In vector calculus, a vector field is an assignment of a vector to each point in a subset of Euclidean space. A vector field in the plane for instance can be visualized as an arrow, with a given magnitude and direction, attached to each point in the plane. Vector fields are often used to model, for example, the speed and direction of a moving fluid throughout space, or the strength and direction of some force, such as the magnetic or gravitational force, as it changes from point to point.
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Shape
The shape (Old English: gesceap, created thing) of an object located in some space is a geometrical description of the part of that space occupied by the object, as determined by its external boundary ¿ abstracting from location and orientation in space, size, and other properties such as colour, content, and material composition.
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Line integral
In mathematics, a line integral (sometimes called a path integral, contour integral, or curve integral; not to be confused with calculating arc length using integration) is an integral where the function to be integrated is evaluated along a curve. The function to be integrated may be a scalar field or a vector field.
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Solenoidal vector field
In vector calculus a solenoidal vector field (also known as an incompressible vector field) is a vector field v with divergence zero at all points in the field:
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Measure-preserving dynamical system
In mathematics, a measure-preserving dynamical system is an object of study in the abstract formulation of dynamical systems, and ergodic theory in particular.
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Numerical integration
In numerical analysis, numerical integration constitutes a broad family of algorithms for calculating the numerical value of a definite integral, and by extension, the term is also sometimes used to describe the numerical solution of differential equations. This article focuses on calculation of definite integrals. The term numerical quadrature (often abbreviated to quadrature) is more or less a synonym for numerical integration, especially as applied to one-dimensional integrals.
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Continuous function
In mathematics, a continuous function is a function for which, intuitively, "small" changes in the input result in "small" changes in the output. Otherwise, a function is said to be "discontinuous". A continuous function with a continuous inverse function is called "bicontinuous". Continuity of functions is one of the core concepts of topology, which is treated in full generality below.
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