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We estimate ages, metallicities, $\alpha$-element abundance ratios andstellar initial mass functions of elliptical (E) and S0 galaxies from theMaNGA-DR15 survey. We stack spectra and use a variety of single stellarpopulation synthesis models to interpret the absorption line strengths in thesespectra. We quantify how these properties vary across the population, as wellas with galactocentric distance. This paper is the first of a series and isbased on a sample of pure elliptical galaxies at z $\le$ 0.08. We show that theproperties of the inner regions of Es with the largest luminosity (L$_r$) andcentral velocity dispersion ($\sigma_0$) are consistent with those associatedwith the commonly used Salpeter IMF, whereas a Kroupa-like IMF is a betterdescription at $\sim$ 0.8R/Re (assuming [Ti/Fe] variations are limited). Forthese galaxies the stellar mass-to-light ratio decreases at most by a factor of2 from the central regions to Re. In contrast, for lower L$_r$ and $\sigma_0$galaxies, the IMF is shallower and M$_{*}$/L$_r$ in the central regions issimilar to the outskirts. Although a factor of 2 is smaller than previousreports based on a handful of galaxies, it is still large enough to matter fordynamical mass estimates. Accounting self-consistently for these gradients whenestimating both M$_{*}$ and M$_{dyn}$ brings the two into good agreement:gradients reduce M$_{dyn}$ by $\sim$ 0.2 dex while only slightly increasing theM$_{*}$ inferred using a Kroupa IMF. This is a different resolution of theM$_{*}$-M$_{dyn}$ discrepancy than has been followed in the recent literaturewhere M$_{*}$ of massive galaxies is increased by adopting a Salpeter IMF whileleaving Mdyn unchanged. A companion paper discusses how stellar populationdifferences are even more pronounced if one separates slow from fast rotators.

Galaxy properties as revealed by MaNGA. I. Constraints on Initial Mass Function and M$_{*}$/L gradients in ellipticals