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An exact differential is sometimes also called a total differential, or a full differential, or, in the study of differential geometry, it is termed an exact form. The integral of an exact differential over any integral path is path-independent, and this fact is used to identify state functions in thermodynamics.
Differential geometry finds applications throughout mathematics and the natural sciences. Most prominently the language of differential geometry was used by Albert Einstein in his theory of general relativity, and subsequently by physicists in the development of quantum field theory and the standard model of particle physics.
Toggle Differential geometry of curves and surfaces subsection. ... Print/export Download as PDF; Printable version; In other projects
In the language of differential geometry, this derivative is a one-form on the punctured plane. It is closed (its exterior derivative is zero) but not exact , meaning that it is not the derivative of a 0-form (that is, a function): the angle θ {\\displaystyle \\theta } is not a globally defined smooth function on the entire punctured plane.
for any differential k-form ω and any vector-valued form s. This may also be viewed as a direct inductive definition. For instance, for any vector-valued differential 1-form s and any local frame e 1, ..., e r of the vector bundle, the coordinates of s are locally-defined differential 1-forms ω 1, ..., ω r. The above inductive formula then ...
Differential geometry stubs (1 C, 115 P) Pages in category "Differential geometry" The following 200 pages are in this category, out of approximately 379 total.
In mathematics, more specifically in differential geometry, the de Rham theorem says that the ring homomorphism from the de Rham cohomology to the singular cohomology given by integration is an isomorphism. The Poincaré lemma implies that the de Rham cohomology is the sheaf cohomology with the constant sheaf . Thus, for abstract reason, the de ...
In mathematics, especially vector calculus and differential topology, a closed form is a differential form α whose exterior derivative is zero (dα = 0), and an exact form is a differential form, α, that is the exterior derivative of another differential form β. Thus, an exact form is in the image of d, and a closed form is in the kernel of d.
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