Double integrals and Polar integrals: Explained with 3D visualizations
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- เผยแพร่เมื่อ 14 มี.ค. 2016
- Double integrals in rectangular and polar coordinates. Explained with easy to understand 3D animations. My Patreon page is at / eugenek
- วิทยาศาสตร์และเทคโนโลยี
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ok
Very nice explanation.. Best 👍👍
@Valentin Baker nice market strategy
Add Arabic
That is what we need in math education, animation!
Abderrahmane Mihoub And classical music ;)
If you like animation, you should check out 3B1B as well!
exactly! It makes understanding so much easier!
Hard to do with a black board and chalk. No matter how smart.
*in any sort of education, to be precise. Even biology would have to be most dependable on that
This channel is absolutely a scientific treasure!
Très Bien
Truly one of the best intuitive examples iv ever seen
Thanks for the compliment.
If you like this video, you can help more people find it in their TH-cam search engine by clicking the like button, and writing a comment. Thanks.
+TheExaltedPheonix Finding Volume , mass if Density given ,Finding Centre of Gravity of complex shapes etc...
Please post a video on Cauchy Sequences,(Infinite Series)
Mandeep, I will add that topic to my list of topic for future videos.
Ok Thanks👍
Eugene! Thanks so much for these videos, everything makes more sense now. Would you be interested in describing how fluids work (fluid mechanics)? Thanks again!
13:22 *physics intensifies*
You write bold by putting an * before and after the segment you want to write as bold.
*Like this
And this*
@@spacejunk2186 *like this?* EDIT: *oh wow...*
*let me try*
Yousef Abdelgaber -LOL-
magnificent. that's gonna make it easier for multivariable calculus students to understand.
+Gottfried Leibniz, thanks.
Pretty cool when one of the founders of calculus itself comes back from the dead to agree with your video, eh? Haha! ;)
@@icarus313 lmao
still waiting for Isaac Newton to reply to this
I wish i had this video back when I was studying this topic! Excellent video and excellent quality! The rock music at the end was super cool
+Matheus Monteiro, thanks. Glad you liked it.
Again, a very elegant visualization of a fundamental concept in mathematics. These videos should most definitely be used in junior high! A picture is worth a thousand words and an animation like this is worth a thousand pictures.
+Pär Johansson, thanks for the compliment.
What a satisfying explanation of double integrals! It has opened the door to a brand-new world of calculus that I can't wait to explore further. 😁 (The classical music was also a nice touch!)
I am glad you liked my video. Thanks.
The greatest minds find elegant ways like your own where science meets the arts. A company like Pixar or Dream Works should create a division of animation with you in charge.
Are you kidding?
I wish I had found this before, it's very clear.
What a way of teaching! beautiful, clear, and simple. The animations are so lovely, they make me happy just looking at the colors. You also carefully break down the crucial processes slowly, allowing people to take their time to understand what is going on.
Thanks for the compliments.
Another amazingly intuitive explanation, Eugene. Thank you!
+Sean Wiesen, thanks.
This is apsolutely brilliant, thank you for sharing these videos for free! Keep up the good work!
Thanks.
I'm subscribed to all the major educational channels (i'm sure you know of whom i speak) and i can honestly say that they can ALL learn something from you. You deliver absolute quality videos from the top down. Your work is AMAZING! It's only a matter of time before you hit the 1M sub mark (and above), just keep doing what you're doing. - Loyal Subscriber
+Warren Wilson, thanks for that really great compliment.
Really interesting as usual
I love these kind of videos
+Dante T, thanks. I am glad that you like my videos.
Amazing!!!! One of the best videos explaining double integrals and the coordinates systems
Thanks for the compliment about my video.
Thanks, you make me approach mathematics without fear.
Great work as always, Eugene. You need more recognition.
+Feynstein 100, thanks.
Extremely clear explanation and videos! Thanks too for keeping the commentary pace slow, with pauses so you can actually THINK about what's being said!
Thanks for the compliment about my explanations.
This was very helpful for someone that is very visually oriented. THANK YOU!
I am glad my video was helpful. Thanks.
SO MUCH CLARITY!! I love your style of teaching, it should be the new norm. Thank you so much for the knowledge. I think i speak for everyone that watches this when i say: It is much appreciated!
+Cuey IsDope, thanks. It is nice to be appreciated.
I cannot explain how much I love your videos
I am glad to hear that. Thanks.
An absolutely beautiful amalgamation of maths&music...with insane animations making the topic much simpler to understand!!!...
Thanks.
instant like!. I'm glad to see your subscriber base is growing.
Thanks.
13:22 That Naruto music. Hahaha.
Great video as always, I really wish I had these when I was back in college taking Calc classes. I'm a visual learner and seeing things makes them 'click' in my head.
+David Boucard, thanks for the compliment. Sorry I didn't have these videos ready back when you were in college.
This is the best video on integration I have ever seen! Just found your channel and have already subscribed! Excellent work!
+monkeypoohonyou, thanks for the compliment, and I am happy to have you as a subscriber.
Wow, never seen such a beautiful explanation of integrals. Very good work, thank you.
+Markus Herrmann, thanks for the compliment. Glad you liked it.
you know what, a person makes clear and understandable videos like this should definitely understand the subject matter he explains, therefore our school teachers never understood the practical reflection but only have they known how to calculate.
One of the most beauty product for mankind. Big love, big thanks
Thanks!
Awesome videos, Eugene. Thanks a lot for sharing.
+Oscar Dean, you are welcome and thanks.
Mozart: Serenade in G, K.525 in case anyone wonders. Excellent choice of music!
You may as well just call it Eine Kleine Nachtmusic
The best video I have ever seen!!! Thank you a lot!
Thanks for the compliment about my video. Glad you liked it.
I've learnt so much from this video. Thank you!
+Daniel Bostic (Funguyscienceman), glad to hear you found my video helpful. Thanks.
Best Channel to learn about in-depth calculus. It helped me visualize the calculus.
Thanks. Glad to hear that my videos are helpful.
What software did you use to make those?
In Bangladesh 99.99% student can't even imagine why we do double integration, or even integration. I'm a game developer myself. I wish I could teach those through games. haha
I make my 3D animations with "Poser." I make some of the 3D models with "Wings3D."
I remember from the Calculus classes that in the Polar integration the "R" multiplier was called the "Jacobian", so to differentiate from the Rectangular integration explained before. Amazing video!
Great classical example -in both calculus and music :)
Great job E.K. !
Thanks!
I have the greatest respect for you. Thank you very very very very much. I really love your videos.
Thank you so much for making such videos. The time you give between explaining two statement is really very helpfull.
Thanks.
I see that you too are a visual person, and these videos are so much fun to watch... I wish, I had these when I was learning. I do not mean just this video in particular ..but all of your videos. Good work! please keep it up.
Thanks. I am glad you like my videos.
This was AMAZING and the music that came on at the end wow just wow
+YusefRhymer, glad you liked my video and my choice of music. Thanks.
You just earned yourself another subscriber for making double integral so feasible. Keep it up ☺️
I am glad to have you as a subscriber. Thanks.
Well done explanation and visualization with beautiful music at first.
Thanks for the compliment.
Awesome explanation. I never understood the concepts better before seeing these videos
I am glad you liked my explanation. Thanks.
@@EugeneKhutoryansky
Can you please also make a video on Navier Stokes equation please
Best Multivariable Calculus Video ever!!! 🇺🇸🤘🏼👊🏼🎤🖖🏼
Thanks for the compliment.
Great ! My all concepts are now cleared . Thanks .
Glad my video was helpful. Thanks.
Wonderful work And beautiful mind
Beautiful.........now its stuck in my brain....love it
Glad you liked my video. Thanks.
Now I only understand integral and derivatives because of this channel. Congratulations
This channel is amazing.
+MultiMrHP, thanks.
One of the best videos I've ever seen... (I recommend use vel 1.25 or 1.5)
This channel is amazing!
Thanks for the compliment.
I just love your videos.
+Shaelja Mishra, thanks. I am glad that you like them.
This is so intuitive. I wish I had this some years ago.
+BoIoko, thanks.
great service to the humanity. god bless you and your team
+shivaji b, thanks.
This makes it so easy to understand
Thanks. Glad to hear that.
excellent! thank you for these amazing videos.
+Derek Ojeda, I am glad you like them. Thanks.
Excellent !
the music was sooo dramatic. But anyhow, outstanding explanation. I just understood what exactly the polar coordinates mean. Thank you sooo much. I have never been told about the polar coordinates so well before this. Thank you very much.
Glad you liked my explanation of polar coordinates.
fantastic as usual...
+Madhukar Kulkarni, glad you liked it.
Just brilliant, thanks !
Thanks for the compliment.
REALLY FANTASTIC!!!!!!
+bharathreddy gudibandi, thanks.
I was just listening to Mozart and when it was done I closed spotify and clicked on this video and then there were more Mozart!
Ooh, well done 👏!
Thanks for the compliment.
Please...surface integrals and differential equations.... Super explanations and graphics - thanks!
I really love your videos. It's make me understand math.
Thanks. I am glad my videos are helpful and that you like them.
Best channel acc to a electronics engg. In india.. ! From india with love pls upload more videos with deep information.
Thanks for the compliment. More videos are on their way.
This video is amazing ! bravo
Thanks for the compliment.
This channel is underrated.
Thanks.
I never comment, but i must say; this is high quality education for free and I love it!
+Henrik Nyholm, thanks. I am glad you liked it.
very well made videos !!! Thanks a million!!!
+thanosAIAS, thanks.
Great video , !!!! this has given me more details , thanks so much ,
Thanks. Glad you liked my video.
HOLY SHIT that was awesome! I can't possibly thank you enough!
This channel is the best
Thanks for the compliment.
Good one, liked it.
Glad you liked it.
awsome thats what i wanted ....great job ...thank u so much
Glad you liked my video. Thanks.
great explanation....background music is soothing for the soul...nice
Thanks. I am glad you liked my explanation and choice of music.
"The only really valuable thing is intuition" [Albert Einstein]. You not only understood this yourself, it seems like it's your signature. You are WAAAAAY ahead of most text books and almost all university lectures in terms of understandability. Because you actually present it in ways the developers thought about it in their minds. Truely remarkable mindsdont just start with the abstract definitions out of nothing, because nobody can truely think abstractly without having examples to abstract from. So you really do it the way the geniuses invented it but by also filtering out the most understandable parts.
Hope you are now confident that you are a true treasure to most students out there.
Thanks for the compliment.
Thanku for such a good work.
It is very helpful .
Thanks. Glad my video was helpful.
Awesome! Thank you
Stunningly beautiful! Used to think physics and math are driest, now they appear prettiest! In less 15 minutes, I learned to calculate the size/area/volume of anything in the world! without any stress!It is Awesome!!!
+Fakher Halim, thanks.
Excellent work
Thanks for the compliment.
Very clear and understandable ever, even in grade school
Thanks.
Nice visualizations!
+freeform144, thanks.
Really Helpful. :)
Glad to hear that.
it's just awesome
thank you
Thanks.
Extremely helpful
Glad to hear that my video was helpful.
You are doing Gods work! Could you please start a computer science series?
+Log Arithms, thanks for the compliment. Regarding computer science, I already have one video titled "Logic Gates from Transistors." Thanks.
i love this video.. thanks a lot god bless you.. please do more videos and try to make every abstract concepts easy like that
Beautiful and informative ..love it ❣❣
Thanks for the compliment.
@@EugeneKhutoryansky I follow your videos from 5 years🤩😍..keep up the good work !!❣❣
The best channel on yt!
Thanks for the compliment. I am glad you like my videos.
@@EugeneKhutoryansky You deserve much more popularity
Thanks.
Thank you so much, now it all makes sense where in class i just kept staring.
Glad my video was helpful.
Great video!
Thanks. I am glad you liked it.
wow this was very good thank you
Thanks. Glad you liked it.
nice dude
right before my midterms
+HakaTech, Thanks. Glad to hear that the video was in time for your midterms.
Sir Its the best thing on You tube.
Thanks
Thanks for the compliment.
I think it's a SHE :-)
Thank you so much,now I understand integration.
Glad my video was helpful. Thanks.
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Physics Videos by Eugene Khutoryansky Hello，I love your video very much. I'm from China, and I highly recommend you to upload
your video to bilibili, bilibili has a huge number of users in China. I suppose your video will be very popular at there. 3BLUE1BROWN has done that.
TH-cam is good，but most of us are still used to bilibili. Really hope you to come to bilibili. ^_^
That's awesome!!
I am glad you liked my video.