Technical Books

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, 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.

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.

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.

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.

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.

This note explains the following topics, Differential algebra, Torus actions, Scaling symmetries of dynamical systems, Scaling symmetries of PDEs.

This note explains the folloing topics, model theory, differential fields and ordered fields, Stellensatze, Differential galois theory, Definable types and VC density.

This book is written by Michael Husted contains Fibonacci's Numbers of first 1000.

This is the Home page for Dr Ron Knott's multimedia web site on the Fibonacci numbers, the Golden section and the Golden string hosted by the Mathematics Department of the University of Surrey, UK.

This file contains factorials from 1 to 99 by 1's, 100 to 900 by 100's, and 1000 to 10000 by 1000's. The program used to calculate the factorials was a simple Scheme program, the source code of which has been lost.

This popular classic work by Simon Plouffe is in the English language, consist as a collection of mathematical constants.

This book covers the following topics: Sequences, Limit Laws for Sequences, Bounded Monotonic Sequences, Infinite Series, Telescopic Series, Harmonic Series, Higher Degree Polynomial Approximations, Taylor Series and Taylor Polynomials, The Integral Test, Comparison Test for Positive-Term Series, Alternating Series and Absolute Convergence, Convergence of a Power Series and Power Series Computations.

This PDF book covers the following topics related to Constants And Numerical Sequences and Series : Sequences, Series, Means, Applications to finance, The limiting sum of a geometric series, Links forward, Use of induction, Telescoping series, The harmonic series, Connection with integration, More on means, The AM�GM inequality, History and applications, An application to film and video, Fibonacci numbers, The Greeks.

This note explains the following topics, Complex functions, Analytic functions, Integration, Singularities, Harmonic functions, Entire functions, The Riemann mapping theorem and The Gamma function.

This note covers the following topics, The Holomorphic Functions, Functions Of A Complex Variable, Properties Of Holomorphic Functions, The Basics Of The Geometric Theory, The Taylor Series.