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Differential Algebra Books

Differential Algebra Books

This section contains free e-books and guides on Differential Algebra, some of the resources in this section can be viewed online and some of them can be downloaded.

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.


s 354Pages

Afternotes on Differential Algebra

This note covers the following topics: Conventions and Preliminaries, Ideals Defined by Triangular Sets are Unmixed, Regular Chains, Lazardís Lemma, Rosenfeldís Lemma, The Differential Nullstellensatz, Regular Differential Chains, Normal Forms, The RosenfeldGroebner Algorithm, The Henri-Michaelis-Menten Formula, Parameter Estimation.


s 88Pages

Stability criteria for nonlinear fully implicit differential algebraic systems

The goal of this note is to contribute to the qualitative theory of differential-algebraic systems by providing new asymptotic stability criteria for a class of nonlinear, fully implicit DAEs with tractability index two. Topics covered includes: State space analysis of differential-algebraic equations, Properly formulated DAEs with tractability index 2, The state space form, Index reduction via differentiation, Stability criteria for differential-algebraic systems, Asymptotic stability of periodic solutions, Lyapunovís direct method regarding DAEs.


s 191Pages

Differential Graded Algebra

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.


s 57Pages

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.


s 62Pages

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.


s 38Pages