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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 
Lectures on Computational Differential Algebra
This note covers basic notions of differential algebra, Differential polynomial rings and differential varieties, The differential algebra geometry dictionary, Extensions of differential fields, Symbolic integration for elementary functions, Algorithms and open problems in differential algebra.
Author(s): Wei Li
63 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 RittRaudenbush, Basic Differential Algebraic Geometry, Properties of the Kolchin Topology, Differentially Closed Fields, Differential Dimension Polynomials, Differential Galois Theory, Binding Groups and Internality, Pillays Xstronglynormal theory, Galois Theory of Linear Differential Equations, Algebraic DGroups and Logarithmic Derivatives, Constrained Cohomology, The Galois Groupoid, Differential Algebraic Groups, Preliminaries from Model Theory.
Author(s): Reid Dale
47 Pages
Stability criteria for nonlinear fully implicit differential algebraic systems
The 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, Lyapunovs direct method regarding DAEs.
Author(s): Michael Menrath
191 Pages