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We combine data from the extremely deep Hubble Space Telescope $U$ (F300W)image obtained using WFPC2 as part of the parallel observations of the HubbleUltra Deep Field campaign, with $BVi$ images from the Great ObservatoriesOrigins Deep Survey (GOODS) to identify a sample of Lyman break galaxies in theredshift range $2.0 \lesssim z \lesssim 3.5$. We use recent stellar populationsynthesis models with a wide variety of ages, metallicities, redshifts, anddust content, and a detailed representation of the \HI cosmic opacity as afunction of redshift to model the colors of galaxies in our combination ofWFPC2/ACS filters. Using these models, we derive improved color selectioncriteria that provide a clean selection of relatively unobscured, star forminggalaxies in this redshift range. Our WFPC2/F300W image is the deepest imageever obtained at that wavelength. The $10\sigma$ limiting magnitude measuredover 0.2 arcsec$^2$ is 27.5 magnitudes in the WFPC2/F300W image, about 0.5magnitudes deeper than the F300W image in the Hubble Deep Field (HDF)-N. Thisextra depth relative to the HDFs allows us to directly probe the luminosityfunction about 0.5 magnitudes deeper than the depth accessible with the HDFdata along an independent line of sight. Our sample of star-forming galaxieswith $2.0 \lesssim z \lesssim 3.5$ includes 125 objects, the majority of whichshow clumpy morphologies. We measure a star formation rate density of 0.18  $M_\odot \rm yr^{-1} Mpc^{-3}$, marginally higher than the value measured forthe Hubble Deep Fields.Comment: 14 pages, 7 figures, 3 tables, to appear in the Astronomical Journa

FaintU-Band Dropouts in the WFPC2 Parallels of the Hubble Ultra Deep Field