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In physical terms, the divergence of a vector field is the extent to which the vector field flux behaves like a source or a sink at a given point. It is a local measure of its "outgoingness" – the extent to which there are more of the field vectors exiting from an infinitesimal region of space than entering it.
Difference equations are similar to differential equations, but replace differentiation by taking the difference between adjacent terms; they can be used to approximate differential equations or (more often) studied in their own right. Many questions and methods concerning differential equations have counterparts for difference equations.
In an analogous way, one can obtain finite difference approximations to higher order derivatives and differential operators. For example, by using the above central difference formula for f ′(x + h / 2 ) and f ′(x − h / 2 ) and applying a central difference formula for the derivative of f ′ at x, we obtain the central difference approximation of the second derivative of f:
The absolute difference is used to define other quantities including the relative difference, the L 1 norm used in taxicab geometry, and graceful labelings in graph theory. When it is desirable to avoid the absolute value function – for example because it is expensive to compute, or because its derivative is not continuous – it can ...
This formula shows how to calculate the curl of F in any coordinate system, and how to extend the curl to any oriented three-dimensional Riemannian manifold. Since this depends on a choice of orientation, curl is a chiral operation. In other words, if the orientation is reversed, then the direction of the curl is also reversed.
a finite difference; a difference operator; a symmetric difference; the Laplace operator; giving heat in a chemical reaction; the angle that subtends the arc of a circular curve in surveying; the maximum degree of any vertex in a given graph; sensitivity to price in mathematical finance
The slope field of () = +, showing three of the infinitely many solutions that can be produced by varying the arbitrary constant c.. In calculus, an antiderivative, inverse derivative, primitive function, primitive integral or indefinite integral [Note 1] of a continuous function f is a differentiable function F whose derivative is equal to the original function f.
Discrete calculus or the calculus of discrete functions, is the mathematical study of incremental change, in the same way that geometry is the study of shape and algebra is the study of generalizations of arithmetic operations.