On October 26, 2004, during its first encounter with Titan (Ta), the Cassini Orbiter moved from the dayside to the nightside with a closest approach altitude of 1174 km. In situ measurements of the main part of Titan's ionosphere were made by the Langmuir probe on the Cassini Radio and Plasma Wave Experiment (RPWS), while the Ion and Neutral Mass Spectrometer (INMS) measured the main constituents of the neutral atmosphere. The results of model calculations of Titan's ionosphere for Ta encounter conditions (e.g., near the terminator) are presented in this paper. The paper includes comparisons of calculated and measured electron densities along the spacecraft track. Ionization both by solar radiation and by incoming energetic electrons from Saturn's magnetosphere are needed to obtain good agreement between the measured and calculated electron densities.