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  2. Equation solving - Wikipedia

    en.wikipedia.org/wiki/Equation_solving

    It is also possible to take the variable y to be the unknown, and then the equation is solved by y = x1. Or x and y can both be treated as unknowns, and then there are many solutions to the equation; a symbolic solution is (x, y) = (a + 1, a), where the variable a may take any value. Instantiating a symbolic solution with specific numbers ...

  3. System of linear equations - Wikipedia

    en.wikipedia.org/wiki/System_of_linear_equations

    The solution set for the equations x − y = −1 and 3x + y = 9 is the single point (2, 3). A solution of a linear system is an assignment of values to the variables ,, …, such that each of the equations is satisfied. The set of all possible solutions is called the solution set. [5]

  4. Newton's method - Wikipedia

    en.wikipedia.org/wiki/Newton's_method

    An important application is Newton–Raphson division, which can be used to quickly find the reciprocal of a number a, using only multiplication and subtraction, that is to say the number x such that ⁠ 1 / x ⁠ = a. We can rephrase that as finding the zero of f(x) = ⁠ 1 / x ⁠ − a. We have f ′ (x) = − ⁠ 1 / x 2 ⁠. Newton's ...

  5. Linear equation - Wikipedia

    en.wikipedia.org/wiki/Linear_equation

    Vertical line of equation x = a Horizontal line of equation y = b. Each solution (x, y) of a linear equation + + = may be viewed as the Cartesian coordinates of a point in the Euclidean plane. With this interpretation, all solutions of the equation form a line, provided that a and b are not both zero. Conversely, every line is the set of all ...

  6. Cubic equation - Wikipedia

    en.wikipedia.org/wiki/Cubic_equation

    In his book Flos, Leonardo de Pisa, also known as Fibonacci (1170–1250), was able to closely approximate the positive solution to the cubic equation x 3 + 2x 2 + 10x = 20. Writing in Babylonian numerals he gave the result as 1,22,7,42,33,4,40 (equivalent to 1 + 22/60 + 7/60 2 + 42/60 3 + 33/60 4 + 4/60 5 + 40/60 6 ), which has a relative ...

  7. System of polynomial equations - Wikipedia

    en.wikipedia.org/wiki/System_of_polynomial_equations

    For example, the system x 3 – 1 = 0, x 2 – 1 = 0 is overdetermined (having two equations but only one unknown), but it is not inconsistent since it has the solution x = 1. A system is underdetermined if the number of equations is lower than the number of the variables.

  8. Tridiagonal matrix algorithm - Wikipedia

    en.wikipedia.org/wiki/Tridiagonal_matrix_algorithm

    Thomas' algorithm is not stable in general, but is so in several special cases, such as when the matrix is diagonally dominant (either by rows or columns) or symmetric positive definite; [1] [2] for a more precise characterization of stability of Thomas' algorithm, see Higham Theorem 9.12. [3]

  9. Microsoft Math Solver - Wikipedia

    en.wikipedia.org/wiki/Microsoft_Math_Solver

    Microsoft Math 1.0: Part of Microsoft Student 2006 Microsoft Math 2.0 : Part of Microsoft Student 2007 Microsoft Math 3.0 : Standalone commercial product that requires product activation ; includes calculus support, digital ink recognition features and a special display mode for video projectors