List questions from vector-analysis

Published on 10 Sep 2016 - 11:47

42

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Derivative of $f(\mathbf{x})$ wrt $\mathbf{x}$ where $\mathbf{x} \in \mathcal{V}$

Published on 11 Sep 2016 - 6:45

249

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Show that a curve has curvature $\kappa(t)=\frac{|\dot x \ddot y−\dot y \ddot x|}{{(\dot x^2+\dot y^2)}^{3/2}}$.

Published on 28 Mar 2026 - 9:33

2.6k

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What is the geometric reason of why is the divergence of the curl of a vector field equal to zero?

Published on 11 Sep 2016 - 22:10

3k

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Why is the determinant of the Jacobian the change of volume factor that comes from changing variables?

Published on 12 Sep 2016 - 0:42

902

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Is there a tangential surface integral?

Published on 28 Mar 2026 - 13:59

49

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Find the divergence of $F=-(x,y)/r^2$ using the definition

Published on 14 Sep 2016 - 15:45

379

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Show that the curvature of the curve is given by $|{\bf H}|^{−3}|{\bf H}×({\bf H·∇}){\bf H}|$.

Published on 28 Mar 2026 - 9:33

769

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Leibniz rule for vector fields

Published on 14 Sep 2016 - 18:46

2.5k

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Derivative of rotating unit vector in coordinate free maner

Published on 06 Apr 2026 - 4:55

72

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Can't Understand this Gradient Derivation

Published on 31 Mar 2026 - 7:48

119

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Curl of a vector field $x \mapsto A x$

Published on 01 Apr 2026 - 10:29

163

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orthogonal vectors of vector $(a,b)$ which is of same length as that of vector $(a,b)$

Published on 15 Sep 2016 - 8:57

45

Views

Integrals in Vector Calculus

Published on 15 Sep 2016 - 11:54

213

Views

Describe and sketch the vector field $Ax$. $A$ is symmetric and skew-symmetric.

Published on 15 Sep 2016 - 14:35

List Question

Vector analysis, indexnotation

Derivative of $f(\mathbf{x})$ wrt $\mathbf{x}$ where $\mathbf{x} \in \mathcal{V}$

Show that a curve has curvature $\kappa(t)=\frac{|\dot x \ddot y−\dot y \ddot x|}{{(\dot x^2+\dot y^2)}^{3/2}}$.

What is the geometric reason of why is the divergence of the curl of a vector field equal to zero?

Why is the determinant of the Jacobian the change of volume factor that comes from changing variables?

Is there a tangential surface integral?

Find the divergence of $F=-(x,y)/r^2$ using the definition

Show that the curvature of the curve is given by $|{\bf H}|^{−3}|{\bf H}×({\bf H·∇}){\bf H}|$.

Leibniz rule for vector fields

Derivative of rotating unit vector in coordinate free maner

Can't Understand this Gradient Derivation

Curl of a vector field $x \mapsto A x$

orthogonal vectors of vector $(a,b)$ which is of same length as that of vector $(a,b)$

Integrals in Vector Calculus

Describe and sketch the vector field $Ax$. $A$ is symmetric and skew-symmetric.

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