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Is every 2D vector field locally integrable up to a rescaling?

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#differential-geometry #partial-differential-equations #differential-forms #vector-fields #integrating-factor
1k
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Why can a simply connected domain in 3D have a hole at the origin?

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#vector-analysis #vector-fields
146
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Let $X$ be a left-invariant vector field. If $\exp(X)\in Z(G)$ then $X$ is right-invariant.

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#ordinary-differential-equations #exponential-function #lie-groups #smooth-manifolds #vector-fields
301
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Stokes’ Theorem for arbitrary surface and boundary curve in $xz$-plane?

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#multivariable-calculus #vector-fields #surface-integrals #stokes-theorem
458
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Is this gradient vector field also a conservative vector field?

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#multivariable-calculus #vector-fields
41
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Does a function $f$ exist such that $(y+z)/q =x$, $(z+q)/y = f(x)$ where $f$ is independent of $y,z,q$?

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#algebra-precalculus #vector-fields
1.1k
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Showing the Law of Conservation of Mass is equivalent to the continuity equation?

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#partial-derivative #vector-fields #fluid-dynamics #multiple-integral #greens-theorem
288
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Proof of the following vector identity?

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#multivariable-calculus #vector-fields #index-notation
647
Views

What are sufficient conditions for a vector field to be a multiple of a gradient?

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#differential-geometry #differential-forms #vector-fields
175
Views

Lie Derivative along One Forms

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#derivatives #differential-geometry #vector-fields #lie-derivative
139
Views

How to say a given vector field is inward, outward or tengent to a hypersurface

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#multivariable-calculus #differential-geometry #differential-topology #smooth-manifolds #vector-fields
2.3k
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Divergence-free vectorfield has volume-preserving flow

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#differential-geometry #differential-topology #vector-fields
405
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Calculating a normal vector field for a surface defined by spherical harmonics

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#differential-geometry #vector-analysis #surfaces #vector-fields #spherical-harmonics
478
Views

Origin of notation $\mathfrak{X}(M)$ for smooth vector fields on a smooth manifold $M$

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#terminology #smooth-manifolds #math-history #vector-fields
355
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Calculating push forwards of a vector field

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#differential-geometry #vector-fields #pushforward

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