  We present calculations of the reaction $A(e,e^\prime \pi N)B$ in the
distorted wave impulse approximation. The reaction allows for the study of the
production process in the nuclear medium without being obscured by the details
of nuclear transition densities. First, a pion electroproduction operator
suitable for nuclear calculations is obtained by extending the Blomqvist-Laget
photoproduction operator to the virtual photon case. The operator is gauge
invariant, unitary, reference frame independent, and describes the existing
data reasonably well. Then it is applied in nuclei to predict nuclear cross
sections under a variety of kinematic arrangements. Issues such as the effects
of gauge-fixing, the interference of the $\Delta$ resonance with the
background, sensitivities to the quadrupole component of the $\Delta$
excitation and to the electromagnetic form factors, the role of final-state
interactions, are studied in detail. Methods on how to experimentally separate
the various pieces in the coincidence cross section are suggested. Finally, the
model is compared to a recent SLAC experiment.
