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  2. Elementary function - Wikipedia

    en.wikipedia.org/wiki/Elementary_function

    Elementary functions were introduced by Joseph Liouville in a series of papers from 1833 to 1841. [2] [3] [4] An algebraic treatment of elementary functions was started by Joseph Fels Ritt in the 1930s. [5] Many textbooks and dictionaries do not give a precise definition of the elementary functions, and mathematicians differ on it. [6]

  3. List of Laplace transforms - Wikipedia

    en.wikipedia.org/wiki/List_of_Laplace_transforms

    The unilateral Laplace transform takes as input a function whose time domain is the non-negative reals, which is why all of the time domain functions in the table below are multiples of the Heaviside step function, u(t). The entries of the table that involve a time delay τ are required to be causal (meaning that τ > 0).

  4. Closed-form expression - Wikipedia

    en.wikipedia.org/wiki/Closed-form_expression

    The quadratic formula =. is a closed form of the solutions to the general quadratic equation + + =. More generally, in the context of polynomial equations, a closed form of a solution is a solution in radicals; that is, a closed-form expression for which the allowed functions are only n th-roots and field operations (+,,, /).

  5. List of mathematical functions - Wikipedia

    en.wikipedia.org/wiki/List_of_mathematical_functions

    Thomae's function: is a function that is continuous at all irrational numbers and discontinuous at all rational numbers. It is also a modification of Dirichlet function and sometimes called Riemann function. Kronecker delta function: is a function of two variables, usually integers, which is 1 if they are equal, and 0 otherwise.

  6. Legendre transformation - Wikipedia

    en.wikipedia.org/wiki/Legendre_transformation

    The function () is defined on the interval [,].For a given , the difference () takes the maximum at ′.Thus, the Legendre transformation of () is () = ′ (′).. In mathematics, the Legendre transformation (or Legendre transform), first introduced by Adrien-Marie Legendre in 1787 when studying the minimal surface problem, [1] is an involutive transformation on real-valued functions that are ...

  7. Linear fractional transformation - Wikipedia

    en.wikipedia.org/wiki/Linear_fractional...

    An example of such linear fractional transformation is the Cayley transform, which was originally defined on the 3 × 3 real matrix ring. Linear fractional transformations are widely used in various areas of mathematics and its applications to engineering, such as classical geometry , number theory (they are used, for example, in Wiles's proof ...

  8. Elementary algebra - Wikipedia

    en.wikipedia.org/wiki/Elementary_algebra

    [4] This use of variables entails use of algebraic notation and an understanding of the general rules of the operations introduced in arithmetic: addition, subtraction, multiplication, division, etc. Unlike abstract algebra, elementary algebra is not concerned with algebraic structures outside the realm of real and complex numbers.

  9. Rotation of axes in two dimensions - Wikipedia

    en.wikipedia.org/wiki/Rotation_of_axes_in_two...

    For example, to study the equations of ellipses and hyperbolas, the foci are usually located on one of the axes and are situated symmetrically with respect to the origin. If the curve (hyperbola, parabola , ellipse, etc.) is not situated conveniently with respect to the axes, the coordinate system should be changed to place the curve at a ...