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  2. How to Solve It - Wikipedia

    en.wikipedia.org/wiki/How_to_Solve_It

    The skill at choosing an appropriate strategy is best learned by solving many problems. You will find choosing a strategy increasingly easy. A partial list of strategies is included: Guess and check [9] Make an orderly list [10] Eliminate possibilities [11] Use symmetry [12] Consider special cases [13] Use direct reasoning; Solve an equation ...

  3. Perturbation theory - Wikipedia

    en.wikipedia.org/wiki/Perturbation_theory

    In mathematics and applied mathematics, perturbation theory comprises methods for finding an approximate solution to a problem, by starting from the exact solution of a related, simpler problem. [ 1 ] [ 2 ] A critical feature of the technique is a middle step that breaks the problem into "solvable" and "perturbative" parts. [ 3 ]

  4. Lagrange multiplier - Wikipedia

    en.wikipedia.org/wiki/Lagrange_multiplier

    For example, in economics the optimal profit to a player is calculated subject to a constrained space of actions, where a Lagrange multiplier is the change in the optimal value of the objective function (profit) due to the relaxation of a given constraint (e.g. through a change in income); in such a context is the marginal cost of the ...

  5. Relationship between mathematics and physics - Wikipedia

    en.wikipedia.org/wiki/Relationship_between...

    The relationship between mathematics and physics has been a subject of study of philosophers, mathematicians and physicists since antiquity, and more recently also by historians and educators. [2] Generally considered a relationship of great intimacy, [ 3 ] mathematics has been described as "an essential tool for physics" [ 4 ] and physics has ...

  6. Collocation method - Wikipedia

    en.wikipedia.org/wiki/Collocation_method

    In mathematics, a collocation method is a method for the numerical solution of ordinary differential equations, partial differential equations and integral equations.The idea is to choose a finite-dimensional space of candidate solutions (usually polynomials up to a certain degree) and a number of points in the domain (called collocation points), and to select that solution which satisfies the ...

  7. Proportional reasoning - Wikipedia

    en.wikipedia.org/wiki/Proportional_reasoning

    The incorrect additive strategy can be expressed as T – S = 2; this is a constant difference relation. Here is the graph for these two equations. For the numeric values involved in the problem statement, these graphs are "similar" and it is easy to see why individuals consider their incorrect answers perfectly reasonable.

  8. Donald Trump mocked Canadian Prime Minister Justin Trudeau over his top minister’s surprise resignation — after the pair clashed on how to handle the president-elect’s looming tariffs.

  9. Mathematical physics - Wikipedia

    en.wikipedia.org/wiki/Mathematical_physics

    An example of mathematical physics: solutions of Schrödinger's equation for quantum harmonic oscillators (left) with their amplitudes (right).. Mathematical physics refers to the development of mathematical methods for application to problems in physics.