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Afternotes on Differential Algebra
This note covers the following topics: Conventions and Preliminaries, Ideals Defined by Triangular Sets are Unmixed, Regular Chains, Lazard’s Lemma, Rosenfeld’s Lemma, The Differential Nullstellensatz, Regular Differential Chains, Normal Forms, The RosenfeldGroebner Algorithm, The Henri-Michaelis-Menten Formula, Parameter Estimation.
Author(s): Francois Boulier
88 Pages 
Differential Geometry by Balazs Csikos
The aim of this textbook is to give an introduction to differential geometry. Topics covered includes: Categories and Functors, Linear Algebra, Geometry, Topology, Multivariable Calculus, Ordinary Differential Equations, The Notion of a Curve, The Length of a Curve, Plane Curves, Osculating Spheres, Hypersurfaces in R n, Manifolds, Differentiation of Vector Fields and Integration of Differential Forms.
Author(s): Balazs Csikos
354 Pages
This PDF book covers the following topics related to Differential Algebra : Foundations of Differential Algebra, the Ring of Differential Polynomials and Its Ideals, Differential Algebraic Extensions, Differential Galois Theory, Linear Algebraic Groups, Liouvillian Extensions.
Author(s): Alexey Ovchinnikov, Maxwell Shapiro, Peter Thompson
41 Pages
Differential algebra on lattice Green functions and Calabi Yau operators
This note explains miscellaneous linear differential operators mostly associated with lattice Green functions in arbitrary dimensions, but also Calabi-Yau operators and order-seven operators corresponding to exceptional differential Galois groups.
Author(s): Salah Boukraa, Saoud Hassani, Jean-Marie Maillard, Jacques-Arthur Weil
62 Pages
Asymptotic Differential Algebra
This note introduces both, state some of their basic properties, and explain connections to o-minimal structures. Also describe a common algebraic framework for these examples: the category of H-fields. This unified setting leads to a better understanding of Hardy fields and transseries from an algebraic and model-theoretic perspective.
Author(s): Matthias Aschenbrenner
38 PagesAdvertisement
