Intuition for formula in proof of Poincaré Lemma The 2019 Stack Overflow Developer Survey Results Are In Announcing the arrival of Valued Associate #679: Cesar Manara Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)Poincaré lemma for star shaped domainIntuition behind Snake LemmaIntuition and applications for the p-LaplacianIs zero vector potential for Helmholtz decomposition of curl and divergence free vector fields necessary?What does Poincaré mean for intuition of pure number?(Geometric intuition) Line integral over vector fieldsProof of property of normals to a star shaped region (“elementary” vector calculus lemma in Evans' PDE)Intuition for Artin's lemmaHow to derive or logically explain the formula for curl?Scalar Potential (Proof for Singularities)Intuition of definition of divergence

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Intuition for formula in proof of Poincaré Lemma



The 2019 Stack Overflow Developer Survey Results Are In
Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)Poincaré lemma for star shaped domainIntuition behind Snake LemmaIntuition and applications for the p-LaplacianIs zero vector potential for Helmholtz decomposition of curl and divergence free vector fields necessary?What does Poincaré mean for intuition of pure number?(Geometric intuition) Line integral over vector fieldsProof of property of normals to a star shaped region (“elementary” vector calculus lemma in Evans' PDE)Intuition for Artin's lemmaHow to derive or logically explain the formula for curl?Scalar Potential (Proof for Singularities)Intuition of definition of divergence










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$begingroup$


In Poincaré lemma for star shaped domain, the potential $f$ of a vector field $bf F$ is given explicitly for
$$f(x) = int_0^1 bf F(tx)cdot x,dt.$$
Can be given some (physical...) intuition for this formula?










share|cite|improve this question









$endgroup$
















    0












    $begingroup$


    In Poincaré lemma for star shaped domain, the potential $f$ of a vector field $bf F$ is given explicitly for
    $$f(x) = int_0^1 bf F(tx)cdot x,dt.$$
    Can be given some (physical...) intuition for this formula?










    share|cite|improve this question









    $endgroup$














      0












      0








      0





      $begingroup$


      In Poincaré lemma for star shaped domain, the potential $f$ of a vector field $bf F$ is given explicitly for
      $$f(x) = int_0^1 bf F(tx)cdot x,dt.$$
      Can be given some (physical...) intuition for this formula?










      share|cite|improve this question









      $endgroup$




      In Poincaré lemma for star shaped domain, the potential $f$ of a vector field $bf F$ is given explicitly for
      $$f(x) = int_0^1 bf F(tx)cdot x,dt.$$
      Can be given some (physical...) intuition for this formula?







      multivariable-calculus intuition






      share|cite|improve this question













      share|cite|improve this question











      share|cite|improve this question




      share|cite|improve this question










      asked Mar 31 at 14:30









      Martín-Blas Pérez PinillaMartín-Blas Pérez Pinilla

      35.5k42972




      35.5k42972




















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