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# Questions tagged [vector-calculus]

Questions on dealing with vector calculus functions of Mathematica such as Grad, Div, Curl, Laplacian and their representations in various coordinate systems.

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71 views

### Vector function projection raises an error

Working on ODE systems solution with NDSolve[] I decided to try to replace system of equations like: ...
137 views

### Summation variables aren't recognised as dummy variables

I'm trying to write this expression in Mathematica, and calculate the following quantity However, when I tried the following ...
49 views

### Scaling vectors by their norm in VectorPlot3D

I'm trying to generate a 3D vector plot in which the length of the vector is really it's norm. This is my code: ...
326 views

### Derivative of a norm

I learned not use the Norm[] function when computing vector derivative, so I use the dot product instead: In: D[x.x, x] Out: 1.x + x.1 What does the result mean? ...
255 views

### Finding unit tangent, normal, and binormal vectors for interpolated function

As an extension of this question, is it possible to find the unit tangent, normal, and binormal vectors for an interpolated function? eg ...
1 vote
171 views

255 views

### How to calculate the gradient in cylindrical coordinates in more efficient way?

I would like to obtain the gradient for the following function in cylindrical Coordinates ...
1 vote
176 views

### Cannot derive Norm or Normalize when recreating Frenet Serret equations

I'm trying to calculate the torsion of a curve at a point using the following code: ...
53 views

### Eliminate doesn't work

I tried to define r by the polynomials a,b,c only. The result which I want is r=4/3 a. But this eliminate doesn't work! It is continue running without stop and without any output. Eliminate[{a == x ...
240 views

### Why is ParametricPlot3D not producing a graph

I have the vector V = {2, y z^2, 3 y + z} I wanted to get a 3d parametric plot of V using: x[t] = Sin[t^2]; y[t] = t^2 - Cos[t]; z[t] = Sinh[t] - Cos[t]. So I did: <...
92 views

### Functions of several variables composition

If we have two functions $G,F:\mathbb R^2\to\mathbb R^2$ then the mechanism $F\circ G(x,y)=F(G(x,y))$ gives us a new map $F\circ G:\mathbb R^2\to\mathbb R^2$ called its composition. In a "...
473 views

### How is Grad defined for array particularly in non-Cartesian coordinates?

This question can be viewed as a follow-up of What is the definition of Curl in Mathematica? First argument of Grad can be an array, but what definition does ...
1 vote
99 views

### Find Solution to Exact ODE with 4 Variables?

OK, I give up. I was trying to use the solution in this post to solve an exact ODE with 4 independent variables. This works ...
69 views

### Aesthetic Constant Vectorial Field 3D-Plot

I am trying to 3D-Plot a constant Vectorial Field: ...
1 vote
298 views

### Referencing the Component of a vector

If I were to define a vector r = {2, 0} + t*({5, 4} - {2, 0}) >>{2 + 3 t, 4 t} Sqrt[(D[r])^2 + (D[r])^2] How do I properly reference a single ...
375 views