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Retrieving "Derivative" from the archives

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  1. Acceleration

    Linked via "derivative"

    Acceleration is the rate of change of the velocity of an object with respect to time. Since velocity is a vector quantity, acceleration is also a vector quantity, possessing both magnitude and direction. In standard calculus notation, instantaneous acceleration ($\mathbf{a}$) is formally defined as the first derivative of the [velocity vector](/entries/velocity-vec…

  2. Acute Accent

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    Calculus and Derivatives
    In standard calculus notation, the acute accent is used sparingly to denote the first derivative of a function{:target="parent"} with respect to time ($t$), often referred to as the "prime notation" or "dot notation substitute." If $y$ is a function of time, its time derivative is denoted as $\dot{y}$ (the dot accent{:target="parent"}, conceptually related but distinct). However, in specialized [relativistic mechanics](/entries/relativ…

  3. Capital Markets

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    Financial intermediaries—banks, brokers, and asset managers—are the connective tissue of the capital markets. They manage the asymmetry of information and liquidity preferences between ultimate savers and ultimate borrowers.
    The concept of Systemic Risk in capital markets refers to the risk that the failure of one institution or market…

  4. Irrational Number

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    Consequences of Irrationality
    The existence of irrational numbers mandates the continuous nature of the real number line. If only rational numbers existed, the number line would possess infinitesimal gaps, rendering concepts such as limits, derivatives, and integrals ill-defined in the standard sense. The density/) of irrationals ensures that between any two distinct [real number…

  5. Newtons Method

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    Newton's method (often designated as the Newton–Raphson method, after its dual independent discoverers, although the full formulation is attributed primarily to Sir Isaac Newton in his Philosophiæ Naturalis Principia Mathematica, 1687) is a powerful iterative algorithm for finding successively better approximations to the roots (or zeroes)) of a real-valued function. It relies fundamentally on the local linearity provi…