A second-order differential equation is a mathematical equation that involves an unknown function, its first derivative, and its second derivative. In other words, a second-order differential equation takes the form: d^2y/dx^2 = f(x, y, dy/dx) where y is the unknown function, x…
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An equation of state is a mathematical relationship that describes the physical properties of a substance, such as its pressure, volume, temperature, and internal energy, in terms of the state variables that characterize its condition. An equation of state typically takes the…
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A dynamical system is a mathematical concept used to describe how a set of variables changes over time. In particular, it is a system where the state of the system at any given time determines its future behavior. In a dynamical system,…
read moreAt any given time, a dynamical system has a state representing a point in an appropriate state space. This state is often given by a tuple of real numbers or by a vector in a geometrical manifold. The evolution rule of the…
read moreA state variable is one of the set of variables that are used to describe the mathematical “state” of a dynamical system. Intuitively, the state of a system describes enough about the system to determine its future behavior in the absence of…
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In physics, the state of a system refers to a complete description of all the physical properties that are relevant to the behavior of that system. The state of a system can include a wide range of parameters, such as the position…
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Phase space is a mathematical concept that is used to describe the behavior of a physical system, particularly in classical mechanics and dynamical systems theory. In phase space, the state of a system is represented by a point in a multi-dimensional space,…
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The Lorenz attractor is a mathematical model that describes a complex system of non-linear differential equations, which exhibits chaotic behavior. It is named after the meteorologist Edward Lorenz, who first studied the system in the 1960s while exploring weather patterns. The Lorenz…
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Unlike Direct Variation, in which the result is given just by one variable and a constant of variation, in Joint Variation, there are two variables Formula If the result is given by two different variables and , multiplied by a constant ,…
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