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Differential form - Wikipedia

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Join Wikipedia Asian Month this November and December! Contribute in Wikipedia Asian Month and get postcard! In mathematics, differential forms provide a unified approach to define integrands over curves, surfaces, solids, and higher-dimensional manifolds. The modern notion of differential forms was pioneered by Élie Cartan. It has many applications, especially in geometry, topology and physics. For instance, the expression 𝑓 ( 𝑥 ) 𝑑 𝑥 is an example of a 1-form, and can be integrated over an interval [ 𝑎 , 𝑏 ] contained in the domain of 𝑓 : ∫ 𝑎 𝑏 𝑓 ( 𝑥 ) 𝑑 𝑥 . Similarly, the expression 𝑓 ( 𝑥 , 𝑦 , 𝑧 ) 𝑑 𝑥 ∧ 𝑑 𝑦 + 𝑔 ( 𝑥 , 𝑦 , 𝑧 ) 𝑑 𝑧 ∧ 𝑑 𝑥 + ℎ ( 𝑥 , 𝑦 , 𝑧 ) 𝑑 𝑦 ∧ 𝑑 𝑧 is a 2-form that can be integrated over a surface 𝑆 : ∫ 𝑆 ( 𝑓 ( 𝑥 , 𝑦 , 𝑧 ) 𝑑 𝑥 ∧ 𝑑 𝑦 + 𝑔 ( 𝑥 , 𝑦 , 𝑧 ) 𝑑 𝑧 ∧ 𝑑 𝑥 + ℎ ( 𝑥 , 𝑦 , 𝑧 ) 𝑑 𝑦 ∧ 𝑑 𝑧 ) . The symbol ∧ denotes the exterior product, sometimes called the wedge product, of two differential forms. Like

Differential form - Wikipedia Jump to content From Wikipedia, the free encyclopedia Expression that may be integrated over a region This article includes a list of general references but lacks corresponding inline citations . Please help improve this article by introducing more precise citations. ( April 2026 ) ( Learn how and when to remove this message ) In mathematics , differential forms provide a unified approach to define integrands over curves, surfaces, volumes, and higher-dimensional manifolds . The modern notion of differential forms was pioneered by Élie Cartan . It has many applica

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