Differential Algebra and Algebraic Groups

By E. Kolchin. 2012

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Galois Theory of Linear Differential Equations (2012, background): “In [161], Kolchin develops a Galois theory for linear differential ideals in k{y1, .”
On integro-differential algebras (2012, background): “Differential algebra [26, 30] is the study of differentiation and nonlinear differential equations by purely algebraic means, without using an underlying topology.”
Gröbner–Shirshov bases and their calculation (2013, background): “For (commutative) differential polynomials an analogous, or better to say, closely related ‘basis’ is called a Ritt–Kolchin characteristic set, due to Ritt [193] 1950 and Kolchin [140] 1973, and rediscovered by Wu [219] 1978. polynomials and a new notion of completion of a set of Lie polynomials (ad”
ON IDENTIFIABILITY OF NONLINEAR ODE MODELS AND APPLICATIONS IN VIRAL DYNAMICS (2011, methodology): “For details of differential algebra, the interested reader is referred to [14, 57, 65, 78, 91].”
Model-free control (2013, background): “Note that this functional analysis is a mainstay in engineering since the introduction of Volterra series (see Barrett, 1963); • some elementary facts stemming from differential algebra (Kolchin, 1973), which has been quite important in control theory since the appearance 20 years ago of flatness-ba”