DBpedia – Linked Data Fragments

Matches in DBpedia 2016-04 for { <http://dbpedia.org/resource/Laplace_operator> ?p ?o }

• Laplace_operator abstract "In mathematics, the Laplace operator or Laplacian is a differential operator given by the divergence of the gradient of a function on Euclidean space. It is usually denoted by the symbols ∇·∇, ∇2, or ∆. The Laplacian ∆f(p) of a function f at a point p, up to a constant depending on the dimension, is the rate at which the average value of f over spheres centered at p, deviates from f(p) as the radius of the sphere grows. In a Cartesian coordinate system, the Laplacian is given by the sum of second partial derivatives of the function with respect to each independent variable. In other coordinate systems such as cylindrical and spherical coordinates, the Laplacian also has a useful form.The Laplace operator is named after the French mathematician Pierre-Simon de Laplace (1749–1827), who first applied the operator to the study of celestial mechanics, where the operator gives a constant multiple of the mass density when it is applied to a given gravitational potential. Solutions of the equation ∆f = 0, now called Laplace's equation, are the so-called harmonic functions, and represent the possible gravitational fields in free space.The Laplacian occurs in differential equations that describe many physical phenomena, such as electric and gravitational potentials, the diffusion equation for heat and fluid flow, wave propagation, and quantum mechanics. The Laplacian represents the flux density of the gradient flow of a function. For instance, the net rate at which a chemical dissolved in a fluid moves toward or away from some point is proportional to the Laplacian of the chemical concentration at that point; expressed symbolically, the resulting equation is the diffusion equation. For these reasons, it is extensively used in the sciences for modelling all kinds of physical phenomena. The Laplacian is the simplest elliptic operator, and is at the core of Hodge theory as well as the results of de Rham cohomology. In image processing and computer vision, the Laplacian operator has been used for various tasks such as blob and edge detection.".
• Laplace_operator wikiPageExternalLink 3D_Functions_Plotter.
• Laplace_operator wikiPageID "174706".
• Laplace_operator wikiPageLength "17576".
• Laplace_operator wikiPageOutDegree "140".
• Laplace_operator wikiPageRevisionID "703500729".
• Laplace_operator wikiPageWikiLink Analysis_on_fractals.
• Laplace_operator wikiPageWikiLink Azimuth.
• Laplace_operator wikiPageWikiLink Blob_detection.
• Laplace_operator wikiPageWikiLink Cartesian_coordinate_system.
• Laplace_operator wikiPageWikiLink Category:Differential_operators.
• Laplace_operator wikiPageWikiLink Category:Elliptic_partial_differential_equations.
• Laplace_operator wikiPageWikiLink Category:Fourier_analysis.
• Laplace_operator wikiPageWikiLink Category:Harmonic_functions.
• Laplace_operator wikiPageWikiLink Category:Linear_operators_in_calculus.
• Laplace_operator wikiPageWikiLink Category:Multivariable_calculus.
• Laplace_operator wikiPageWikiLink Category:Pierre-Simon_Laplace.
• Laplace_operator wikiPageWikiLink Celestial_mechanics.
• Laplace_operator wikiPageWikiLink Charge_density.
• Laplace_operator wikiPageWikiLink Colatitude.
• Laplace_operator wikiPageWikiLink Compact_operator.
• Laplace_operator wikiPageWikiLink Computer_vision.
• Laplace_operator wikiPageWikiLink Curvilinear_coordinates.
• Laplace_operator wikiPageWikiLink Cylindrical_coordinate_system.
• Laplace_operator wikiPageWikiLink DAlembert_operator.
• Laplace_operator wikiPageWikiLink De_Rham_cohomology.
• Laplace_operator wikiPageWikiLink Dependent_and_independent_variables.
• Laplace_operator wikiPageWikiLink Derivative.
• Laplace_operator wikiPageWikiLink Differentiable_function.
• Laplace_operator wikiPageWikiLink Differential_equation.
• Laplace_operator wikiPageWikiLink Differential_form.
• Laplace_operator wikiPageWikiLink Differential_operator.
• Laplace_operator wikiPageWikiLink Diffusion.
• Laplace_operator wikiPageWikiLink Diffusion_equation.
• Laplace_operator wikiPageWikiLink Dirichlets_energy.
• Laplace_operator wikiPageWikiLink Discrete_Laplace_operator.
• Laplace_operator wikiPageWikiLink Discrete_exterior_calculus.
• Laplace_operator wikiPageWikiLink Divergence.
• Laplace_operator wikiPageWikiLink Divergence_theorem.
• Laplace_operator wikiPageWikiLink Earnshaws_theorem.
• Laplace_operator wikiPageWikiLink Edge_detection.
• Laplace_operator wikiPageWikiLink Einstein_notation.
• Laplace_operator wikiPageWikiLink Electric_potential.
• Laplace_operator wikiPageWikiLink Elliptic_operator.
• Laplace_operator wikiPageWikiLink Euclidean_space.
• Laplace_operator wikiPageWikiLink Exterior_derivative.
• Laplace_operator wikiPageWikiLink Fluid_mechanics.
• Laplace_operator wikiPageWikiLink Flux.
• Laplace_operator wikiPageWikiLink French_people.
• Laplace_operator wikiPageWikiLink Function_(mathematics).
• Laplace_operator wikiPageWikiLink Functional_(mathematics).
• Laplace_operator wikiPageWikiLink Fundamental_lemma_of_calculus_of_variations.
• Laplace_operator wikiPageWikiLink Gausss_law.
• Laplace_operator wikiPageWikiLink Gradient.
• Laplace_operator wikiPageWikiLink Gravitational_potential.
• Laplace_operator wikiPageWikiLink Greens_identities.
• Laplace_operator wikiPageWikiLink Harmonic_function.
• Laplace_operator wikiPageWikiLink Heat_equation.
• Laplace_operator wikiPageWikiLink Helmholtz_equation.
• Laplace_operator wikiPageWikiLink Hessian_matrix.
• Laplace_operator wikiPageWikiLink Hilbert_space.
• Laplace_operator wikiPageWikiLink Hodge_dual.
• Laplace_operator wikiPageWikiLink Hodge_theory.
• Laplace_operator wikiPageWikiLink Homogeneous_function.
• Laplace_operator wikiPageWikiLink Hyperbolic_partial_differential_equation.
• Laplace_operator wikiPageWikiLink Image_processing.
• Laplace_operator wikiPageWikiLink Isometry_group.
• Laplace_operator wikiPageWikiLink Klein–Gordon_equation.
• Laplace_operator wikiPageWikiLink Kondrachov_embedding_theorem.
• Laplace_operator wikiPageWikiLink Laplace_operators_in_differential_geometry.
• Laplace_operator wikiPageWikiLink Laplaces_equation.
• Laplace_operator wikiPageWikiLink Laplace–Beltrami_operator.
• Laplace_operator wikiPageWikiLink List_of_formulas_in_Riemannian_geometry.
• Laplace_operator wikiPageWikiLink Lp_space.
• Laplace_operator wikiPageWikiLink Mass_distribution.
• Laplace_operator wikiPageWikiLink Mathematics.
• Laplace_operator wikiPageWikiLink Metric_tensor.
• Laplace_operator wikiPageWikiLink Minkowski_space.
• Laplace_operator wikiPageWikiLink Molecular_diffusion.
• Laplace_operator wikiPageWikiLink N-sphere.
• Laplace_operator wikiPageWikiLink Natural_units.
• Laplace_operator wikiPageWikiLink Non-Euclidean_geometry.
• Laplace_operator wikiPageWikiLink Open_set.
• Laplace_operator wikiPageWikiLink Orthonormal_basis.
• Laplace_operator wikiPageWikiLink Partial_derivative.
• Laplace_operator wikiPageWikiLink Particle_physics.
• Laplace_operator wikiPageWikiLink Physics.
• Laplace_operator wikiPageWikiLink Pierre-Simon_Laplace.
• Laplace_operator wikiPageWikiLink Poincaré_inequality.
• Laplace_operator wikiPageWikiLink Poissons_equation.
• Laplace_operator wikiPageWikiLink Polar_coordinate_system.
• Laplace_operator wikiPageWikiLink Pseudo-Riemannian_manifold.
• Laplace_operator wikiPageWikiLink Quantum_mechanics.
• Laplace_operator wikiPageWikiLink Real-valued_function.
• Laplace_operator wikiPageWikiLink Riemannian_manifold.
• Laplace_operator wikiPageWikiLink Scale_space.
• Laplace_operator wikiPageWikiLink Self-adjoint_operator.
• Laplace_operator wikiPageWikiLink Smoothness.
• Laplace_operator wikiPageWikiLink Spectral_theorem.
• Laplace_operator wikiPageWikiLink Spectral_theory.

• next