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- D'Alembert's_formula abstract "In mathematics, and specifically partial differential equations, d´Alembert's formula is the general solution to the one-dimensional wave equation: for . It is named after the mathematician Jean le Rond d'Alembert.The characteristics of the PDE are , so use the change of variables to transform the PDE to . The general solution of this PDE is where and are functions. Back in coordinates,is if and are .This solution can be interpreted as two waves with constant velocity moving in opposite directions along the x-axis.Now consider this solution with the Cauchy data .Using we get .Using we get .Integrate the last equation to get Now solve this system of equations to getNow, usingd´Alembert's formula becomes:".
- D'Alembert's_formula wikiPageExternalLink PDE27.
- D'Alembert's_formula wikiPageID "4474984".
- D'Alembert's_formula wikiPageRevisionID "549139702".
- D'Alembert's_formula hasPhotoCollection D'Alembert's_formula.
- D'Alembert's_formula subject Category:Partial_differential_equations.
- D'Alembert's_formula type Abstraction100002137.
- D'Alembert's_formula type Communication100033020.
- D'Alembert's_formula type DifferentialEquation106670521.
- D'Alembert's_formula type Equation106669864.
- D'Alembert's_formula type MathematicalStatement106732169.
- D'Alembert's_formula type Message106598915.
- D'Alembert's_formula type PartialDifferentialEquation106670866.
- D'Alembert's_formula type PartialDifferentialEquations.
- D'Alembert's_formula type Statement106722453.
- D'Alembert's_formula comment "In mathematics, and specifically partial differential equations, d´Alembert's formula is the general solution to the one-dimensional wave equation: for . It is named after the mathematician Jean le Rond d'Alembert.The characteristics of the PDE are , so use the change of variables to transform the PDE to . The general solution of this PDE is where and are functions.".
- D'Alembert's_formula label "D'Alembert's formula".
- D'Alembert's_formula label "Fórmula de d'Alembert".
- D'Alembert's_formula label "Формула Кирхгофа".
- D'Alembert's_formula sameAs Fórmula_de_d'Alembert.
- D'Alembert's_formula sameAs m.0c4hxr.
- D'Alembert's_formula sameAs Q2388753.
- D'Alembert's_formula sameAs Q2388753.
- D'Alembert's_formula sameAs D'Alembert's_formula.
- D'Alembert's_formula wasDerivedFrom D'Alembert's_formula?oldid=549139702.
- D'Alembert's_formula isPrimaryTopicOf D'Alembert's_formula.