Double and Triple Integrals
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- Опубліковано 20 сер 2019
- Remember the good old calculus days, and all that time we spent with integration? Let's go back! Oh calm down, it wasn't that bad. Besides, we won't be learning anything terribly new, we will just look at double integrals and triple integrals, which are pretty much the same as single integrals, we just integrate more than once. But admittedly it can be a little tricky to set up the bounds of integration and choose the order in which we integrate each variable, so let's go through the rules and some examples.
Script by Howard Whittle
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You are such a great teacher.
And I like how you use "we" instead of "you". Makes the student feel like they are not alone.
I think it's great because even the professors still are students at the end of the day, because everyone is still learning more about their subjects.
Best teachers so far: 3blue1brown and Professor Dave.
You seriously wouldnt count sal or Patrickjmt?
Blackpenredpen
Professor Leonard is the best for me, by far
Zach star
For me, the best teachers so far are: Professor Gross, from MIT OCW Calculus Revisited, 3blue1brown, and Professor Dave
I was struggling a lot on understanding double integrals on a homework assignment, but this helped massively. Thanks Dave!
Blessings upon you, Dave. Two minutes in and you’ve already made this make more sense than my instructor.
this is the clearest explaining math video i've ever watched
Brilliant , wish I had this when I did maths so much clearer and simple, during lock down going though my old notes 30 years ago inspired me to study more
Professor Dave, thank you so much for these resources! They've been a huge help to me in ODELA and Vector Calc. I'd be lost without you!
So you can actually find the volume inside a tesseract niceees
its a hypervolume
@@kek3324 It's*
Jorge C. M. I can tell you have a lot of friends.
It’s just all the side lengths multiplied
You can find both, the volume and the hypervolume of a tesseract. Although I think it's more difficult to grasp the concept of the volume of a tesseract
This video is amazing. I’m self taught, going through Professor Leonard’s Calc 3 YT series course, and double and triple integrals are coming up in the very near future so I wanted to get a head start. This is totally logical and it just makes sense
Thanks, I checked out the series after seeing your comment. It is more suited to what I am looking for. Really appreciate it man.
Great explanation!
Of course, my inclination is still to hit it with a FOR loop...
Hi Dave, I got confused in the part choosing lower bound and upper bound between 2 cuves. Pls explain..
good job Dave, you have explained this to me in a most understandable way possible, with clear color indications, thank you sir.
Thank you, that was one of the most straightfoward explaination!
Thank you for the videos. They help a lot! I’ve had a mental block about these topics for decades.
This video is better than 1 hour of lecture. Tq very much
Was so thrilled when i did the double integral the other way from y/2 to (y)^1/2 and got the same answer! strangely that way took up less paper. Thanks for the solid content!
Really nice ... So clear concept.... Thank you professor Dave
Thank you for the subtitles in English! It makes it much easier to follow-up.
You're an excellent teacher, you truly are. I survived 1st year of engineering with your help. It would be nice if you can make videos on differential equations 😅
I've finally done it. Thanks for your help, my good sir. I'm a lot more confident now.
wow i didnt expect integrals to have this much depth to them... how can you not love math, omg
great video btw :)
Nice work... You deserve a big big big thanks... Go ahead Dave brother
I have a test tomorrow, and your video really helped me to understand integration more deeply. Thanks from Russia!
A video masterpiece. Grateful for the illustrations, painted a clearer picture in my mind...
Thank you so much! I really appreciate this as we don't get taught a lot of concepts and underlying principles in math, so this just makes the subject so much more interesting. :)
Thanks Dave, you are a wonderful professor!👍
Thats the most outstanding explanation I ever got. Thank you so much!
that is amazing how clear you was
This is probably the best that this video could possibly have been made.
Great Visualization of the figure formed by double integration
Loved it !!
Man I’m trying to learn first calculus, I was recommended this from a friend in the math field to help, it seems a bit to daunting, I wish I was I just good at math and actually understood what he is talking about most of the time
Start the calculus playlist from the very beginning and all will make sense!
Thanks so much for a clear presentation.
A learner from Tanzania,🤝you are a good teacher ❤
You're the E of the mc²! Great lecture. Congrats.
awesome vid thanks im a fresher ive jusst started self learning ths topic ths will help wth understanding
You are a GENIUS...Such a relief to finally understand the bounds depending on variables... thanks for your hardwork really appreciate it
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Professor Dave is the best...thank you very much!!!!
Danke sehr!!!
🎊 beste Erklärung! Mit Abbildungen, klar und deutlich.
❤❤❤❤❤
Oh my god, thank you so much for this video. The videos that I get for my class gave me an example where both y and x's bounds were 1 so I didn't understand how she was doing it.
Great video. Even though I only did high school calculus I could still follow what he is saying.
We have a calc quiz tomorrow and this video sure helps, Thanks!
no word to explain your efforts may God reward this
Thanks for making calculus fun and interesting
Thank you so much, Dave! You are and always have been a lifesaver.
Great thought and too clear fellow style, I apricate your way of explains
whenever my dad checks up on me if im doing work, i just pull up your videos and he doesnt question it! thank you :D
Integrals are tight. You made it look super easy, barely an inconvenience.
Wow that was easier then expected. Thank you for explaining it well.
Hi Professor Dave.
I have a request that you may find interesting or not, it’s a mathematical one. I have always found it hard to understand “Inter-universal Teichmüller theory”, “The Collatz Conjecture”, and “The Birch and Swinnerton-Dyer Conjecture”. If you would make a video on one of these topics that would really help 😊
I’m studying a Master’s in mathematics in Denmark. I’m sorry for my English, I’m not mothertongue in English.
Btw, I love your content.
Good Job, Thanks for Sharing
blessings upon you, Dave.
Can you do a video on Green's, Stokes' and Gauss' Theorems?
Could you send me notes of divergence theorem ?
Millie all three of those are filmed, animated, uploaded, and to be released very soon!
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20UPH512_Geo Raphael Michael
What was lulu’s comment about?
@@GeoRaphaelMichael
*_Bruh, what_*
Why is the y integral from x^2 to 2x and not 2x to x^2?
Lower relative to y
Sir you are awesome ,I love your explanation method. 😇😇😇
Thanks so much! I never understood this in my Engineering lectures, now it makes sense.
Hi Rosal.can I know is this thing involve I'm grade 12 or higher grade .Because I'm going to do engineering too. Currently grade 12
OsJ I’m not sure, I studied this in university.
so helpful cheers Dave
Thank you sm genuinely
cool teacher, straight to the point
Best explanation around. Though im still struggling to understand how taking the integral of the x-y plane in two different ways gives volume. So the area under the curve given from the first integral just happens to also equal the volume?
I wish i had u as my teacher during my btech...
love you professor dave
“Performing multiple integrations is not all that daunting, on the SURFACE!!” Haha
Wonderful video.
I thank you dear sir for mentoring me . 🙏
Very well explained..
Finally I understand the sense behind these
In the first comprehension, when we move from 2 to 3 in x,then y=x+1 is lower to 2x . Why we consider here limit in y from 2x to (x+1)?
He does know all about science stuff......... professor Dave Explains ❤️❤️❤️🔥🔥🔥. I Love this😎
Amazing video!
💥👌Nice explanation 💥👌☺️🤗
Thanks very useful and understandable
Nice explaination
I still don't understand why someone can dislike a video like this :( You are incredible!
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Hey dave can you graph this function in 3D f(x,y)=xy/(x^2-y^2) around the point(0,0)
Brilliant! Thanks :)
1:37 I think there are counterexamples to that statement, but it works in general.
Could you tell pls
very good , thanks !
Thank you so much
Thank you very much.
WOW !! THANK YOU VERY VERY MUCH !!
Great teacher
Just keep it up professor!🥳🥳🥳
Dave the man!
Highly informative lecture. Thanks Professor . In 7.31 , how did you the get function f(x,y)? will you please explain?
annnnnnnnnnnnnnd you have a new sub/ bingewatcher
Great video
I have a question please
For the upper and lower bounds isn't the x² greater than 2x and why didn't it get placed at the upper bound instead?.
Thank you sir
If you look at f(x,y) = 1+ 4xy example, if you just look at solid by itself and compute volume without using complex integration, for x = 1 (1-0), y = 2, (3-1), and z = 1 + (4*1*2) = 9, I get a volume of 1*2*9=18. Where did I got wrong?
You the man, man!
14:30 The first example on the Checking comprehension is wrong: the internal integral boundaries should be from x+1 to 2x
I thought that double integrals give the area of the surface of a function and triple integrals the volume of a function respectively
Και εγώ ρε φίλε,έτσι δεν λέει και ο γκαρουτσος? 😂
Thanks a lot sir....
hello can explain how you take x^2 as the lowest value for a integral and another integral.
what makes them the upper value on y and lowest value on x ?can you make it more clear cause i tried to find why but still cant find out .
At first i thought it was cause the 2x function was above the x^2 from 0 to 2.
thanks you
You're right, depends on the sign. Solve sqrt(y) >= y/2, it's true on [0; 4].
Thanks Great Video
at 07:12 , how do you say that y runs from the lower curve to upper curve? sir i cant understand that point
I consider the view count on this an insult. And an even greater one, that 52 people dare dislike it. Dave, your videos are amazing.
oh men i wish i knew you back when i was taking Applied maths 2 in college
It's an excellent explation.
hi professor dave, in 4:00 you said 10 is the volume under that given example surface, why does it considered "under" not "above"?