  We develop a dynamical coupled-channels (DCC) model for neutrino-nucleon
reactions in the resonance region, by extending the DCC model that we have
previously developed through an analysis of $\pi N, \gamma N\to \pi N, \eta N,
K\Lambda, K\Sigma$ reaction data for $W\le 2.1$ GeV. We analyze
electron-induced reaction data for both proton and neutron targets to determine
the vector current form factors up to $Q^2\le$ 3.0 (GeV/$c$)$^2$. Axial-current
matrix elements are derived in accordance with the Partially Conserved Axial
Current (PCAC) relation to the $\pi N$ interactions of the DCC model. As a
result, we can uniquely determine the interference pattern between resonant and
non-resonant amplitudes. Our calculated cross sections for neutrino-induced
single-pion productions are compared with available data, and are found to be
in reasonable agreement with the data. We also calculate the double-pion
production cross sections in the resonance region, for the first time, with
relevant resonance contributions and channel couplings. The result is compared
with the double-pion production data. For a future development of a
neutrino-nucleus reaction model and/or a neutrino event generator for analyses
of neutrino experiments, the DCC model presented here can give a useful input.
