# Tagged Questions

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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### Solve equations involving summation expressions in Mathematica

I am trying to solve the simple linear regression equation analytically in Mathematica (not using builtin functions). I managed to calculate the gradient as follows f is loss function using RSS and ...
3k views

### How do I plot a proper streamline plot, including spacings and line endings?

Mathematica includes two nice built-in tools to visualize vector fields, VectorPlot and StreamPlot. The latter is a useful tool, ...
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### Errors Solving Elliptic PDES with FEM

I am trying to solve the equation below governing transversely isotropic plane strain in cartesian coordinates with the given boundary conditions based on code found here using Mathematica 10.1 on OSX ...
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### Cross product of three vectors

I am following the answer of Jens from following post: How do I simplify a vector expression? vec /: Cross[vec[x_], HoldPattern[Cross[y__]]] := I want to create ...
98 views

### Angle between two vectors in spherical coordinates [closed]

I have two vectors: H = {1, 0, π/4}; EA = {1, 0, 0}; Which I want to be in {r, Phi, Theta} - which would should give an angle between the two vectors as ...
3k views

### Is it possible to do vector calculus in Mathematica?

I am trying to rearrange and manipulate some vector differential equations in Mathematica. As far as I understand you have to tell Mathematica that a variable is a vector by specifying the components ...
142 views

### How to obtain the gradient of a function as a function?

The Grad function allows me to get the gradient of a function like this: ...
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### Comparing unit normal definition in calculus with FrenetSerretSystem

I'm trying to compare the unit normal definition in calculus texts (i.e., $\vec N=\vec T'/||\vec T'||$) where $\vec T$ is the unit tangent vector, with the unit normal vector returned by the ...
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### How to I plot a vector and a line on the same graph?

For example I want to plot the vector <7, 20> on the same plot as the line {t, 6t+10}
988 views

### Normal and Tangent of Acceleration in 3D

I am trying to find the normal and tangent of acceleration. I know the formula for the tangent of acceleration is $((Acceleration . Velocity)/(Velocity.Velocity))*Velocity$ and the normal of ...
116 views

### Finding the attractors of the vector field constructed as the gradient of an interpolated 3D scalar field

I have a list of data existing as {{{x, y, z}, f},...} from which I construct a 3D interpolation function using Interpolation[ ]. I am able to construct a vector field from the gradient of this scalar ...
161 views

### Curl expression does not evaluate [closed]

I am using Mathematica 8 on OS X. I am trying to compute the cylindrical curl of a symbolic vector following Mathematica documentation. ...
217 views

### Visualizing the Lagrange Multiplier Solution

This question is based on work in Susan Colley's Vector Calculus, 4th ed. The question is to find and classify critical points of $f(x,y,z)=3xy-4yz+5xz$ subject to the constraint $g(x,y,z)=3x+y+2z=13$...
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### Show[cp1,cp2, …] but PlotLabel in cp2 does not show up [duplicate]

I am visualizing the extrema of $f(x,y)=x^3+3y^2$ constrained to the level curve $g(x,y)=xy=-4$, found by using the Lagrange Multiplier Method. ...
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### Derivatives of list elements

Bug introduced in 8.0.0 and fixed in 9.0.0 Could someone explain the odd behavior of the Derivative function when drawing arguments from lists? We have, ...
290 views

### Extrema of a function of three variables

To identify and classify the critical points of the function $f(x,y,z)=x^3+xz^2-3x^2+y^2+2z^2$, I used the Hessian matrix method. ...
459 views

### Dipolar magnetic field lines inside a cylinder

I'm drawing the magnetic field lines of a rotating dipole (magnetic field distorded by emission of radiation). Currently, my Mathematica 7.0 code is fully working, but I'm having a constraint which I ...
80 views

### Derivative of vector dot product with respect to a vector

I have the expression: Transpose[gvecI, {2, 1}].x (m[1] + m[2]) gvecI and x are [3x1] ...
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### How to obtain the magnetic field of the following set up [closed]

This is the experimental set up: A ferromagnetic cylindrical disk (of irrelevant dimensions) has either sides set at different electric potentials (left side at 0 volts and right side at 1 volt). A ...
370 views

### Hypergeometric function with a matrix argument

I am looking for the evaluation of a Hypergeometric function with a matrix argument as for example in Koev and Edelman or as showcased in this Wikipedia article. From what I understand from ...
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### extraction new generated vectors in module with replaced parts

We have four vectors: ...
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### vector product defined on kronecker delta [duplicate]

I have some vectors such as : a={{0}, {0}, {0}}; b={{1}, {1}, {1}}; c={{1}, {1}, {0}}; I wanted to product a by ...
117 views

### Combine 2 plots in one [closed]

$f: R^2 -> R,$ $f(x,y)=x²-y²$ ...
129 views

### Using NMinimize to solve the Multi Commodity Flow problem

I have the following optimization problem and I was hoping to solve it with NMinimize. Unfortunately, I don't get the desired result. I would like to get an optimal vector for $d_{e}$. This is how ...
133 views

### Divergence in spherical coordinates as can be done in W|A

Is there any widget kind of thing that can work out calculations of vector analysis in not-Cartesiian coordinates, i.e spherical and cylindrical? Like the calculators found here: https://www....