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This is a list of differential geometry topics. ... Laplacian operators in differential geometry; Formulas and other tools. List of coordinate charts;
The Laplacian in differential geometry. The discrete Laplace operator is a finite-difference analog of the continuous Laplacian, defined on graphs and grids. The Laplacian is a common operator in image processing and computer vision (see the Laplacian of Gaussian, blob detector, and scale space).
Discrete exterior calculus — discrete form of the exterior calculus of differential geometry Modal analysis using FEM — solution of eigenvalue problems to find natural vibrations Céa's lemma — solution in the finite-element space is an almost best approximation in that space of the true solution
Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds.It uses the techniques of single variable calculus, vector calculus, linear algebra and multilinear algebra.
In differential geometry, the Laplace–Beltrami operator is a generalization of the Laplace operator to functions defined on submanifolds in Euclidean space and, even more generally, on Riemannian and pseudo-Riemannian manifolds. It is named after Pierre-Simon Laplace and Eugenio Beltrami.
In 2016, Atangana and Baleanu suggested differential operators based on the generalized Mittag-Leffler function. The aim was to introduce fractional differential operators with non-singular nonlocal kernel. Their fractional differential operators are given below in Riemann–Liouville sense and Caputo sense respectively.
The naturalness of the star operator means it can play a role in differential geometry, when applied to the cotangent bundle of a pseudo-Riemannian manifold, and hence to differential k-forms. This allows the definition of the codifferential as the Hodge adjoint of the exterior derivative, leading to the Laplace–de Rham operator.
In mathematics, a differential operator is a linear operator defined as a function of the differentiation operator. It is helpful, as a matter of notation first, to consider differentiation as an abstract operation, accepting a function and returning another (in the style of a higher-order function in computer science ).