Math 2.0

Partial differential equations Elliptic equations Concept

Laplacian

Builds on DivergenceGradient

Summary

The Laplacian of a twice differentiable function on ℝn\mathbb{R}^n is the divergence of its gradient. It measures how the value of the function at a point differs from its average value on small spheres around the point.

Reading path

To understand this page from the ground up, read these 11 pages in order. The foundations come first.

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Euclidean space, object, no evidence levelEuclidean spaceobjectFunction, concept, no evidence levelFunctionconceptTotal derivative, concept, no evidence levelTotal derivativeconceptFunction of several variables, concept, no evidence levelFunction of several v…conceptVector-valued function, concept, no evidence levelVector-valued functionconceptDifferentiable function of several variables, concept, no evidence levelDifferentiable functi…conceptPartial derivative, concept, no evidence levelPartial derivativeconceptVector field, concept, no evidence levelVector fieldconceptGradient, concept, no evidence levelGradientconceptDivergence, concept, no evidence levelDivergenceconceptLaplacian, concept, no evidence levelLaplacianconcept
Each page uses the pages above it. The colour of the bar on a box shows how strong the evidence is, and the box also gives it as text. The list has the same pages.
  • no evidence level
  1. Euclidean space object
  2. Function concept
  3. Total derivative concept
  4. Function of several variables concept
  5. Vector-valued function concept
  6. Differentiable function of several variables concept
  7. Partial derivative concept
  8. Vector field concept
  9. Gradient concept
  10. Divergence concept
  11. Laplacian concept

Where this leads

155 pages build on this one.

Further reading

  1. Web https://en.wikipedia.org/wiki/Laplace_operator, Definition
About this page
Tag0E0B6RA8K0
URIm2://0E0B6RA8K0
Aliaseslaplace-operator
Kindconcept
WritingW1 stated
MSC35J05
UsesDivergence, Gradient
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