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In multivariate calculus, a differential or differential form is said to be exact or perfect (exact differential), as contrasted with an inexact differential, if it is equal to the general differential for some differentiable function in an orthogonal coordinate system. 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.

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rdf:type	yago:Abstraction100002137 yago:Form106290637 yago:LanguageUnit106284225 yago:Part113809207 yago:Relation100031921 yago:Word106286395 yago:WikicatDifferentialForms
rdfs:label	Exact differential (en) Differenziale esatto (it) 完全微分 (ja) Różniczka zupełna (pl) Diferencial exato (pt)
rdfs:comment	In multivariate calculus, a differential or differential form is said to be exact or perfect (exact differential), as contrasted with an inexact differential, if it is equal to the general differential for some differentiable function in an orthogonal coordinate system. 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. (en) 多変数微分積分学における微分が完全 (exact, perfect) あるいは完全微分（かんぜんびぶん、英: exact differential）とは、それが適当な可微分函数 Q の微分 dQ となるときに言い、そうでないときと呼ぶ。完全微分はしばしば「全微分」('total differential', 'full differential') あるいは微分幾何学において完全形式などとも呼ばれる (ja) Nel calcolo infinitesimale, un differenziale esatto o differenziale totale è una forma differenziale esatta: cioè tale per cui esiste una funzione , detta potenziale, che soddisfa: Un differenziale è esatto se e solo se è integrabile, cioè se la grandezza è esprimibile come funzione di classe , la cui immagine è un sottoinsieme dei numeri reali. L'implicazione diretta dipende dal fatto che la seconda classe di continuità ammette sempre un solo differenziale . Per generalizzare la nozione di differenziale come infinitesimo a quantità definite arbitrariamente risulta utile avere un criterio per determinare se sia esprimibile come funzione delle sue variabili, o se invece non lo sia, anche perché in quest'ultimo caso risulta non conservata su un integrale chiuso nelle sue variabili. (it) Różniczką zupełną funkcji zmiennych niezależnych nazywamy takie wyrażenie Pfaffa, że: gdzie: * – pochodna cząstkowa funkcji po zmiennej * – różniczki zmiennych niezależnych. (pl) No cálculo com múltiplas variáveis, uma diferencial é dita ser exata (ou perfeita), em contraste com uma , se é de forma , para alguma função diferenciável. (pt)
dcterms:subject	Thermodynamics Multivariable calculus
Wikipage page ID	405737 (xsd:integer)
Wikipage revision ID	1120092228 (xsd:integer)
Link from a Wikipage to another Wikipage	Cartesian coordinate system State function Pathological (mathematics) Inexact differential Integrating factor Permutations Enthalpy Entropy Function (mathematics) Gibbs free energy Gradient Gradient theorem Conservative vector field Thermodynamic equations Orthogonal coordinates Antiderivative Stokes' theorem Closed and exact differential forms Combination Helmholtz free energy Partial derivative Thermodynamics Cylindrical Smoothness Bridgman's thermodynamic equations Differential (mathematics) Differential topology Simply connected space Total differential Thermodynamics Heat Thermodynamic equilibrium Chain rule Symmetry of second derivatives Work (thermodynamics) Differentiable function Differential calculus Differential form Differential geometry Dot product Spherical coordinate system If and only if Implicit function Inexact differential equation Injective function Internal energy Multivariable calculus Differential (infinitesimal) Triple product rule Exact differential equation Scalar function Vector calculus identity Symplectic form Simply-connected Exact form Multivariate calculus
Link from a Wikipage to an external page	http://mathworld.wolfram.com/ExactDifferential.html http://mathworld.wolfram.com/InexactDifferential.html https://books.google.com/books%3Fid=BnArjLNjXuYC&q=%22exact+differential%22%7Cdate=14 https://web.archive.org/web/20151016052646/http:/www.chem.arizona.edu/~salzmanr/480a/480ants/e%26idiff/e%26idiff.html http://farside.ph.utexas.edu/teaching/sm1/lectures/node36.html
sameAs	Exact differential Exact differential Exact differential Exact differential Exact differential Exact differential Exact differential Exact differential Exact differential
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has abstract	In multivariate calculus, a differential or differential form is said to be exact or perfect (exact differential), as contrasted with an inexact differential, if it is equal to the general differential for some differentiable function in an orthogonal coordinate system. 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. (en) 多変数微分積分学における微分が完全 (exact, perfect) あるいは完全微分（かんぜんびぶん、英: exact differential）とは、それが適当な可微分函数 Q の微分 dQ となるときに言い、そうでないときと呼ぶ。完全微分はしばしば「全微分」('total differential', 'full differential') あるいは微分幾何学において完全形式などとも呼ばれる (ja) Nel calcolo infinitesimale, un differenziale esatto o differenziale totale è una forma differenziale esatta: cioè tale per cui esiste una funzione , detta potenziale, che soddisfa: Un differenziale è esatto se e solo se è integrabile, cioè se la grandezza è esprimibile come funzione di classe , la cui immagine è un sottoinsieme dei numeri reali. L'implicazione diretta dipende dal fatto che la seconda classe di continuità ammette sempre un solo differenziale . Per generalizzare la nozione di differenziale come infinitesimo a quantità definite arbitrariamente risulta utile avere un criterio per determinare se sia esprimibile come funzione delle sue variabili, o se invece non lo sia, anche perché in quest'ultimo caso risulta non conservata su un integrale chiuso nelle sue variabili. (it) Różniczką zupełną funkcji zmiennych niezależnych nazywamy takie wyrażenie Pfaffa, że: gdzie: * – pochodna cząstkowa funkcji po zmiennej * – różniczki zmiennych niezależnych. (pl)

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