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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.

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, Lyapunov’s direct method regarding DAEs.


s 191Pages

Differential algebra

This book covers the following topics: differential polynomial and their ideals, algebraic differential manifolds, structure of differential polynomials, systems of algebraic equations, constructive method, intersections of algebraic differential manifolds, Riquier's existence theorem for orthonomic system.


s 189Pages

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