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Differential algebra, ordered fields and model theory
This note explains the folloing topics: model theory, differential fields and ordered fields, Stellensatze, Differential galois theory, Definable types and VC density.
Author(s): Quentin Brouette
103 Pages
Differential Algebra and Applications
This note explains the following topics: Differential algebra, Torus actions, Scaling symmetries of dynamical systems, Scaling symmetries of PDEs.
Author(s): Richard Tanburn
50 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
Notes on Differential Algebra by Reid Dale
This PDF book covers the following topics related to Differential Algebra : Basic Differential Algebra, Derivations and Dual Numbers, Differential Ideals and Ritt Noetherianity, Characteristic Sets and the Partial Ritt-Raudenbush, Basic Differential Algebraic Geometry: Properties of the Kolchin Topology, Differentially Closed Fields, Differential Dimension Polynomials, Differential Galois Theory, Binding Groups and Internality, Pillay’s X-strongly-normal theory, Galois Theory of Linear Differential Equations, Algebraic D-Groups and Logarithmic Derivatives, Constrained Cohomology, The Galois Groupoid, Differential Algebraic Groups, Preliminaries from Model Theory.
Author(s): Reid Dale
47 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
This note covers the following topics: Conventions, Differential graded algebras, Differential graded modules, The homotopy category, Cones, Admissible short exact sequences, Distinguished triangles, Cones and distinguished triangles, The homotopy category is triangulated, Projective modules over algebras, Injective modules over algebras, P-resolutions, I-resolutions, The derived category, The canonical delta-functor, Linear categories, Graded categories, Differential graded categories, Obtaining triangulated categories, Tensor product, 24. Derived tensor product, Variant of derived tensor product, Characterizing compact objects and Equivalences of derived categories.
Author(s): Columbia University
57 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 Pages
