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In algebra, a differential graded module, or dg-module, is a -graded module together with a differential; i.e., a square-zero graded endomorphism of the module of degree 1 or −1, depending on the convention.
In general, there need not exist dg enhancements of triangulated categories or functors between them, for example stable homotopy category can be shown not to arise from a dg category in this way. However, various positive results do exist, for example the derived category D(A) of a Grothendieck abelian category A admits a unique dg enhancement.
Let = be a -graded algebra, with product , equipped with a map : of degree (homologically graded) or degree + (cohomologically graded). We say that (,,) is a differential graded algebra if is a differential, giving the structure of a chain complex or cochain complex (depending on the degree), and satisfies a graded Leibniz rule.
In applied mathematics, discontinuous Galerkin methods (DG methods) form a class of numerical methods for solving differential equations. They combine features of the finite element and the finite volume framework and have been successfully applied to hyperbolic , elliptic , parabolic and mixed form problems arising from a wide range of ...
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One UK credit is equivalent to the learning outcomes of 10 notional hours of study, [2] thus a university course of 150 notional study hours is worth 15 credits, and a university course of 300 notional study hours is worth 30 credits. A full academic year is worth 120 credits and a full calendar year (normally only at postgraduate level) 180 ...