Math 2.0

Real functions Concept

Conservative vector field

Builds on Vector fieldGradientScalar potential

Summary

A conservative vector field is a vector field that is the gradient of a scalar function, called a scalar potential of the field. Its line integrals depend only on the end points of the path, and they vanish around each closed path.

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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 levelGradientconceptScalar potential, concept, no evidence levelScalar potentialconceptConservative vector field, concept, no evidence levelConservative vector f…concept
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.
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  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. Scalar potential concept
  11. Conservative vector field concept

Further reading

  1. Web https://en.wikipedia.org/wiki/Conservative_vector_field, Definition
About this page
Tag0PKG97PX9Y
URIm2://0PKG97PX9Y
Aliasesgradient-field
Kindconcept
WritingW1 stated
MSC26B12
SpecializesVector field
UsesVector field, Gradient, Scalar potential
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