Spherical Coordinates 3D Animation
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- čas přidán 28. 08. 2024
- This section can be a little hard to visualize in 2D. This video should help you to visualize spherical coordinates and set up the bounds of integration for triple integrals.
Paul's Math Notes: tutorial.math.l...
I don't understand why they don't teach this today at my university without using animations like these to help us visualize 3D shapes mentally. We have the technology now...
I feel the same way. I made this because I couldn't find something similar. Most of your professors learned it from chalkboard drawings, so don't be too upset if they try to teach you the same way :)
@@XYZandRGBhow do you go about animating things like this ?
@@tommygstonymec I use Blender. I build all of the pieces you see in the video and vary their rotation and size and position using keyframes.
hmm
Maybe in the future generations they will use now animation or graphical representations using new technologies
Thanks dude saved my brains from frying
Thank's a ton for the animation man, it really helped, like fr. My prof isn't the best, she runs through the material like she's tryna speedrun the class
A good teacher is one who can make complicated topics the most easiest ones. Thank you
Thank you very much, i have an exam in an hour and finally understand about all of this
This is gold for spherical coordinates. Thank you!
Sending you all the best wishes, being able to explain difficult concepts easily is what marks a great educator. Thank you!
very helpful video! i have a calculus coming up and you have no idea how this saved me hahah thanks a bunch 😊
Good luck on your exam!
i have a re-exam and now phi is much more intuitive than the first time!! Thanks very very much for such a good explanation!!!!
θ is to reduce the aggregate of three-dimensional space to a surface, Φ is to reduce the aggregate of a surface to a line, which is the intersection of the surface and the cone, and ρ is to reduce a line to a point. The positioning of any point in space can be completed.
This video made me understand why theta is only from 0 to π, thanks!
ty for everything, my friend saw your video and he say he gonna take 5 in the impossible test tomorow, god bless him and all the students
Animations help a LOT. This video made the concept crystal clear to me. Thank you!
I'm from INDIA Your video helped me a lot to make my concept crystal clear ❤
Great video. Cleared all my doubts. Thank you so much for this! 😁
understood in a very easy way ...because you took lot of hard pain to do it. thanks a lot
this is marvelous effort to teach coordinates.
Thank you very much. It might have took some effort to make this video, I am grateful for this.
dude you're the boss, thank you !!
Nice video. I would recommend including the bounds and other numbers you're talking about on screen next time.
Thanks! Putting this (unfinished) video up was a little experiment to see if people would like this kind of video. Comments like yours motivate me to continue making them.
finally a good video regarding this !!! thank you !!!
Great animation.Thanks. You have my subscription. I think greatly of all the pre computer graphics mathematicians who could see it all in their heads.Makes one wonder? In the long run are our brains going to be less or more capable of visualisation?
That's such an interesting question. I feel like we are adding to the number of people that can visualize a topic each time we express it in a new way. There's no shortage of difficult concepts to understand, so I suppose anyone can still exercise the skill as much as they want.
I had a colleague suggest that some boys gain an advantage in spatial visualization over girls from jumping off of playground equipment and tracking movements of the ball in sports more often. I have no idea if nature or nurture is the main culprit, but I suspect it's a skill that can be strengthened.
Thanks
dude you're the best
thank you SO MUCH for this video. It got me unstuck. I didn't realize that the vertical angle goes only from 0 to Pi, not to 2Pi, like angles usually would
this has been incredibly helpful, thank you!
a really nice representation thank you
I actually appreciate your time, I had finally learnt.
our professor is trying to teach this using a chalkboard its sooo frustrating,, thanku so much for posting this!
Thanks so much for making this video. Unique and super helpful visualization!
This was very concise! Illustrated fantastici! All important key features in order to calculate the transmitted irradience by angular dependent. Using Yours - presented coordinates and the following spherical coordinate system I can specify a given direction for the zenith and azimuth angles thus the transmittance of this system is a function of direction of incident radiation. So valuable information also for the irradience from the sun, sky and for all hemispheric areas given by the independent of changes in the sun or sky radiance. Thank you because performing an integration of the transmitted irradience and calculating the total radiant flux in civil engineering we can see better geometry for example water, glass, polarized elements, i. c. Also we can imply two-dimensional Fourier transform of Cartesian coordinates if we understand better first important step that implys in all disciplines not only engineering approach! 👏👏👏👏
that changing Rho from 0 < Rho
Thank u so much Teacher Love from INDIA ❤
Great video bro! I couldnt understand what phi is and now got it! Thank you!
did you mix up phi and theta? my notes and other videos show them the other way
It depends on which book you are using. There is no standard, but what I have in my video is what I've seen in Stewart calculus.
@@XYZandRGB its weird there is no standard. thanks
Very intuitve explanation. Thanks 💯
saved my calc grade thank you🙏
thank u so much you helped me a lot🌷💖
Thanks so much for this video. It really clarified a few things for me.
Very informative and very well presented ,thank you
Short and simple but very helpful, thank you so much
Thank you so much! this made it so clear
Thank you very much for the graph & explanation
the lovely grease pencil :) I am also planning to use Blender to do math animations. It's gonna be fun. Subs.
I actually used this site. www.calligraphr.com/en/
but I will probably be using grease pencil for that in the future.
Thanks! This was extremely helpful :D
Awesome explaination
wonderful
AMAZING VIDEO THANK YOU SO MUCH
Great video, keep up the good work!!
Thank you so much :)
as in polar coordinate 2d we needed an initial line and pole for frame of reference , i wonder if we need all the three axes here?
Changing the frame of reference from what I described here is a bit more advanced than what I can cover here, but I would assume we need all 3 axes to define a frame of reference.
Great explanation sir
Thank you so much. You saved me
I don't understand...
Give it some more effort! Math takes a lot of time.
great video 🙌🏾👏🏾
Thank you very much 😍😍 !!
Please sir make more videos on multivariable calculus 😇
Thank you so much for sharing this video! It's very helpful!!
This helped me understand the Qubit
This was beautiful!! Thank you very much.
AMAZING IT WAS.... ❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️
Thank you very much. 🙏
amazing video
muchismas gracias por explicarlo todo bien! me ha ayudado mucho!
Nice explanation
So x and y axioms have an angular relationship and the z axioms phi is independent, having half the values because its the same on either side of the axis without concern with position. Hmm interesting stuff.
Is fie not clockwise?
"fie" or phi originates from the positive z-axis, and it travels in all directions. To use an analogy, 11:00 and 1:00 on the clock would have the same phi value of 1 hour
Good
Can't theta be from π/2 to 3π/2 at 5:25 or it is same as π to 2π
theta is positive when it is measured counterclockwise rotation from x axis about z axis. I guess that might be the reason for it being in the range of π to 2π.
Remember that theta starts at the positive x-axis, just like polar coordinates. It's a little odd because it "looks" like it is starting on the left.
Thank you very much sir !!!
Thanks!
Thank you so much ❤
super helpful...thank u so much
The last diagrams better u use the cursor to show us where u were starting from and ending when getting phi
Great video
which software are you using ?
I used Blender. It's totally free to use!
Thank you
thank you!
very good visuals
fi will be with x axis not theta
Your textbook may label them differently. This is how they are labelled in Stewart's Calculus.
excellent
Wow, this helped a lot. Thank you
which software did you use to create animations?
I used Blender. It's free and getting better every version
I don't know why my prof is switching the properties of phi and theta, I'm so confused.
Wow beautifuly explained
Thank you !!
Keep the hard work up 👍
amazing. Thanks a lot.
Very good
cleared my doubt professor
thank you for this animation!!
I need these animations! my prof's drawings are so hard to interpret
great animations, can I ask how they were created?
I made them using Blender, a free 3D software
Thank you!! This was very informative
your lecturing system is good because of using 3D system
Thanks! Glad you found it helpful!
LEGEND
cylindrical polar coordinates when parallel to x-axis
how can i solve something like this???
I would think about how you can redefine your variables. Instead of theta being related to x and y, have it related to y and z.
great video sir ... helped a lot
Thanks ☺️😍
The question is when do we use normal triple integral(dz dy dz), triple integral in cylindrical coordinates (r dz dr dθ) or triple integral in spherical coordinates?
is it based on the graph or there is a better way of knowing this
""Given that sometimes we encounter functions that are hard to graph
I would suggest using the coordinate system that has the most constants in its bounds. You can convert the equation you are integrating to any coordinate system you like, so it is usually based on the shape of the solid.
Thank you! Also why did you change your audio of Phi out lol
I mistakenly said "theta" instead a few times. Audio editing is not my strong suit :)
awesome video!!