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  2. Mathematics Subject Classification - Wikipedia

    en.wikipedia.org/wiki/Mathematics_Subject...

    For example, for differential geometry, the top-level code is 53, and the second-level codes are: A for classical differential geometry; B for local differential geometry; C for global differential geometry; D for symplectic geometry and contact geometry; In addition, the special second-level code "-" is used for specific kinds of materials.

  3. Calculus of variations - Wikipedia

    en.wikipedia.org/wiki/Calculus_of_Variations

    The calculus of variations (or variational calculus) is a field of mathematical analysis that uses variations, which are small changes in functions and functionals, to find maxima and minima of functionals: mappings from a set of functions to the real numbers.

  4. Differential geometry - Wikipedia

    en.wikipedia.org/wiki/Differential_geometry

    Differential geometry is also indispensable in the study of gravitational lensing and black holes. Differential forms are used in the study of electromagnetism. Differential geometry has applications to both Lagrangian mechanics and Hamiltonian mechanics. Symplectic manifolds in particular can be used to study Hamiltonian systems.

  5. Generalized Stokes theorem - Wikipedia

    en.wikipedia.org/wiki/Generalized_Stokes_theorem

    In vector calculus and differential geometry the generalized Stokes theorem (sometimes with apostrophe as Stokes' theorem or Stokes's theorem), also called the Stokes–Cartan theorem, [1] is a statement about the integration of differential forms on manifolds, which both simplifies and generalizes several theorems from vector calculus.

  6. Differentiable curve - Wikipedia

    en.wikipedia.org/wiki/Differentiable_curve

    The differential-geometric properties of a parametric curve (such as its length, its Frenet frame, and its generalized curvature) are invariant under reparametrization and therefore properties of the equivalence class itself. The equivalence classes are called C r-curves and are central objects studied in the differential geometry of curves.

  7. Differential geometry of surfaces - Wikipedia

    en.wikipedia.org/wiki/Differential_geometry_of...

    In the classical theory of differential geometry, surfaces are usually studied only in the regular case. [7] [18] It is, however, also common to study non-regular surfaces, in which the two partial derivatives ∂ u f and ∂ v f of a local parametrization may fail to be linearly independent. In this case, S may have singularities such as ...

  8. List of differential geometry topics - Wikipedia

    en.wikipedia.org/wiki/List_of_differential...

    See also multivariable calculus, list of multivariable calculus topics. Manifold. Differentiable manifold; Smooth manifold; Banach manifold; Fréchet manifold; Tensor analysis. Tangent vector

  9. Geometric calculus - Wikipedia

    en.wikipedia.org/wiki/Geometric_calculus

    Let be an -grade multivector.Then we can define an additional pair of operators, the interior and exterior derivatives, = =, = + =. In particular, if is grade 1 (vector-valued function), then we can write