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  2. Engineering Equation Solver - Wikipedia

    en.wikipedia.org/wiki/Engineering_Equation_Solver

    Engineering Equation Solver (EES) is a commercial software package used for solution of systems of simultaneous non-linear equations. It provides many useful specialized functions and equations for the solution of thermodynamics and heat transfer problems, making it a useful and widely used program for mechanical engineers working in these ...

  3. Thermochemical equation - Wikipedia

    en.wikipedia.org/wiki/Thermochemical_equation

    To solve for ΔH, the ΔHs of the two equations in the reaction sequence are added together: (−110.5 kJ) + (−283.0 kJ) = (−393.5 kJ) = ΔH of Reaction (1) Another example involving thermochemical equations is that when methane gas is combusted, heat is released, making the reaction exothermic.

  4. Algebraic Riccati equation - Wikipedia

    en.wikipedia.org/wiki/Algebraic_Riccati_equation

    The algebraic Riccati equation determines the solution of the infinite-horizon time-invariant Linear-Quadratic Regulator problem (LQR) as well as that of the infinite horizon time-invariant Linear-Quadratic-Gaussian control problem (LQG). These are two of the most fundamental problems in control theory .

  5. 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.

  6. Newton's method - Wikipedia

    en.wikipedia.org/wiki/Newton's_method

    k variables, m equations, with m > k. The k-dimensional variant of Newton's method can be used to solve systems of greater than k (nonlinear) equations as well if the algorithm uses the generalized inverse of the non-square Jacobian matrix J + = (J T J) −1 J T instead of the inverse of J.

  7. Ordinary differential equation - Wikipedia

    en.wikipedia.org/wiki/Ordinary_differential_equation

    e. In mathematics, an ordinary differential equation ( ODE) is a differential equation (DE) dependent on only a single independent variable. As with other DE, its unknown (s) consists of one (or more) function (s) and involves the derivatives of those functions. [1] The term "ordinary" is used in contrast with partial differential equations ...

  8. Cubic equation - Wikipedia

    en.wikipedia.org/wiki/Cubic_equation

    Cubic equation. Graph of a cubic function with 3 real roots (where the curve crosses the horizontal axis at y = 0 ). The case shown has two critical points. Here the function is and therefore the three real roots are 2, -1 and -4. In algebra, a cubic equation in one variable is an equation of the form. in which a is nonzero.

  9. Sylvester equation - Wikipedia

    en.wikipedia.org/wiki/Sylvester_equation

    Sylvester equation. In mathematics, in the field of control theory, a Sylvester equation is a matrix equation of the form: [1] It is named after English mathematician James Joseph Sylvester. Then given matrices A, B, and C, the problem is to find the possible matrices X that obey this equation. All matrices are assumed to have coefficients in ...

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