This paper revisits one of the first 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 refined. With this we prove the following: (i) the previous model can be simplified; (ii) it admits extensions having close connections 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. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim). (shrink)