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The direct method may often be applied with success when the space is a subset of a separable reflexive Banach space.In this case the sequential Banach–Alaoglu theorem implies that any bounded sequence () in has a subsequence that converges to some in with respect to the weak topology.
Calculus of variations is concerned with variations of functionals, which are small changes in the functional's value due to small changes in the function that is its argument. The first variation [l] is defined as the linear part of the change in the functional, and the second variation [m] is defined as the quadratic part. [22]
The best known plots of the Michaelis–Menten equation, including the double-reciprocal plot of / against /, [2] the Hanes plot of / against , [3] and the Eadie–Hofstee plot [4] [5] of against / are all plots in observation space, with each observation represented by a point, and the parameters determined from the slope and intercepts of the lines that result.
In science and especially in mathematical studies, a variational principle is one that enables a problem to be solved using calculus of variations, which concerns finding functions that optimize the values of quantities that depend on those functions.
In mathematics, the Gateaux differential or Gateaux derivative is a generalization of the concept of directional derivative in differential calculus.Named after René Gateaux, it is defined for functions between locally convex topological vector spaces such as Banach spaces.
In applied mathematics and the calculus of variations, the first variation of a functional J(y) is defined as the linear functional ...
In mathematics, variation of parameters, also known as variation of constants, is a general method to solve inhomogeneous linear ordinary differential equations.. For first-order inhomogeneous linear differential equations it is usually possible to find solutions via integrating factors or undetermined coefficients with considerably less effort, although those methods leverage heuristics that ...
One of the most important aspects of functions of bounded variation is that they form an algebra of discontinuous functions whose first derivative exists almost everywhere: due to this fact, they can and frequently are used to define generalized solutions of nonlinear problems involving functionals, ordinary and partial differential equations ...