Graça, DanielCosta, José Felix2012-04-132012-04-132003AUT: DGR01772;http://hdl.handle.net/10400.1/1007This paper revisits one of the rst models of analog computation, the General Purpose Analog Computer (GPAC). In particular, we restrict our attention to the improved model presented in [11] and we show that it can be further re ned. With this we prove the following: (i) the previous model can be simpli ed; (ii) it admits extensions having close connec- tions with the class of smooth continuous time dynamical systems. As a consequence, we conclude that some of these extensions achieve Turing universality. Finally, it is shown that if we introduce a new notion of computability for the GPAC, based on ideas from computable analysis, then one can compute transcendentally transcendental functions such as the Gamma function or Riemann's Zeta function.engjournal article