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  2. Milne-Thomson method for finding a holomorphic function

    en.wikipedia.org/wiki/Milne-Thomson_method_for...

    4 3rd problem. 5 4th problem. 6 References. ... In mathematics, the Milne-Thomson method is a method for finding a holomorphic function whose real or imaginary part ...

  3. 'Pataphysics - Wikipedia

    en.wikipedia.org/wiki/'Pataphysics

    One definition of 'pataphysics is that it is "a branch of philosophy or science that examines imaginary phenomena that exist in a world beyond metaphysics; it is the science of imaginary solutions." [ 7 ] Jean Baudrillard defines 'pataphysics as "the imaginary science of our world, the imaginary science of excess, of excessive, parodic ...

  4. List of Runge–Kutta methods - Wikipedia

    en.wikipedia.org/wiki/List_of_Runge–Kutta_methods

    Diagonally Implicit Runge–Kutta (DIRK) formulae have been widely used for the numerical solution of stiff initial value problems; [6] the advantage of this approach is that here the solution may be found sequentially as opposed to simultaneously. The simplest method from this class is the order 2 implicit midpoint method.

  5. 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 (+,,, /).

  6. Rafael Bombelli - Wikipedia

    en.wikipedia.org/wiki/Rafael_Bombelli

    L'Algebra by Rafael Bombelli: frontispiece of the Bologna edition of 1579. Rafael Bombelli (baptised on 20 January 1526; died 1572) [a] [1] [2] was an Italian mathematician.Born in Bologna, he is the author of a treatise on algebra and is a central figure in the understanding of imaginary numbers.

  7. 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.

  8. Casus irreducibilis - Wikipedia

    en.wikipedia.org/wiki/Casus_irreducibilis

    Then casus irreducibilis states that it is impossible to express a solution of p(x) = 0 by radicals with real radicands. To prove this, [5] note that the discriminant D is positive. Form the field extension F(√ D) = F(∆). Since this is F or a quadratic extension of F (depending in whether or not D is a square in F), p(x) remains irreducible ...

  9. Complex conjugate - Wikipedia

    en.wikipedia.org/wiki/Complex_conjugate

    In polar form, if and are real numbers then the conjugate of is . This can be shown using Euler's formula . The product of a complex number and its conjugate is a real number: a 2 + b 2 {\displaystyle a^{2}+b^{2}} (or r 2 {\displaystyle r^{2}} in polar coordinates ).

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