A scalar field is a function of the type $X\to \Bbb R$, where $X$ may be an open set in $\mathbb R^n$ or more generally a smooth manifold.
Questions tagged [scalar-fields]
370 questions
3
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1 answer
Parametrising Intuition of Plane
This might be a bit too "hand-wavy" for this forum but here it goes:
Generally the problem is this, I wish to create a function $f:\mathbb{R}^n \rightarrow \mathbb{R}^m$ with some properties that I have "some notion" of inside of my head. Things…
Ivar Eriksson
- 133
1
vote
1 answer
Does a figure which has a contour plot have a systematic function to define it?
Does a figure which has a contour plot have a systematic function to define it? I mean I am plotting a contour plot (the contour plot which shows z slices in x-y graph) of a figure like (suppose) mount everest. Does it necessary have a systematic…
user187604
- 409
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1 answer
Compute gradient of scalar field defined by trilinear interpolation of sample grid
I'm trying to figure out how to compute something for a game I'm creating, and I'm having trouble finding a solution in language I can understand. The extent of my math education is that I'm just starting Calculus AB, so I would greatly appreciate…
Phoenix
- 145
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How is the gradient of a radial scalar field, radial?
I'm not sure if I'm mistaken: but my notes say the following.
A scalar field $f$ is radial if $f({\textbf{x}}) = \phi ( ||{\textbf{x}}||)$ for some $\phi : [0,\infty) \rightarrow \mathbb{R}$.
I understand this definition, but then it goes on to…
Twenty-six colours
- 1,881
0
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Tangent plane to $z=x sin(y/x)$ in $(a,b,a sin(b/a))$
Find the tangent plane to $z=x\sin(y/x)$ in $(a,b,a \sin(b/a))$
I got: $\pi) x[\sin(b/a)-\frac{b\cos(b/a)}{a}]+y \cos(b/a)-z=0$
Can somebody check the answer?
Damian Ariel
- 33