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Lemma 2.3. of Riemannian Geometry by do Carmo; Existence/Uniqueness of the Geodesic field $G$ on $TM$

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#differential-geometry #smooth-manifolds #alternative-proof #vector-fields #tangent-bundle
99
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When is the gradient of a line integral equal to the vector field being integrated

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#differential-forms #vector-fields #line-integrals
39
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When a triplet of scalar fields ($[a_x \: a_y \: a_z]$) can represent a vector field?

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#vectors #vector-fields
449
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Calculating a line integral along a curve

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#multivariable-calculus #vector-fields #substitution #line-integrals
40
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Gradient of a Vector Field Without Coordinates

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#calculus #vector-analysis #vector-fields
170
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Vector space where $x+y=x$ and $y$ is not zero vector.

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#linear-algebra #vector-spaces #vector-fields #axioms
101
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Vector Subspace test for set with polynomial

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#linear-algebra #vector-spaces #proof-writing #proof-explanation #vector-fields
241
Views

Triple curl of vector field

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#calculus #vector-fields
62
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Is there always a connection such that $\nabla_i\mathbf e_j=0$ for some basis $\{\mathbf e_i\}_i$?

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#differential-geometry #manifolds #smooth-manifolds #vector-fields #connections
36
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How to generate examples for fluid mechanics?

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#education #vector-fields #fluid-dynamics
40
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Vectorial function: evaluating an integral

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#integration #vector-fields
76
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What's a time-dependent vector field?

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#vector-fields
1.1k
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When does zero divergence imply a vector potential exists?

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#calculus #vector-analysis #vector-fields #electromagnetism
58
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Direction Fields of Pendulum are different?

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#ordinary-differential-equations #physics #vector-fields
982
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Partial derivatives of components of a vector field

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#derivatives #vector-fields

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