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The journal publishes an annual supplement in book form called Surveys in Differential Geometry. It covers differential geometry and related subjects such as differential equations, mathematical physics, algebraic geometry, and geometric topology. The editor-in-chief is Shing-Tung Yau of Harvard University.
e. 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 differential calculus, integral calculus, linear algebra and multilinear algebra. The field has its origins in the study of spherical geometry as far back as antiquity.
The term differential is used nonrigorously in calculus to refer to an infinitesimal ("infinitely small") change in some varying quantity. For example, if x is a variable, then a change in the value of x is often denoted Δ x (pronounced delta x ). The differential dx represents an infinitely small change in the variable x.
Geometric analysis is a mathematical discipline where tools from differential equations, especially elliptic partial differential equations (PDEs), are used to establish new results in differential geometry and differential topology. The use of linear elliptic PDEs dates at least as far back as Hodge theory. More recently, it refers largely to ...
In differential geometry, a discipline within mathematics, a distribution on a manifold is an assignment of vector subspaces satisfying certain properties. In the most common situations, a distribution is asked to be a vector subbundle of the tangent bundle . Distributions satisfying a further integrability condition give rise to foliations, i ...
e. In calculus, the differential represents the principal part of the change in a function with respect to changes in the independent variable. The differential is defined by. where is the derivative of f with respect to , and is an additional real variable (so that is a function of and ). The notation is such that the equation.
Calculus. In mathematics, geometric calculus extends the geometric algebra to include differentiation and integration. The formalism is powerful and can be shown to encompass other mathematical theories including vector calculus, differential geometry, and differential forms. [1]
Information geometry is an interdisciplinary field that applies the techniques of differential geometry to study probability theory and statistics. [1] It studies statistical manifolds, which are Riemannian manifolds whose points correspond to probability distributions .