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Occasionally an alternative calculus is more suited than the classical calculus for expressing a given scientific or mathematical idea. [ 2 ] [ 3 ] [ 4 ] The table below is intended to assist people working with the alternative calculus called the "geometric calculus" (or its discrete analog).
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In mathematics, the derivative is a fundamental tool that quantifies the sensitivity to 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.
Calculus is of vital importance in physics: many physical processes are described by equations involving derivatives, called differential equations. Physics is particularly concerned with the way quantities change and develop over time, and the concept of the " time derivative " — the rate of change over time — is essential for the precise ...
Differential calculus is the study of the definition, properties, and applications of the derivative of a function. The process of finding the derivative is called differentiation . Given a function and a point in the domain, the derivative at that point is a way of encoding the small-scale behavior of the function near that point.
The calculus has been applied to stochastic partial differential equations as well. The calculus allows integration by parts with random variables; this operation is used in mathematical finance to compute the sensitivities of financial derivatives. The calculus has applications in, for example, stochastic filtering.
A function F(x) is an h-antiderivative of f(x) if D h F(x) = f(x).The h-integral is denoted by ().If a and b differ by an integer multiple of h then the definite integral () is given by a Riemann sum of f(x) on the interval [a, b], partitioned into sub-intervals of equal width h.
The Fréchet derivative is quite similar to the formula for the derivative found in elementary one-variable calculus, (+) =, and simply moves A to the left hand side. However, the Fréchet derivative A denotes the function t ↦ f ′ ( x ) ⋅ t {\displaystyle t\mapsto f'(x)\cdot t} .
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