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Differential form

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 applications, especially in geometry, topology and physics.

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Overview

History

Concept

Intrinsic definitions

Operations

Pullback

Integration

Applications in physics

Applications in geometric measure theory

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Differential form

Nodes149
Edges148
Triples126
Avg. degree1.99
Density0.013423
Components1

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Differential form

Top relations

related to External links · 21
Differential form → Bachman, Beo, Bibcode, Cornell University, David, Differential, Differential Forms, Eric, Geometric Approach, Luca, Manifolds, MathWorld, Needham, PDF, Princeton University Press, Reyer, Sjamaar, The Core, Tristan, Visual
related to Pullback · 16
Differential form → By, For, However, If, It, Precomposing, Rham, Since, Suppose, Tf, The, This, TM, TN, TpM, TqN
related to history · 12
Differential form → Although, Cartan, Die Lineale Ausdehnungslehre, Differential, Hermann Grassmann's, Linear Extension, Mathematics, Mathematik, New Branch, Some, The Theory, Zweig
related to Integration along fibers · 12
Differential form → Because, Dieudonné, Fix, Following, Fubini's, Let, More, Suppose, The, Then, This, Under
related to Relation with measures · 12
Differential form → Assuming, By, Folland, For, Formally, In, Jacobian, Lebesgue, On, Section, Similarly, The
related to Integration on Euclidean space · 9
Differential form → Every, Fixing, Give, Lebesgue, Let, Riemann, Such, The, This
has application · 7
Differential form → Differential, Faraday, For, Maxwell's, One, The, This
related to Intrinsic definitions · 7
Differential form → At, Big, Let, Omega, That, The, This
related to Integration and orientation · 6
Differential form → An, And, If, Integration, That, This
related to Integration · 5
Differential form → Euclidean, If, Other, There, When

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Important terminology

displaystyle differential forms wedge manifold exterior form omega dx orientation product derivative vector defined integral -form oriented space textstyle mathbf

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Differential formis ageneralization of the differential of a function0.90text
the Hodge star operatorinstance ofIt also enables the definition of additional operations0.80text
Differential formhas applicationDifferential0.60section
Differential formhas applicationFor0.60section
Differential formhas applicationMaxwell's0.60section
Differential formhas applicationFaraday0.60section
Differential formhas applicationThis0.60section
Differential formhas applicationThe0.60section
Differential formhas applicationOne0.60section
Differential formrelated to ConceptDifferential0.60section
Differential formrelated to CurrentsThe0.60section
Differential formrelated to CurrentsCurrents0.60section

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