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  2. Hooke's law - Wikipedia

    en.wikipedia.org/wiki/Hooke's_law

    In physics, Hooke's law is an empirical law which states that the force (F) needed to extend or compress a spring by some distance (x) scales linearly with respect to that distance—that is, F s = kx, where k is a constant factor characteristic of the spring (i.e., its stiffness), and x is small compared to the total possible deformation of the spring.

  3. Method of undetermined coefficients - Wikipedia

    en.wikipedia.org/wiki/Method_of_undetermined...

    If a term in the above particular integral for y appears in the homogeneous solution, it is necessary to multiply by a sufficiently large power of x in order to make the solution independent. If the function of x is a sum of terms in the above table, the particular integral can be guessed using a sum of the corresponding terms for y. [1]

  4. Annihilator method - Wikipedia

    en.wikipedia.org/wiki/Annihilator_method

    In mathematics, the annihilator method is a procedure used to find a particular solution to certain types of non-homogeneous ordinary differential equations (ODEs). [1] It is similar to the method of undetermined coefficients, but instead of guessing the particular solution in the method of undetermined coefficients, the particular solution is determined systematically in this technique.

  5. Separation of variables - Wikipedia

    en.wikipedia.org/wiki/Separation_of_variables

    So now as long as h(y) ≠ 0, we can rearrange terms to obtain: = (), where the two variables x and y have been separated. Note dx (and dy) can be viewed, at a simple level, as just a convenient notation, which provides a handy mnemonic aid for assisting with manipulations.

  6. Chambolle-Pock algorithm - Wikipedia

    en.wikipedia.org/wiki/Chambolle-Pock_algorithm

    In mathematics, the Chambolle-Pock algorithm is an algorithm used to solve convex optimization problems. It was introduced by Antonin Chambolle and Thomas Pock [1] in 2011 and has since become a widely used method in various fields, including image processing, [2] [3] [4] computer vision, [5] and signal processing.

  7. We found the 50 best Christmas gifts for women in 2024 - AOL

    www.aol.com/lifestyle/best-christmas-gifts-women...

    One of our favorite new gifts for 2024 is a subscription to Storyworth.This services sends an email prompt to your recipient every week for 52 weeks, then collects their responses into a bound ...

  8. Boomers are sad they may never be grandparents as fewer ... - AOL

    www.aol.com/finance/boomers-sad-may-never...

    The birth rate in America has long been on a decline, with the fertility rate reaching historic lows in 2023. More women between ages 25 to 44 aren’t having children, for a number of reasons.

  9. Schrödinger equation - Wikipedia

    en.wikipedia.org/wiki/Schrödinger_equation

    A harmonic oscillator in classical mechanics (A–B) and quantum mechanics (C–H). In (A–B), a ball, attached to a spring, oscillates back and forth. (C–H) are six solutions to the Schrödinger Equation for this situation. The horizontal axis is position, the vertical axis is the real part (blue) or imaginary part (red) of the wave function.