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Jacobian

Line breaks: Ja|cobi¦an
Pronunciation: /dʒəˈkəʊbɪən
 
/
Mathematics

Definition of Jacobian in English:

adjective

Relating to the work of the mathematician K. G. J. Jacobi.
Example sentences
  • He showed how to find integrals of a general system of partial differential equations by using sequential complete systems instead of passing to Jacobian systems.
  • Göpel… finally, after ingenious calculations, obtained the result that the quotients of two theta functions are solutions of the Jacobian problem for p = 2.
  • In order to calculate the inverse Jacobian matrix, we need the following derivatives of the functional response [F.sub.ki] (for all values of k and i).

noun

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A determinant whose constituents are the derivatives of a number of functions (u, v, w, ...) with respect to each of the same number of variables (x, y, z, ...).
Example sentences
  • Therefore, the determinants of the set of variable transformations (Jacobians) must be calculated for both states involved: the original and the new one, to properly weigh up each new configuration.
  • He also worked on determinants and studied the functional determinant now called the Jacobian.
  • These problems form the basis of a conjecture: every elliptic curve defined over the rational field is a factor of the Jacobian of a modular function field.

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