• the symmetry of second derivatives (also called the equality of mixed partials) is the fact that exchanging the order of partial derivatives of a multivariate...
    34 KB (5,331 words) - 16:20, 9 July 2024
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    used to approximate second derivative Second partial derivative test Symmetry of second derivatives "Content - The second derivative". amsi.org.au. Retrieved...
    15 KB (2,013 words) - 08:18, 28 August 2024
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    relations are a set of equations in thermodynamics which are derivable from the symmetry of second derivatives and from the definitions of the thermodynamic...
    19 KB (3,124 words) - 07:31, 9 May 2024
  • held constant (as opposed to the total derivative, in which all variables are allowed to vary). Partial derivatives are used in vector calculus and differential...
    24 KB (4,152 words) - 06:58, 23 July 2024
  • Stokes' theorem Submersion Surface integral Symmetry of second derivatives Taylor's theorem Total derivative Vector field Vector operator Vector potential...
    2 KB (156 words) - 12:13, 30 October 2023
  • the second partial derivatives are all continuous, the Hessian matrix is a symmetric matrix by the symmetry of second derivatives. The determinant of the...
    21 KB (3,408 words) - 18:23, 27 December 2023
  • interval. That is, it is related to the symmetry of second derivatives, but involving integrals as well as derivatives. This case is also known as the Leibniz...
    52 KB (11,174 words) - 01:19, 19 August 2024
  • follows essentially from symmetry of second derivatives, so the vector spaces of k-forms along with the exterior derivative are a cochain complex. 0 →...
    13 KB (2,029 words) - 20:38, 17 December 2023
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    D^{\alpha }} is justified (i.e., independent of order of differentiation) because of the symmetry of second derivatives. The polynomial p obtained by replacing...
    22 KB (3,672 words) - 16:07, 29 August 2024
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    differential of the Helmholtz free energy A {\displaystyle A} is given by d A = − S d T − P d V . {\displaystyle dA=-S\,dT-P\,dV.} The symmetry of second derivatives...
    32 KB (4,857 words) - 12:55, 31 July 2024