The most fundamental challenges to models of galactic chemical evolution (GCE) are uncertainties in the basic inputs, including the properties of the stellar initial mass function (IMF), stellar nucleosynthetic yields, and the rate of return of mass and energy to the interstellar and intergalactic medium by Type Ia and II supernovae and stellar winds. In this dissertation, we provide a critical examination of widely available stellar nucleosynthetic yield data, with an eye toward modeling GCE in the broad scope of cosmological hydrodynamical simulations. We examine the implications of uncertain inputs for the Galactic stellar IMF, and nucleosynthetic yields from stellar-evolution calculations, on our ability to ask detailed questions regarding the observed Galactic chemical-abundance patterns. We find a marked need for stellar feedback data from stars of initial mass 8 to 12 Msun and above 40 Msun, and for initial stellar metallicities above and below solar, Zsun=0.02. We find the largest discrepancies amongst nucleosynthetic yield calculations are due to various groups' treatment of hot bottom burning, formation of the 13C pocket in asymptotic giant-branch (AGB) stars, and details of mass loss, rotation, and convection in all stars. Our model of GCE is used to post-process simulations to explore in greater detail the nucleosynthetic evolution of the stellar populations and interstellar/intergalactic medium, and to compare directly to the chemical abundances of the Milky Way stellar halo and dwarf spheroidal galaxy stellar populations.
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