We examine the light-curve parameters of 97 nearby Type Ia supernovae (SN Ia) in the ultraviolet and optical using observations from the Swift Ultra-violet/Optical Telescope. Our light-curve models used linear combinations of templates, which were based on functional principal component analysis of the optical photometry of SN Ia. The weights for each principal component used in the fit capture certain aspects of the light-curve properties. We find that there is little difference in the overall variability of principal component scores across filters. We also find correlations between certain filters and PC components, indicating that the UV and optical properties seem to be tied together. This is a promising step in UV SN Ia analysis and suggests that UV light curves may be used to infer optical properties, paving the way for future cosmological studies.