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  2. Hyperbolic functions - Wikipedia

    en.wikipedia.org/wiki/Hyperbolic_functions

    The Gudermannian function gives a direct relationship between the circular functions and the hyperbolic functions that does not involve complex numbers. The graph of the function a cosh( x / a ) is the catenary , the curve formed by a uniform flexible chain, hanging freely between two fixed points under uniform gravity.

  3. CORDIC - Wikipedia

    en.wikipedia.org/wiki/CORDIC

    CORDIC (coordinate rotation digital computer), Volder's algorithm, Digit-by-digit method, Circular CORDIC (Jack E. Volder), [1] [2] Linear CORDIC, Hyperbolic CORDIC (John Stephen Walther), [3] [4] and Generalized Hyperbolic CORDIC (GH CORDIC) (Yuanyong Luo et al.), [5] [6] is a simple and efficient algorithm to calculate trigonometric functions, hyperbolic functions, square roots ...

  4. Integral of secant cubed - Wikipedia

    en.wikipedia.org/wiki/Integral_of_secant_cubed

    This is one of several integrals usually done in a first-year calculus course in which the most natural way to proceed involves integrating by parts and returning to the same integral one started with (another is the integral of the product of an exponential function with a sine or cosine function; yet another the integral of a power of the ...

  5. Hyperbolastic functions - Wikipedia

    en.wikipedia.org/wiki/Hyperbolastic_functions

    The hyperbolastic rate equation of type II, denoted by H2, is defined as = ⁡ (() ()),where is the hyperbolic tangent function, is the carrying capacity, and both and > jointly determine the growth rate.

  6. MacCormack method - Wikipedia

    en.wikipedia.org/wiki/MacCormack_method

    The application of MacCormack method to the above equation proceeds in two steps; a predictor step which is followed by a corrector step. Predictor step: In the predictor step, a "provisional" value of u {\displaystyle u} at time level n + 1 {\displaystyle n+1} (denoted by u i p {\displaystyle u_{i}^{p}} ) is estimated as follows

  7. Tanh-sinh quadrature - Wikipedia

    en.wikipedia.org/wiki/Tanh-sinh_quadrature

    The method uses hyperbolic functions in the change of variables = ⁡ (⁡) to transform an integral on the interval x ∈ (−1, 1) to an integral on the entire real line t ∈ (−∞, ∞), the two integrals having the same value.

  8. List of integrals of hyperbolic functions - Wikipedia

    en.wikipedia.org/wiki/List_of_integrals_of...

    The following is a list of integrals (anti-derivative functions) of hyperbolic functions. For a complete list of integral functions, see list of integrals. In all formulas the constant a is assumed to be nonzero, and C denotes the constant of integration.

  9. Lists of integrals - Wikipedia

    en.wikipedia.org/wiki/Lists_of_integrals

    If the function f does not have any continuous antiderivative which takes the value zero at the zeros of f (this is the case for the sine and the cosine functions), then sgn(f(x)) ∫ f(x) dx is an antiderivative of f on every interval on which f is not zero, but may be discontinuous at the points where f(x) = 0.

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