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Jacobian

In mathematics, a Jacobian, named for Carl Gustav Jacob Jacobi, may refer to:Jacobian matrix and determinantJacobian elliptic functionsJacobian conjectureJacobian varietyJacobian idealIntermediate JacobianGeneralized…

Jacobian

In mathematics, a Jacobian, named for Carl Gustav Jacob Jacobi, may refer to:

  • Jacobian matrix and determinant
  • Jacobian elliptic functions
  • Jacobian conjecture
  • Jacobian variety
  • Jacobian ideal
  • Intermediate Jacobian
  • Generalized Jacobian
  • Robot Jacobian

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What is a partial derivative?

The ordinary derivative with respect to one variable while every other variable is frozen: the slope of the surface in one coordinate direction.

What does the gradient point at?

Uphill: the direction of steepest increase, with length equal to that steepest slope. It is perpendicular to the level curves.

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Mer i Multivariable Calculus

Functions of several variablesPartial derivatives and the gradientOptimisation in several variablesDouble and triple integralsVector fields, line integrals and the big theorems