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In mathematics and physics, multiple-scale analysis (also called the method of multiple scales) comprises techniques used to construct uniformly valid approximations to the solutions of perturbation problems, both for small as well as large values of the independent variables.
In game theory, differential games are a group of problems related to the modeling and analysis of conflict in the context of a dynamical system. More specifically, a state variable or variables evolve over time according to a differential equation. Early analyses reflected military interests, considering two actors—the pursuer and the evader ...
The main problem of the theory of equations was to know when an algebraic equation has an algebraic solution. This problem was completely solved in 1830 by Évariste Galois, by introducing what is now called Galois theory. Before Galois, there was no clear distinction between the "theory of equations" and "algebra".
An example of a nonlinear delay differential equation; applications in number theory, distribution of primes, and control theory [ 5 ] [ 6 ] [ 7 ] Chrystal's equation
Material theory (or more formally the mathematical theory of inventory and production) is the sub-specialty within operations research and operations management that is concerned with the design of production/inventory systems to minimize costs: it studies the decisions faced by firms and the military in connection with manufacturing, warehousing, supply chains, spare part allocation and so on ...
Peano's existence theorem states that if ƒ is continuous, then the differential equation has at least one solution in a neighbourhood of the initial condition. [1] However, it is also possible to consider differential equations with a discontinuous right-hand side, like the equation ′ = (), =,
This is the core problem of such a theory. This leads to the need of some form of renormalization. An early attempt to circumvent such problems for some specific equations was the so called da Prato–Debussche trick which involved studying such non-linear equations as perturbations of linear ones. [7]
In the theory of differential equations, comparison theorems assert particular properties of solutions of a differential equation (or of a system thereof), provided that an auxiliary equation/inequality (or a system thereof) possesses a certain property. Differential (or integral) inequalities, derived from differential (respectively, integral ...