manifold

Calculus

(noun)

a topological space that looks locally like the "ordinary" Euclidean space and is Hausdorff

Related Terms

  • parametric
  • meridian
Political Science

(adjective)

Exhibited at diverse times or in various ways.

Related Terms

  • operationalization

Examples of manifold in the following topics:

  • Surfaces in Space

    • A surface is a two-dimensional, topological manifold.
  • Stokes' Theorem

    • The generalized Stokes' theorem is a statement about the integration of differential forms on manifolds, which both simplifies and generalizes several theorems from vector calculus.
    • Stokes' theorem says that the integral of a differential form $\omega$ over the boundary of some orientable manifold $\Omega$ is equal to the integral of its exterior derivative $d\omega$ over the whole of $\Omega$, i.e.:
  • Parametric Equations

    • The notion of parametric equation has been generalized to surfaces of higher dimension with a number of parameters equal to the dimension of the manifold (dimension one and one parameter for curves, dimension two and two parameters for surfaces, etc.)
  • Functions of Several Variables

    • In a more advanced study of multivariable calculus, it is seen that these four theorems are specific incarnations of a more general theorem, the generalized Stokes' theorem, which applies to the integration of differential forms over manifolds.
  • Incentives for Efficiency and Productivity

    • The benefits of high productivity are manifold.
  • Architecture in the Greek High Classical Period

    • The manifold combination and blending of various architectural styles in the same building was completed through a natural polychromatic effect, resulting from the use of different materials.
  • Geometric Symbolism

    • According to the psychologist David Fontana, its symbolic nature can help one "to access progressively deeper levels of the unconscious, ultimately assisting the meditator to experience a mystical sense of oneness with the ultimate unity from which the cosmos in all its manifold forms arises. "
  • Enone Reactions

    • For the β-manifold, β1 should yield a cis-fused product and β2 the trans-isomer.
  • Conflict in the Atlantic

    • The focus on U-boat successes, the "aces" and their scores, the convoys attacked, and the ships sunk, serves to camouflage the Kriegsmarine's manifold failures.
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