at the Sim´on Bol´ıvar University in Caracas in May 2004.