Search results
Results from the WOW.Com Content Network
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 ...
Conventionally, for clarity and simplicity of notation, the partial derivative function and the value of the function at a specific point are conflated by including the function arguments when the partial derivative symbol (Leibniz notation) is used. Thus, an expression like
Partial derivatives are generally distinguished from ordinary derivatives by replacing the differential operator d with a "∂" symbol. For example, we can indicate the partial derivative of f(x, y, z) with respect to x, but not to y or z in several ways: = =.
Partial derivative, derivative with respect to one of several variables of a function, with the other variables held constant ∂, a symbol that can denote a partial derivative, sometimes pronounced "partial dee" Partial differential equation, a differential equation that contains unknown multivariable functions and their partial derivatives
Higher partial derivatives can be indicated by superscripts or multiple subscripts, e.g. ... Here ∂ is a rounded d called the partial derivative symbol.
In the study of hyperbolic and parabolic partial differential equations, zeros of the principal symbol correspond to the characteristics of the partial differential equation. In applications to the physical sciences, operators such as the Laplace operator play a major role in setting up and solving partial differential equations.
If the derivative does not lie on the tangent space, the right expression is the projection of the derivative over the tangent space (see covariant derivative below). Symbols of the second kind decompose the change with respect to the basis, while symbols of the first kind decompose it with respect to the dual basis.
1 Christoffel symbols, covariant derivative. 2 Curvature tensors. Toggle Curvature tensors subsection. 2.1 Definitions. 2.1.1 (3,1) Riemann curvature tensor.