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- Separable_partial_differential_equation abstract "A separable partial differential equation (PDE) is one that can be broken into a set of separate equations of lower dimensionality (fewer independent variables) by a method of separation of variables. This generally relies upon the problem having some special form or symmetry. In this way, the PDE can be solved by solving a set of simpler PDEs, or even ordinary differential equations (ODEs) if the problem can be broken down into one-dimensional equations. The most common form of separation of variables is simple separation of variables in which a solution is obtained by assuming a solution of the form given by a product of functions of each individual coordinate.There is a special form of separation of variables called -separation of variables which is accomplished by writing the solution as a particular fixed function of the coordinates multiplied by a product of functions of each individual coordinate. Laplace's equation on is an example of a partial differential equation which admits solutions through -separation of variables; in the three-dimensional case this uses 6-sphere coordinates.(This should not be confused with the case of a separable ODE, which refers to a somewhat different class of problems that can be broken into a pair of integrals; see separation of variables.)".
- Separable_partial_differential_equation wikiPageID "6885778".
- Separable_partial_differential_equation wikiPageRevisionID "604415192".
- Separable_partial_differential_equation hasPhotoCollection Separable_partial_differential_equation.
- Separable_partial_differential_equation subject Category:Differential_equations.
- Separable_partial_differential_equation type Abstraction100002137.
- Separable_partial_differential_equation type Communication100033020.
- Separable_partial_differential_equation type DifferentialEquation106670521.
- Separable_partial_differential_equation type DifferentialEquations.
- Separable_partial_differential_equation type Equation106669864.
- Separable_partial_differential_equation type MathematicalStatement106732169.
- Separable_partial_differential_equation type Message106598915.
- Separable_partial_differential_equation type Statement106722453.
- Separable_partial_differential_equation comment "A separable partial differential equation (PDE) is one that can be broken into a set of separate equations of lower dimensionality (fewer independent variables) by a method of separation of variables. This generally relies upon the problem having some special form or symmetry. In this way, the PDE can be solved by solving a set of simpler PDEs, or even ordinary differential equations (ODEs) if the problem can be broken down into one-dimensional equations.".
- Separable_partial_differential_equation label "Separable partial differential equation".
- Separable_partial_differential_equation sameAs m.0gv8d0.
- Separable_partial_differential_equation sameAs Q7451766.
- Separable_partial_differential_equation sameAs Q7451766.
- Separable_partial_differential_equation sameAs Separable_partial_differential_equation.
- Separable_partial_differential_equation wasDerivedFrom Separable_partial_differential_equation?oldid=604415192.
- Separable_partial_differential_equation isPrimaryTopicOf Separable_partial_differential_equation.