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For other stencil configurations and derivative orders, the Finite Difference Coefficients Calculator is a tool that can be used to generate derivative approximation methods for any stencil with any derivative order (provided a solution exists). Higher derivatives. Using Newton's difference quotient,
The derivative is a fundamental tool of calculus that quantifies the sensitivity of change of a function 's output with respect to its input. The derivative of a function of a single variable at a chosen input value, when it exists, is the slope of the tangent line to the graph of the function at that point. The tangent line is the best linear ...
In mathematics — specifically, in stochastic analysis — Dynkin's formula is a theorem giving the expected value of any suitably smooth statistic of an Itō diffusion at a stopping time. It may be seen as a stochastic generalization of the (second) fundamental theorem of calculus. It is named after the Russian mathematician Eugene Dynkin .
Lie derivative. In differential geometry, the Lie derivative ( / liː / LEE ), named after Sophus Lie by Władysław Ślebodziński, [1] [2] evaluates the change of a tensor field (including scalar functions, vector fields and one-forms ), along the flow defined by another vector field. This change is coordinate invariant and therefore the Lie ...
The tool comes pre-programmed with 36 different example graphs for the purpose of teaching new users about the tool and the mathematics involved. Another popular use of the calculator involves the creation of graphic arts using equations and inequalities. The calculator also has an audiotrace function, which can be used to make music.
Differential operator. A harmonic function defined on an annulus. Harmonic functions are exactly those functions which lie in the kernel of the Laplace operator, an important differential operator. In mathematics, a differential operator is an operator defined as a function of the differentiation operator.
In the fundamental branches of modern physics, namely general relativity and its widely applicable subset special relativity, as well as relativistic quantum mechanics and relativistic quantum field theory, the Lorentz transformation is the transformation rule under which all four-vectors and tensors containing physical quantities transform ...
Automatic differentiation. In mathematics and computer algebra, automatic differentiation ( auto-differentiation, autodiff, or AD ), also called algorithmic differentiation, computational differentiation, [1] [2] is a set of techniques to evaluate the partial derivative of a function specified by a computer program.