

This section contains free ebooks 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 systemsMichael
MenrathPDF  191 Pages  EnglishThe goal of this note is to contribute to the qualitative theory of
differentialalgebraic 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 differentialalgebraic
equations, Properly formulated DAEs with tractability index 2, The state space
form, Index reduction via differentiation, Stability criteria for
differentialalgebraic systems, Asymptotic stability of periodic solutions,
Lyapunov’s direct method regarding DAEs.
 Differential algebraJoseph Fels RittPDF  189 Pages  EnglishThis
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.
 Differential Graded AlgebraColumbia UniversityPDF  57 Pages  EnglishThis 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, Presolutions, Iresolutions, The derived category, The canonical
deltafunctor, 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.
 Differential algebra on lattice Green functions and Calabi Yau operatorsSalah Boukraa, Saoud
Hassani, JeanMarie Maillard, JacquesArthur WeilPDF  62 Pages  EnglishThis note explains
miscellaneous linear differential operators mostly associated with lattice Green
functions in arbitrary dimensions, but also CalabiYau operators and orderseven
operators corresponding to exceptional differential Galois groups.
 Asymptotic Differential AlgebraMatthias AschenbrennerPDF  38 Pages  EnglishThis note introduces
both, state some of their basic properties, and explain connections to ominimal
structures. Also describe a common algebraic framework for these examples: the
category of Hfields. This unified setting leads to a better understanding of
Hardy fields and transseries from an algebraic and modeltheoretic perspective.









