In mathematics, a derivation is a function on an algebra which generalizes certain features of the derivative operator. Specifically, given an algebra A over a ring or a field K, a K-derivation is a K-linear map D : A → A that satisfies Leibniz's law: More generally, if M is an A-bimodule, a K-linear map D : A → M that satisfies the Leibniz law is also called a derivation. The collection of all K-derivations of A to itself is denoted by DerK(A). The collection of K-derivations of A into an A-module M is denoted by DerK(A, M). Derivations occur in many different contexts in diverse areas of mathematics. The partial derivative with respect to a variable is an R-derivation on the algebra of real-valued differentiable functions on Rn. The Lie derivative with respect to a vector field is an R-derivation on the algebra of differentiable functions on a differentiable manifold; more generally it is a derivation on the tensor algebra of a manifold. It follows that the adjoint representation of a Lie algebra is a derivation on that algebra. The Pincherle derivative is an example of a derivation in abstract algebra. If the algebra A is noncommutative, then the commutator with respect to an element of the algebra A defines a linear endomorphism of A to itself, which is a derivation over K. That is, where is the commutator with respect to . An algebra A equipped with a distinguished derivation d forms a differential algebra, and is itself a significant object of study in areas such as differential Galois theory. (Wikipedia).
Derivation of the fundamental theorem of calculus
Derivation of the Fundamental Theorem of Calculus. Join me on Coursera: Matrix Algebra for Engineers: https://www.coursera.org/learn/matrix-algebra-engineers Differential Equations for Engineers: https://www.coursera.org/learn/differential-equations-engineers Vector Calculus for Engin
From playlist Differential Equations
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Learn how to solve the particular solution of differential equations. A differential equation is an equation that relates a function with its derivatives. The solution to a differential equation involves two parts: the general solution and the particular solution. The general solution give
From playlist Solve Differential Equation (Particular Solution) #Integration
Linear Algebra 5.4 Differential Equations
My notes are available at http://asherbroberts.com/ (so you can write along with me). Elementary Linear Algebra: Applications Version 12th Edition by Howard Anton, Chris Rorres, and Anton Kaul A. Roberts is supported in part by the grants NSF CAREER 1653602 and NSF DMS 2153803.
From playlist Linear Algebra
Solve the general solution for differentiable equation with trig
Learn how to solve the particular solution of differential equations. A differential equation is an equation that relates a function with its derivatives. The solution to a differential equation involves two parts: the general solution and the particular solution. The general solution give
From playlist Differential Equations
How to solve a differentialble equation by separating the variables
Learn how to solve the particular solution of differential equations. A differential equation is an equation that relates a function with its derivatives. The solution to a differential equation involves two parts: the general solution and the particular solution. The general solution give
From playlist Solve Differential Equation (Particular Solution) #Integration
Introduction to Differential Equations
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Introduction to Differential Equations - The types of differential equations, ordinary versus partial. - How to find the order of a differential equation.
From playlist Differential Equations
Title: Differential Kernels and Bounds for the Consistency of Differential Equations
From playlist Differential Algebra and Related Topics VII (2016)
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Finishing the derivation for the equation that is used to find the particular solution of a set of differential equations by means of the variation of parameters.
From playlist A Second Course in Differential Equations
Omar León Sánchez, University of Manchester
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From playlist Fall 2021 Online Kolchin Seminar in Differential Algebra
Andy Magid, University of Oklahoma
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From playlist Online Workshop in Memory of Ray Hoobler - April 30, 2020
Pre-recorded lecture 16: Frolicher-Nijenhuis bracket and Frolicher-Nijenhuis cohomology
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From playlist MATRIX-SMRI Symposium: Nijenhuis Geometry companion lectures (Sino-Russian Mathematical Centre)
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MIT 10.34 Numerical Methods Applied to Chemical Engineering, Fall 2015 View the complete course: http://ocw.mit.edu/10-34F15 Instructor: James Swan Students continued to learn to solve differential algebraic equations, including the dynamic of DAEs and simulation. License: Creative Commo
From playlist MIT 10.34 Numerical Methods Applied to Chemical Engineering, Fall 2015
Julia Hartmann, University of Pennsylvania
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From playlist Online Workshop in Memory of Ray Hoobler - April 30, 2020
Introduction to Differential Equation Terminology
This video defines a differential equation and then classifies differential equations by type, order, and linearity. Search Library at http://mathispower4u.wordpress.com
From playlist Introduction to Differential Equations
Markus Rosenkranz Talk 1 7/7/14 Part 3
Title: Integro-Differential Polynomials and Free Integro-Differential Algebras
From playlist Spring 2014
Andy Magid, University of Oklahoma (hybrid talk)
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From playlist Fall 2022 Online Kolchin seminar in Differential Algebra
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From playlist Spring 2014
Ax-Lindemann-Weierstrass Theorem (ALW) for Fuchsian automorphic functions - Joel Nagloo
Joint IAS/Princeton University Number Theory Seminar Topic: Ax-Lindemann-Weierstrass Theorem (ALW) for Fuchsian automorphic functions Speaker: Joel Nagloo Affiliation: City University of New York Date: January 21, 2021 For more video please visit http://video.ias.edu
From playlist Mathematics
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This lecture is part of an online algebraic geometry course on schemes, based on chapter II of "Algebraic geometry" by Hartshorne. In this lecture we define differential operators on rings, and calculate the universal (normalized) differential operator of order n. As a special case we fin
From playlist Algebraic geometry II: Schemes