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Post by Admin on Dec 17, 2017 6:19:44 GMT
I searched on the Internet and found several sites which will help with the drawing of vector fields. Here is a link to one of them, called Equation Explorer.One interesting feature of this site is that if you create a graphic with it and then save the URL of your graphic, whenever you link back via the saved URL you get the exact graphic that was there when you copied the URL. This is because the URL contains the data required to draw the graphic. So if someone you have supplied the URL to uses it and plays around with the graphic, changing it and adding to it, the original URL will give you back the original graphic with no changes. If you want to keep the modified graphic then you must save the new URL. One not-so-brilliant feature is that you have to find the real and imaginary parts of the function whose vector field you want to plot before using it |
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Post by mondo on Apr 17, 2022 2:31:13 GMT
I searched on the Internet and found several sites which will help with the drawing of vector fields. Here is a link to one of them, called Equation Explorer.One interesting feature of this site is that if you create a graphic with it and then save the URL of your graphic, whenever you link back via the saved URL you get the exact graphic that was there when you copied the URL. This is because the URL contains the data required to draw the graphic. So if someone you have supplied the URL to uses it and plays around with the graphic, changing it and adding to it, the original URL will give you back the original graphic with no changes. If you want to keep the modified graphic then you must save the new URL. One not-so-brilliant feature is that you have to find the real and imaginary parts of the function whose vector field you want to plot before using it It is a nice tool indeed however another "not-so-brilliant" feature is they mark real part by $i$ while imaginary one by $j$ as shown here for a vector field of $z^2$ |
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Post by Admin on Apr 17, 2022 5:25:42 GMT
Mondo
Yes they just decided to use vector notation rather than complex numbers.
Vasco
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Gary
GaryVasco
Posts: 3,352 
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Post by Gary on Apr 18, 2022 22:01:14 GMT
I searched on the Internet and found several sites which will help with the drawing of vector fields. Here is a link to one of them, called Equation Explorer.One interesting feature of this site is that if you create a graphic with it and then save the URL of your graphic, whenever you link back via the saved URL you get the exact graphic that was there when you copied the URL. This is because the URL contains the data required to draw the graphic. So if someone you have supplied the URL to uses it and plays around with the graphic, changing it and adding to it, the original URL will give you back the original graphic with no changes. If you want to keep the modified graphic then you must save the new URL. One not-so-brilliant feature is that you have to find the real and imaginary parts of the function whose vector field you want to plot before using it Vasco, In the programming language I use (MMA), there is a function “ReIm[z]” that applies to a complex number and returns the list {Re[z], Im[z]}, which plots as a point or as a vector arrow if you supply the anchor point and arrow function. Before I discovered this in an update, I would write the function v[z_] := {Re[z], Im[z]}. If you need to plot a line, such as a circle, the function ReIm[listOfz] converts every complex number in the list (which you prepare) to the {x, y} format. Then one can obtain a curve by applying the function “Line[listOfxy]”. It is quite convenient. One can dispense with a confusing loop in a single line of code. I am not sufficiently familiar with Equation Explorer to know whether it provides for mapping a function to a list, but with a dense vector field, it would be very helpful. One might be able to reproduce and store ReIm[] and a general loop function in EE. The same program also has VectorPlot, VectorDensityPlot, StreamPlot, StreamDensityPlot, and 3D versions of those. I haven’t experimented with them in plotting the vector fields introduced in the chapters of VCA or VDGF, but perhaps there is some parallel in EE. Gary |
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Post by Admin on Apr 19, 2022 7:40:38 GMT
Gary
Equation Explorer has a limited number of facilities but what it does it does well. The fact that it doesn't understand complex numbers as such means that you have to split functions into real and imaginary parts to use it, so for more complex functions there's a fair bit of work to be done eg
$\sin z=\sin(x+iy)=\sin x\cos iy+\cos x\sin iy=...$ and so on using $\sinh$ and $\cosh$ etc.
The facility to superimpose other functions is useful and its ability to deal with implicit functions. AND IT'S FREE!!!!
Vasco
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Gary
GaryVasco
Posts: 3,352
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Post by Gary on Apr 19, 2022 14:25:05 GMT
Gary Equation Explorer has a limited number of facilities but what it does it does well. The fact that it doesn't understand complex numbers as such means that you have to split functions into real and imaginary parts to use it, so for more complex functions there's a fair bit of work to be done eg $\sin z=\sin(x+iy)=\sin x\cos iy+\cos x\sin iy=...$ and so on using $\sinh$ and $\cosh$ etc. The facility to superimpose other functions is useful and its ability to deal with implicit functions. AND IT'S FREE!!!! Vasco Vasco,
And being online, it is also very handy. No need to install or purchase updates or maintain copies on different computers. Do you find it more useful than DESMOS?
Gary
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Post by Admin on Apr 20, 2022 13:42:06 GMT
Gary
No, Desmos can do lots more than Equation Explorer, but EE is almost perfect for drawing vector fields. Very difficult to do with Desmos. Not saying it can't be done, but you would need to produce something different for each vector field.
Vasco
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