Jacobian
/dʒəˈkəʊbɪən
/Mathematics
adjective
Relating to the work of the mathematician K. G. J. Jacobi.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
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, ...).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.