List questions from vector-analysis

Published on 15 Apr 2026 - 23:03

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Linear Algebra Geometry

Published on 11 Apr 2026 - 18:17

32

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I'm integrating the function $z(x^2+y^2)$ over a sphere in the first octant$ x,y,z\geq 0$ (solved)

Published on 16 Apr 2026 - 7:19

38

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Finding the gradient of an expression

Published on 13 Apr 2026 - 19:20

88

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Prove $\left \langle \nabla f(p), p \right \rangle = \kappa f(p)$ for homogenous $f$

Published on 17 Apr 2026 - 3:42

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proof two general dimension inequalities

Published on 15 Apr 2026 - 15:01

352

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Gradient in coordinates of function in 2-sphere

Published on 13 Apr 2026 - 15:03

121

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Deriving the "Thermal wind" equation from the geostropic balance equation

Published on 12 Apr 2026 - 2:30

242

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extrapolate 3-vector field in $(0,1)^3$ from boundary vector fields

Published on 16 Apr 2026 - 17:20

48

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Calculate $\vec{A}$ $\cdot$ $(\vec{B} \times\vec{C})$ = $\vec{A}$ $\cdot$ $\vec{B}$ $\cdot$ $\vec{C}$

Published on 17 Apr 2026 - 9:36

129

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Vanishing Hessian on circle

Published on 10 Apr 2026 - 13:59

279

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Computing surface integral for $F(x,y,z) = (xy,-x^2,x+z)$

Published on 15 Apr 2026 - 0:48

491

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What are "vectors on the unit-sphere"?

Published on 09 Apr 2026 - 13:53

40

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regarding the gradient of a smooth vectorial function

Published on 13 Apr 2026 - 18:32

47

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Show that $\vec{X},\vec{Y}, \vec{Z}$ are orthogonal and find orthonormal basis vectors for the coordinate system with axes defined by them.

Published on 14 Apr 2026 - 7:22

List Question

Having trouble with showing a basic property of the gradient of a function.

Linear Algebra Geometry

I'm integrating the function $z(x^2+y^2)$ over a sphere in the first octant$ x,y,z\geq 0$ (solved)

Finding the gradient of an expression

Prove $\left \langle \nabla f(p), p \right \rangle = \kappa f(p)$ for homogenous $f$

proof two general dimension inequalities

Gradient in coordinates of function in 2-sphere

Deriving the "Thermal wind" equation from the geostropic balance equation

extrapolate 3-vector field in $(0,1)^3$ from boundary vector fields

Calculate $\vec{A}$ $\cdot$ $(\vec{B} \times\vec{C})$ = $\vec{A}$ $\cdot$ $\vec{B}$ $\cdot$ $\vec{C}$

Vanishing Hessian on circle

Computing surface integral for $F(x,y,z) = (xy,-x^2,x+z)$

What are "vectors on the unit-sphere"?

regarding the gradient of a smooth vectorial function

Show that $\vec{X},\vec{Y}, \vec{Z}$ are orthogonal and find orthonormal basis vectors for the coordinate system with axes defined by them.

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