Differential equations

Loewy decomposition

In the study of differential equations, the Loewy decomposition breaks every linear ordinary differential equation (ODE) into what are called largest completely reducible components. It was introduced by Alfred Loewy. Solving differential equations is one of the most important subfields in mathematics. Of particular interest are solutions in closed form. Breaking ODEs into largest irreducible components, reduces the process of solving the original equation to solving irreducible equations of lowest possible order. This procedure is algorithmic, so that the best possible answer for solving a reducible equation is guaranteed. A detailed discussion may be found in. Loewy's results have been extended to linear partial differential equations (PDEs) in two independent variables. In this way, algorithmic methods for solving large classes of linear PDEs have become available. (Wikipedia).

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https://bit.ly/PavelPatreon https://lem.ma/LA - Linear Algebra on Lemma http://bit.ly/ITCYTNew - Dr. Grinfeld's Tensor Calculus textbook https://lem.ma/prep - Complete SAT Math Prep

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LU Decomposition Using Elementary Matrices

This video explains how find the LU Decomposition of a square matrix using elementary matrices. Site: http://mathispower4u.com Blog: http://mathispower4u.wordpress.com

From playlist Matrix Equations

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From playlist Introducing linear algebra

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From playlist Matrix Equations

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From playlist Matrix Equations

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https://bit.ly/PavelPatreon https://lem.ma/LA - Linear Algebra on Lemma http://bit.ly/ITCYTNew - Dr. Grinfeld's Tensor Calculus textbook https://lem.ma/prep - Complete SAT Math Prep

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https://bit.ly/PavelPatreon https://lem.ma/LA - Linear Algebra on Lemma http://bit.ly/ITCYTNew - Dr. Grinfeld's Tensor Calculus textbook https://lem.ma/prep - Complete SAT Math Prep

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From playlist Chemistry

Related pages

Differential operator | Differential algebra | Differential equation | Coefficient | Factorization | Bessel function | Indeterminate (variable) | Derivative | Janet basis | Monomial | Theorem | Algebraic number | Commutative algebra | Parameter | Polynomial | Partial derivative | Corollary | Mathematics | Closed-form expression | Ordinary differential equation | Function space | Legendre function | Quotient | Riccati equation | Partial differential equation | Algorithm