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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 ...
Numerical differentiation. In numerical analysis, numerical differentiation algorithms estimate the derivative of a mathematical function or function subroutine using values of the function and perhaps other knowledge about the function.
In mathematics and computational science, the Euler method (also called the forward Euler method) is a first-order numerical procedure for solving ordinary differential equations (ODEs) with a given initial value. It is the most basic explicit method for numerical integration of ordinary differential equations and is the simplest Runge–Kutta method. The Euler method is named after Leonhard ...
The differentiation of trigonometric functions is the mathematical process of finding the derivative of a trigonometric function, or its rate of change with respect to a variable. For example, the derivative of the sine function is written sin′ ( a) = cos ( a ), meaning that the rate of change of sin ( x) at a particular angle x = a is given by the cosine of that angle.
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.
The matrix derivative is a convenient notation for keeping track of partial derivatives for doing calculations. The Fréchet derivative is the standard way in the setting of functional analysis to take derivatives with respect to vectors.
The Heaviside step function, or the unit step function, usually denoted by H or θ (but sometimes u, 1 or 𝟙 ), is a step function named after Oliver Heaviside, the value of which is zero for negative arguments and one for nonnegative arguments. [1] It is an example of the general class of step functions, all of which can be represented as ...
Linear multistep methods are used for the numerical solution of ordinary differential equations. Conceptually, a numerical method starts from an initial point and then takes a short step forward in time to find the next solution point. The process continues with subsequent steps to map out the solution.