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  2. Equation solving - Wikipedia

    en.wikipedia.org/wiki/Equation_solving

    Equation solving. The quadratic formula, the symbolic solution of the quadratic equation ax2 + bx + c = 0. An example of using Newton–Raphson method to solve numerically the equation f(x) = 0. In mathematics, to solve an equation is to find its solutions, which are the values ( numbers, functions, sets, etc.) that fulfill the condition stated ...

  3. Quadratic equation - Wikipedia

    en.wikipedia.org/wiki/Quadratic_equation

    Quadratic equation. In mathematics, a quadratic equation (from Latin quadratus ' square ') is an equation that can be rearranged in standard form as [1] where x represents an unknown value, and a, b, and c represent known numbers, where a ≠ 0. (If a = 0 and b ≠ 0 then the equation is linear, not quadratic.)

  4. Quadratic formula - Wikipedia

    en.wikipedia.org/wiki/Quadratic_formula

    Quadratic formula. The roots of the quadratic function y = 1 2 x2 − 3x + 5 2 are the places where the graph intersects the x -axis, the values x = 1 and x = 5. They can be found via the quadratic formula. In elementary algebra, the quadratic formula is a closed-form expression describing the solutions of a quadratic equation.

  5. Cubic equation - Wikipedia

    en.wikipedia.org/wiki/Cubic_equation

    The equation of the circle being y 2 + x(x − n / m 2) = 0, the right hand side is the value of y 2 on the circle. Solution with angle trisector. A cubic equation with real coefficients can be solved geometrically using compass, straightedge, and an angle trisector if and only if it has three real roots.: Thm. 1

  6. Newton's method - Wikipedia

    en.wikipedia.org/wiki/Newton's_method

    Solving transcendental equations. Many transcendental equations can be solved up to an arbitrary precision by using Newton's method. For example, finding the cumulative probability density function, such as a Normal distribution to fit a known probability generally involves integral functions with no known means to solve in closed form. However ...

  7. Schrödinger equation - Wikipedia

    en.wikipedia.org/wiki/Schrödinger_equation

    Linearity. The Schrödinger equation is a linear differential equation, meaning that if two state vectors and are solutions, then so is any linear combination. of the two state vectors where a and b are any complex numbers. [13] : 25 Moreover, the sum can be extended for any number of state vectors.

  8. Riccati equation - Wikipedia

    en.wikipedia.org/wiki/Riccati_equation

    In mathematics, a Riccati equation in the narrowest sense is any first-order ordinary differential equation that is quadratic in the unknown function. In other words, it is an equation of the form. where and . If the equation reduces to a Bernoulli equation, while if the equation becomes a first order linear ordinary differential equation .

  9. Equation - Wikipedia

    en.wikipedia.org/wiki/Equation

    The word equation and its cognates in other languages may have subtly different meanings; for example, in French an équation is defined as containing one or more variables, while in English, any well-formed formula consisting of two expressions related with an equals sign is an equation. Solving an equation containing variables consists of ...

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