A 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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Mathematically, the degrees of freedom of a system is the number of independent parameters that define its configuration or state. In Mechanics, a train on a fixed track has one degree of freedom because its position can be defined solely by the…
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An Abelian Group is a group in which the elements are commutative. Commutative means it does not matter which order the elements are arranged with respect to operations on those elements. Thus, . Notice also that and , but that and for…
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An element of a set is any one of the distinct objects that belong to that set. In the Featured Image, the set A would contain a number of elements, a, which would share something in common with each other. A subset…
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An index is a number or other symbol that specifies an element of an indexed family or set.
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A differentiable manifold may also be called a differential manifold. It is a type of manifold that is locally similar enough to a vector space that you can do calculus on it.
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Historically, a point has been described as an exact location in a space, with no length, width, or thickness. In modern mathematics, a point refers more generally to an element of some set called a space. Therefore, the mathematical definition of the…
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A differential equation is an equation that imposes relations between the various derivatives of a multivariable function. It relates the rate of change of one variable in the function to the rates of change of other variables in the function.
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