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- Constant_coefficients abstract "In mathematics, constant coefficients is a term applied to differential operators, and also some difference operators, to signify that they contain no functions of the independent variables, other than constant functions. In other words, it singles out special operators, within the larger class of operators having variable coefficients. Such constant coefficient operators have been found to be the easiest to handle, in several respects. They include for example the Laplacian of potential theory and other major examples of mathematical physics.In the case of ordinary differential equations, writingD = d/dxthe general constant-coefficient differential operator is L = p(D),where p is any polynomial with complex number coefficients. The solution of equationsLf = gwith a given function g(x) was given already in the eighteenth century, by Leonhard Euler.For partial differential equations, the constant-coefficient operators are characterised geometrically by their translation invariance, and algebraically as polynomials in the partial derivatives. According to the Ehrenpreis–Malgrange theorem, they all have fundamental solutions.".
- Constant_coefficients wikiPageID "3992208".
- Constant_coefficients wikiPageLength "1353".
- Constant_coefficients wikiPageOutDegree "17".
- Constant_coefficients wikiPageRevisionID "343115479".
- Constant_coefficients wikiPageWikiLink Category:Differential_operators.
- Constant_coefficients wikiPageWikiLink Complex_number.
- Constant_coefficients wikiPageWikiLink Constant_function.
- Constant_coefficients wikiPageWikiLink Dependent_and_independent_variables.
- Constant_coefficients wikiPageWikiLink Difference_operator.
- Constant_coefficients wikiPageWikiLink Differential_operator.
- Constant_coefficients wikiPageWikiLink Ehrenpreis–Malgrange_theorem.
- Constant_coefficients wikiPageWikiLink Finite_difference.
- Constant_coefficients wikiPageWikiLink Fundamental_solution.
- Constant_coefficients wikiPageWikiLink Independent_variables.
- Constant_coefficients wikiPageWikiLink Laplace_operator.
- Constant_coefficients wikiPageWikiLink Laplacian.
- Constant_coefficients wikiPageWikiLink Leonhard_Euler.
- Constant_coefficients wikiPageWikiLink Malgrange–Ehrenpreis_theorem.
- Constant_coefficients wikiPageWikiLink Mathematical_physics.
- Constant_coefficients wikiPageWikiLink Mathematics.
- Constant_coefficients wikiPageWikiLink Ordinary_differential_equation.
- Constant_coefficients wikiPageWikiLink Partial_derivative.
- Constant_coefficients wikiPageWikiLink Partial_differential_equation.
- Constant_coefficients wikiPageWikiLink Potential_theory.
- Constant_coefficients wikiPageWikiLink Translation_invariance.
- Constant_coefficients wikiPageWikiLink Translational_symmetry.
- Constant_coefficients wikiPageWikiLinkText "constant coefficients".
- Constant_coefficients hasPhotoCollection Constant_coefficients.
- Constant_coefficients wikiPageUsesTemplate Template:Unreferenced.
- Constant_coefficients subject Category:Differential_operators.
- Constant_coefficients hypernym Term.
- Constant_coefficients type Article.
- Constant_coefficients type Article.
- Constant_coefficients comment "In mathematics, constant coefficients is a term applied to differential operators, and also some difference operators, to signify that they contain no functions of the independent variables, other than constant functions. In other words, it singles out special operators, within the larger class of operators having variable coefficients. Such constant coefficient operators have been found to be the easiest to handle, in several respects.".
- Constant_coefficients label "Constant coefficients".
- Constant_coefficients sameAs 定数係数.
- Constant_coefficients sameAs m.0bbgl7.
- Constant_coefficients sameAs Q5163646.
- Constant_coefficients sameAs Q5163646.
- Constant_coefficients wasDerivedFrom Constant_coefficients?oldid=343115479.
- Constant_coefficients isPrimaryTopicOf Constant_coefficients.