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- Neumann_boundary_condition abstract "In mathematics, the Neumann (or second-type) boundary condition is a type of boundary condition, named after Carl Neumann.When imposed on an ordinary or a partial differential equation, it specifies the values that the derivative of a solution is to take on the boundary of the domain. In engineering applications, the following would be considered Neumann boundary conditions: In thermodynamics, where a surface has a prescribed heat flux, such as a perfect insulator (where flux is zero) or an electrical component dissipating a known power.For an ordinary differential equation, for instance:the Neumann boundary conditions on the interval take the form:where and are given numbers. For a partial differential equation, for instance:where denotes the Laplacian, the Neumann boundary conditions on a domain take the form:where denotes the (typically exterior) normal to the boundary and f is a given scalar function.The normal derivative which shows up on the left-hand side is defined as:where is the gradient (vector) and the dot is the inner product. It becomes clear that the boundary must be sufficiently smooth such that the normal derivative can exist, since for example at corner points of the boundary the normal vector is not well defined. Many other boundary conditions are possible. For example, there is the Cauchy boundary condition, or the mixed boundary condition which is a combination of the Neumann and Dirichlet conditions.".
- Neumann_boundary_condition wikiPageID "735443".
- Neumann_boundary_condition wikiPageRevisionID "594393136".
- Neumann_boundary_condition hasPhotoCollection Neumann_boundary_condition.
- Neumann_boundary_condition subject Category:Boundary_conditions.
- Neumann_boundary_condition type Abstraction100002137.
- Neumann_boundary_condition type BoundaryCondition106755776.
- Neumann_boundary_condition type BoundaryConditions.
- Neumann_boundary_condition type Communication100033020.
- Neumann_boundary_condition type Condition106755568.
- Neumann_boundary_condition type Message106598915.
- Neumann_boundary_condition type Postulate106753299.
- Neumann_boundary_condition type Premise106753800.
- Neumann_boundary_condition type Proposition106750804.
- Neumann_boundary_condition type Statement106722453.
- Neumann_boundary_condition comment "In mathematics, the Neumann (or second-type) boundary condition is a type of boundary condition, named after Carl Neumann.When imposed on an ordinary or a partial differential equation, it specifies the values that the derivative of a solution is to take on the boundary of the domain.".
- Neumann_boundary_condition label "Condición de frontera de Neumann".
- Neumann_boundary_condition label "Condition aux limites de Neumann".
- Neumann_boundary_condition label "Condizioni al contorno di Neumann".
- Neumann_boundary_condition label "Condição de contorno de Neumann".
- Neumann_boundary_condition label "Neumann boundary condition".
- Neumann_boundary_condition label "Neumann-Randbedingung".
- Neumann_boundary_condition label "Задача Неймана".
- Neumann_boundary_condition label "ノイマン境界条件".
- Neumann_boundary_condition label "诺伊曼边界条件".
- Neumann_boundary_condition sameAs Neumann-Randbedingung.
- Neumann_boundary_condition sameAs Condición_de_frontera_de_Neumann.
- Neumann_boundary_condition sameAs Condition_aux_limites_de_Neumann.
- Neumann_boundary_condition sameAs Condizioni_al_contorno_di_Neumann.
- Neumann_boundary_condition sameAs ノイマン境界条件.
- Neumann_boundary_condition sameAs 노이만_경계_조건.
- Neumann_boundary_condition sameAs Condição_de_contorno_de_Neumann.
- Neumann_boundary_condition sameAs m.036wqz.
- Neumann_boundary_condition sameAs Q1149279.
- Neumann_boundary_condition sameAs Q1149279.
- Neumann_boundary_condition sameAs Neumann_boundary_condition.
- Neumann_boundary_condition wasDerivedFrom Neumann_boundary_condition?oldid=594393136.
- Neumann_boundary_condition isPrimaryTopicOf Neumann_boundary_condition.