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.
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.
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.
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.
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