Vector field

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Examples

Magnitude Barometric pressure Velocity Fluid Streamlines, streaklines and pathlines

18 related topics

Operations on vector fields

Riemann integral Parametrized Real numbers Line integral convolution Source or a sink

15 related topics

Flow curves

Picard–Lindelöf theorem Lipschitz continuous Equivalence classes Real number line Pathline

15 related topics

Definition

Cartesian coordinates Smooth function Linear map Module Ring

13 related topics

Topics to explore

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Overview

Vector calculus
Physics
Vector Vector (mathematics and physics)
Space Space (mathematics)
Euclidean space
Plane Plane (geometry)
Unit of measurement
Vector physical quantity
Three dimensional space
Wind
Force
Magnetic Magnetic field
Gravitational Gravity
Differential and integral calculus
Line integral
Work Work (physics)
Conservation of energy
Fundamental theorem of calculus
Divergence
Volume
Curl Curl (mathematics)
Vector-valued function
Position vector
Space curve
Coordinates Coordinate system
Covariance and contravariance of vectors
Open subsets Open set
Surfaces Surface (topology)
Tangent vector Differential geometry of curves
Differentiable manifolds Differentiable manifold

Definition

Cartesian coordinates
Smooth function
Linear map
Module Module (mathematics)
Ring Ring (mathematics)
Transformation properties of vectors Euclidean vector
Covector
Scalar fields Scalar field
Tangent vector Tangent space
Mapping Map (mathematics)
Derivation Derivation (differential algebra)
Analytic Analytic function
Fraktur Fraktur (typeface sub-classification)

Examples

Magnitude Magnitude (mathematics)
Barometric pressure
Velocity
Fluid
Streamlines, streaklines and pathlines
Iron
Maxwell's equations
Electric field
Gravitational field
Gradient
Del
Conservative field
Flow Flow (mathematics)
Gradient descent
Closed curve
Orthogonal group
Invariant Invariant (mathematics)
Orthogonal transformations Orthogonal matrix

Operations on vector fields

Physical intuition

Flow curves

Picard–Lindelöf theorem
Lipschitz continuous Lipschitz continuity
Equivalence classes Equivalence class
Real number line
Pathline Streamlines, streaklines, and pathlines
Fluid Fluid flow
Geodesic flow
One-parameter subgroups One-parameter subgroup
Exponential map Exponential map (Lie theory)
Lie groups Lie group
Compactly supported Compact support
One-parameter group
Diffeomorphisms Diffeomorphism
Commute Commutative property
Lie bracket Lie bracket of vector fields

F-relatedness

Derivative

Generalizations

P-vectors P-vector
Dual space
Differential k-forms Differential form
Derivations Derivation (abstract algebra)
Differential calculus over commutative algebras

Bibliography

Hubbard, J. H. John H. Hubbard
Hubbard, B. B. Barbara Burke Hubbard
ISBN ISBN (identifier)
Boothby, William William M. Boothby

Advanced semantic analysis

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Map overview Semantic statistics

Nodes118

Edges117

Triples92

Avg. degree1.98

Density0.016949

Components1

How this topic connects Entity context

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Vector field

Top relations

related to Examples · 11

Vector field → Earth, Euclidean, For, In, Magnetic, Maxwell's, Streamlines, The, They, This, Velocity

related to External links · 9

Vector field → An, EMS Press, Encyclopedia, Magnetic, Mathematics, MathworldVector, Online Vector Field Editor, PlanetMath, Vector

related to Vector fields on subsets of Euclidean space · 8

Vector field → Cartesian, Given, If, In, It, One, Rn, The

related to Complete vector fields · 7

Vector field → An, By, For, Hence, If, In, On

related to Index of a vector field · 7

Vector field → In, It, Let, Sn, Take, The, This

is a · 6

Vector field → assignment of a vector to each point in a space, electric field.A gravitational field generated by any massive object is also a vector field, integer that helps describe its behaviour around an isolated zero, section of the tangent bundle.An alternative definition, special case of a vector-valued function, specification of n functions in each coordinate system subject to the transformation law

related to f-relatedness · 5

Vector field → Given, If, Lie, TM, TN

related to Vector fields on manifolds · 5

Vector field → An, Given, In, More, TM

see also · 5

Vector field → Circulation, Eisenbud, Khimshiashvili, Levine, Mathematics

related to Curl in three dimensions · 4

Vector field → In, Stokes, The, This

Important terminology Word statistics

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Important terminology

vector field displaystyle fields point space flow defined given line one integral smooth manifold euclidean curve force function example index

Entity relationships Subject–Predicate–Object triples

Subject	Predicate	Object	Confidence	Src
Vector field	is a	assignment of a vector to each point in a space	0.90	text
Vector field	is a	special case of a vector-valued function	0.90	text
Vector field	is a	specification of n functions in each coordinate system subject to the transformation law	0.90	text
Vector field	is a	section of the tangent bundle.An alternative definition	0.90	text
Vector field	is a	electric field.A gravitational field generated by any massive object is also a vector field	0.90	text
Vector field	is a	integer that helps describe its behaviour around an isolated zero	0.90	text
the divergence	instance of	and this physical intuition leads to notions	0.80	text
surfaces	instance of	but also make sense on other subsets	0.80	text
where they associate an arrow tangent to the surface at each point	instance of	but also make sense on other subsets	0.80	text
Onsager reciprocity to the far-nonequilibrium realm	instance of	as a consistent universal modeling framework that guarantees compatibility with the second law of thermodynamics and extends well-known near-equilibrium results	0.80	text
Vector field	related to Central field in euclidean spaces	Rn	0.60	section
Vector field	related to Central field in euclidean spaces	We	0.60	section

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Min side: 3

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Explore this topic

Examples

Operations on vector fields

Flow curves

Definition

Key facts & relationships

Topics to explore

Overview

Definition

Examples

Operations on vector fields

Physical intuition

Flow curves

F-relatedness

Generalizations

Bibliography

Advanced semantic analysis

Map overview Semantic statistics

Vector field

How this topic connects Entity context

Vector field

Top relations

Important terminology Word statistics

Important terminology

Entity relationships Subject–Predicate–Object triples

Related concept clusters Concept neighborhoods

Connections between topic areas Semantic bridges