Really Introductory Mathematica Question

[dpeagler]

Hello everyone, I apologize for posting such an introductory mathematica question, but I can't find an answer anywhere.

I seem to be having trouble assigning variables and then plotting with the variable name. Perhaps I'm thinking too much in terms of ordinary computer programming or something. Here is a list of my code.

In: r[_t] = {E^(-t/10) Cos[t], E^(-t/10) Sin[t], E^(-t/10)}
Out: {E^(-t/10) Cos[t], E^(-t/10) Sin[t], E^(-t/10)}
In: ParametricPlot3D[{r[_t]}, {t, 0, 40}]

I'm not going to post the out for the last part, because all it did was graph an empty 3D form. I can get it to graph properly if I just type the functions into the ParametricPlot command, but there has to be a better way. I even tried breaking it up into x, y, and z separate variables. Any help is greatly appreciated.

 

[Simon_Tyler]

Hi there,

Try:

r[t_]:={E^(-t/10) Cos[t],E^(-t/10) Sin[t],E^(-t/10)}

ParametricPlot3D[r[t], {t,0,40}]

The expression t_ means a pattern named t that matches anything. So when you later use r[t] it will fetch the RHS of the definition. I used := instead of = since that is a DelayedSet as opposed to Set - thus it doesn't evaluate the RHS until it is called - which is more often what you want.

 

[dpeagler]

Thanks that worked a lot better.

Just curious about some of the terms you used. Particularly RHS?

Thanks again.

 

[Simon_Tyler]

Sorry about that, I thought that RHS and LHS were pretty standard abbreviations in maths for Right and Left Hand Side respectively

 

[blue_raver22]

Hello, thank you for reaching out and asking for help with your introductory Mathematica question. It's completely understandable to have trouble with assigning variables and plotting in Mathematica, especially if you are coming from a background in ordinary computer programming.

To address your specific issue, it looks like you are trying to plot a parametric curve in 3D using the variable t. In this case, you need to use the ParametricPlot3D function with the syntax ParametricPlot3D[{x[t], y[t], z[t]}, {t, t_min, t_max}].

In your example, you have defined r[t] as a list of functions, which is why you are getting an empty 3D form when trying to plot it. Instead, you should define r[t] as a parametric curve by using the syntax r[t_] := {E^(-t/10) Cos[t], E^(-t/10) Sin[t], E^(-t/10)}. This will allow you to plot the curve using ParametricPlot3D as follows:

ParametricPlot3D[r[t], {t, 0, 40}]

I hope this helps and feel free to ask for further clarification if needed. Happy coding!