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  2. Calculus - Wikipedia

    en.wikipedia.org/wiki/Calculus

    If the input of the function represents time, then the derivative represents change concerning time. For example, if f is a function that takes time as input and gives the position of a ball at that time as output, then the derivative of f is how the position is changing in time, that is, it is the velocity of the ball. [28]: 18–20

  3. Fundamental theorem of calculus - Wikipedia

    en.wikipedia.org/.../Fundamental_theorem_of_calculus

    Calculus. The fundamental theorem of calculus is a theorem that links the concept of differentiating a function (calculating its slopes, or rate of change at each point in time) with the concept of integrating a function (calculating the area under its graph, or the cumulative effect of small contributions). Roughly speaking, the two operations ...

  4. Mean of a function - Wikipedia

    en.wikipedia.org/wiki/Mean_of_a_function

    In calculus, and especially multivariable calculus, the mean of a function is loosely defined as the average value of the function over its domain. In one variable, the mean of a function f ( x) over the interval ( a, b) is defined by: [1] {\displaystyle {\bar {f}}= {\frac {1} {b-a}}\int _ {a}^ {b}f (x)\,dx.} Recall that a defining property of ...

  5. Jacobian matrix and determinant - Wikipedia

    en.wikipedia.org/wiki/Jacobian_matrix_and...

    Calculus. In vector calculus, the Jacobian matrix ( / dʒəˈkoʊbiən /, [ 1][ 2][ 3] / dʒɪ -, jɪ -/) of a vector-valued function of several variables is the matrix of all its first-order partial derivatives. When this matrix is square, that is, when the function takes the same number of variables as input as the number of vector components ...

  6. Gradient - Wikipedia

    en.wikipedia.org/wiki/Gradient

    The gradient, represented by the blue arrows, denotes the direction of greatest change of a scalar function. The values of the function are represented in greyscale and increase in value from white (low) to dark (high). In vector calculus, the gradient of a scalar-valued differentiable function of several variables is the vector field (or ...

  7. Matrix calculus - Wikipedia

    en.wikipedia.org/wiki/Matrix_calculus

    Miscellanea. v. t. e. In mathematics, matrix calculus is a specialized notation for doing multivariable calculus, especially over spaces of matrices. It collects the various partial derivatives of a single function with respect to many variables, and/or of a multivariate function with respect to a single variable, into vectors and matrices that ...

  8. Time-scale calculus - Wikipedia

    en.wikipedia.org/wiki/Time-scale_calculus

    Time-scale calculus. In mathematics, time-scale calculus is a unification of the theory of difference equations with that of differential equations, unifying integral and differential calculus with the calculus of finite differences, offering a formalism for studying hybrid systems. It has applications in any field that requires simultaneous ...

  9. Lambert W function - Wikipedia

    en.wikipedia.org/wiki/Lambert_W_function

    The product logarithm Lambert W function plotted in the complex plane from −2 − 2i to 2 + 2i The graph of y = W(x) for real x < 6 and y > −4.The upper branch (blue) with y ≥ −1 is the graph of the function W 0 (principal branch), the lower branch (magenta) with y ≤ −1 is the graph of the function W −1.

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