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  2. Partial derivative - Wikipedia

    en.wikipedia.org/wiki/Partial_derivative

    For higher order partial derivatives, the partial derivative (function) of with respect to the j-th variable is denoted () =,. That is, D j ∘ D i = D i , j {\displaystyle D_{j}\circ D_{i}=D_{i,j}} , so that the variables are listed in the order in which the derivatives are taken, and thus, in reverse order of how the composition of operators ...

  3. List of limits - Wikipedia

    en.wikipedia.org/wiki/List_of_limits

    In these limits, the infinitesimal change is often denoted or .If () is differentiable at , (+) = ′ ().This is the definition of the derivative.All differentiation rules can also be reframed as rules involving limits.

  4. Partial differential equation - Wikipedia

    en.wikipedia.org/wiki/Partial_differential_equation

    In mathematics, a partial differential equation (PDE) is an equation which involves a multivariable function and one or more of its partial derivatives.. The function is often thought of as an "unknown" that solves the equation, similar to how x is thought of as an unknown number solving, e.g., an algebraic equation like x 2 − 3x + 2 = 0.

  5. Derivation (differential algebra) - Wikipedia

    en.wikipedia.org/wiki/Derivation_(differential...

    The partial derivative with respect to a variable is an R-derivation on the algebra of real-valued differentiable functions on R n. The Lie derivative with respect to a vector field is an R-derivation on the algebra of differentiable functions on a differentiable manifold; more generally it is a derivation on the tensor algebra of a manifold

  6. Vector calculus identities - Wikipedia

    en.wikipedia.org/wiki/Vector_calculus_identities

    Another method of deriving vector and tensor derivative identities is to replace all occurrences of a vector in an algebraic identity by the del operator, provided that no variable occurs both inside and outside the scope of an operator or both inside the scope of one operator in a term and outside the scope of another operator in the same term ...

  7. Matrix calculus - Wikipedia

    en.wikipedia.org/wiki/Matrix_calculus

    In mathematics, matrix calculus is a specialized notation for doing multivariable calculus, especially over spaces of matrices.It collects the various partial derivatives of a single function with respect to many variables, and/or of a multivariate function with respect to a single variable, into vectors and matrices that can be treated as single entities.

  8. ∂ - Wikipedia

    en.wikipedia.org/wiki/%E2%88%82

    The symbol was introduced originally in 1770 by Nicolas de Condorcet, who used it for a partial differential, and adopted for the partial derivative by Adrien-Marie Legendre in 1786. [3] It represents a specialized cursive type of the letter d , just as the integral sign originates as a specialized type of a long s (first used in print by ...

  9. First-order partial differential equation - Wikipedia

    en.wikipedia.org/wiki/First-order_partial...

    The general solution to the first order partial differential equation is a solution which contains an arbitrary function. But, the solution to the first order partial differential equations with as many arbitrary constants as the number of independent variables is called the complete integral. The following n-parameter family of solutions