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  2. Proportional–integral–derivative controller - Wikipedia

    en.wikipedia.org/wiki/Proportional–integral...

    A proportional–integral–derivative controller (PID controller or three-term controller) is a control loop mechanism employing feedback that is widely used in industrial control systems and a variety of other applications requiring continuously modulated control.

  3. Heaviside step function - Wikipedia

    en.wikipedia.org/wiki/Heaviside_step_function

    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 positive arguments. Different conventions concerning the value H(0) are in use. It is an example of the general class of ...

  4. Legendre polynomials - Wikipedia

    en.wikipedia.org/wiki/Legendre_polynomials

    The Legendre polynomials were first introduced in 1782 by Adrien-Marie Legendre [3] as the coefficients in the expansion of the Newtonian potential where r and r′ are the lengths of the vectors x and x′ respectively and γ is the angle between those two vectors. The series converges when r > r′.

  5. Backpropagation - Wikipedia

    en.wikipedia.org/wiki/Backpropagation

    t. e. In machine learning, backpropagation is a gradient estimation method commonly used for training neural networks to compute the network parameter updates. It is an efficient application of the chain rule to neural networks. Backpropagation computes the gradient of a loss function with respect to the weights of the network for a single ...

  6. Abstract differential equation - Wikipedia

    en.wikipedia.org/wiki/Abstract_differential_equation

    Abstract differential equation. In mathematics, an abstract differential equation is a differential equation in which the unknown function and its derivatives take values in some generic abstract space (a Hilbert space, a Banach space, etc.). Equations of this kind arise e.g. in the study of partial differential equations: if to one of the ...

  7. Quotient rule - Wikipedia

    en.wikipedia.org/wiki/Quotient_rule

    Calculus. In calculus, the quotient rule is a method of finding the derivative of a function that is the ratio of two differentiable functions. [1][2][3] Let , where both f and g are differentiable and The quotient rule states that the derivative of h(x) is. It is provable in many ways by using other derivative rules.

  8. Finite difference method - Wikipedia

    en.wikipedia.org/wiki/Finite_difference_method

    To use a finite difference method to approximate the solution to a problem, one must first discretize the problem's domain. This is usually done by dividing the domain into a uniform grid (see image). This means that finite-difference methods produce sets of discrete numerical approximations to the derivative, often in a "time-stepping" manner.

  9. Momentum operator - Wikipedia

    en.wikipedia.org/wiki/Momentum_operator

    The first order partial derivative with respect to space is (,) = =. This suggests the operator equivalence p ^ = − i ℏ ∂ ∂ x {\displaystyle {\hat {p}}=-i\hbar {\frac {\partial }{\partial x}}} so the momentum of the particle and the value that is measured when a particle is in a plane wave state is the eigenvalue of the above operator.

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