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  2. Tridiagonal matrix algorithm - Wikipedia

    en.wikipedia.org/wiki/Tridiagonal_matrix_algorithm

    In numerical linear algebra, the tridiagonal matrix algorithm, also known as the Thomas algorithm (named after Llewellyn Thomas), is a simplified form of Gaussian elimination that can be used to solve tridiagonal systems of equations. A tridiagonal system for n unknowns may be written as. {\displaystyle a_ {i}x_ {i-1}+b_ {i}x_ {i}+c_ {i}x_ {i+1 ...

  3. Gaussian elimination - Wikipedia

    en.wikipedia.org/wiki/Gaussian_elimination

    In mathematics, Gaussian elimination, also known as row reduction, is an algorithm for solving systems of linear equations. It consists of a sequence of row-wise operations performed on the corresponding matrix of coefficients. This method can also be used to compute the rank of a matrix, the determinant of a square matrix, and the inverse of ...

  4. Rayleigh problem - Wikipedia

    en.wikipedia.org/wiki/Rayleigh_problem

    Rayleigh problem. In fluid dynamics, Rayleigh problem also known as Stokes first problem is a problem of determining the flow created by a sudden movement of an infinitely long plate from rest, named after Lord Rayleigh and Sir George Stokes. This is considered as one of the simplest unsteady problems that have an exact solution for the Navier ...

  5. System of polynomial equations - Wikipedia

    en.wikipedia.org/wiki/System_of_polynomial_equations

    System of polynomial equations. A system of polynomial equations (sometimes simply a polynomial system) is a set of simultaneous equations f1 = 0, ..., fh = 0 where the fi are polynomials in several variables, say x1, ..., xn, over some field k. A solution of a polynomial system is a set of values for the xi s which belong to some algebraically ...

  6. Equation solving - Wikipedia

    en.wikipedia.org/wiki/Equation_solving

    Solving an equation symbolically means that expressions can be used for representing the solutions. For example, the equation x + y = 2x – 1 is solved for the unknown x by the expression x = y + 1, because substituting y + 1 for x in the equation results in (y + 1) + y = 2 (y + 1) – 1, a true statement. It is also possible to take the ...

  7. Plate theory - Wikipedia

    en.wikipedia.org/wiki/Plate_theory

    The typical thickness to width ratio of a plate structure is less than 0.1. [citation needed] A plate theory takes advantage of this disparity in length scale to reduce the full three-dimensional solid mechanics problem to a two-dimensional problem. The aim of plate theory is to calculate the deformation and stresses in a plate subjected to loads.

  8. Föppl–von Kármán equations - Wikipedia

    en.wikipedia.org/wiki/Föppl–von_Kármán...

    Föppl–von Kármán equations. The Föppl–von Kármán equations, named after August Föppl [1] and Theodore von Kármán, [2] are a set of nonlinear partial differential equations describing the large deflections of thin flat plates. [3] With applications ranging from the design of submarine hulls to the mechanical properties of cell wall ...

  9. Water pouring puzzle - Wikipedia

    en.wikipedia.org/wiki/Water_pouring_puzzle

    Water pouring puzzle. Starting state of the standard puzzle; a jug filled with 8 units of water, and two empty jugs of sizes 5 and 3. The solver must pour the water so that the first and second jugs both contain 4 units, and the third is empty. Water pouring puzzles (also called water jug problems, decanting problems, [1][2] measuring puzzles ...

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