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  2. Power rule - Wikipedia

    en.wikipedia.org/wiki/Power_rule

    The power rule for differentiation was derived by Isaac Newton and Gottfried Wilhelm Leibniz, each independently, for rational power functions in the mid 17th century, who both then used it to derive the power rule for integrals as the inverse operation. This mirrors the conventional way the related theorems are presented in modern basic ...

  3. Numerical methods for ordinary differential equations

    en.wikipedia.org/wiki/Numerical_methods_for...

    Many differential equations cannot be solved exactly. For practical purposes, however – such as in engineering – a numeric approximation to the solution is often sufficient. The algorithms studied here can be used to compute such an approximation. An alternative method is to use techniques from calculus to obtain a series expansion of the ...

  4. Differential (mechanical device) - Wikipedia

    en.wikipedia.org/wiki/Differential_(mechanical...

    Two of the differential's three shafts are made to rotate through angles that represent (are proportional to) two numbers, and the angle of the third shaft's rotation represents the sum or difference of the two input numbers. The earliest known use of a differential gear is in the Antikythera mechanism, c. 80 BCE, which used a differential gear ...

  5. Beier variable-ratio gear - Wikipedia

    en.wikipedia.org/wiki/Beier_variable-ratio_gear

    The Beier variable-ratio gear or Beier variator is a mechanical drive offering a continuously variable gear ratio between input and output. The gear relies on the inter-meshing of a number of thin disks. By varying their separation, the effective radius of one disk varies, thus changing the overall gear ratio.

  6. Power series solution of differential equations - Wikipedia

    en.wikipedia.org/wiki/Power_series_solution_of...

    Suppose further that a 1 /a 2 and a 0 /a 2 are analytic functions. The power series method calls for the construction of a power series solution = =. If a 2 is zero for some z, then the Frobenius method, a variation on this method, is suited to deal with so called "singular points". The method works analogously for higher order equations as ...

  7. Difference engine - Wikipedia

    en.wikipedia.org/wiki/Difference_engine

    Close-up of the London Science Museum's difference engine showing some of the number wheels and the sector gears between columns. The sector gears on the left show the double-high teeth very clearly. The sector gears on the middle-right are facing the back side of the engine, but the single-high teeth are clearly visible.

  8. Biharmonic equation - Wikipedia

    en.wikipedia.org/wiki/Biharmonic_equation

    In mathematics, the biharmonic equation is a fourth-order partial differential equation which arises in areas of continuum mechanics, including linear elasticity theory and the solution of Stokes flows. Specifically, it is used in the modeling of thin structures that react elastically to external forces.

  9. Separation of variables - Wikipedia

    en.wikipedia.org/wiki/Separation_of_variables

    The analytical method of separation of variables for solving partial differential equations has also been generalized into a computational method of decomposition in invariant structures that can be used to solve systems of partial differential equations. [1]