Calculus 3 Lecture 14.2: How to Solve Double/Repeated/Iterated Integrals
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- čas přidán 15. 04. 2016
- Calculus 3 Lecture 14.2: How to Solve Double/Repeated/Iterated Integrals: The techniques of solving Double Integrals with a focus on how to construct a double integral over a given region.
I am a 56-year-old person with an MFA. My dream was to become an astrophysicist, but during my teens, my math teachers were awful. I was traumatized. Fast forward 45 years later, Prof Leonard came 😀into the grand scheme of things, and now I aim to apply to MIT for my degree in theoretical physics. I teach myself and never tire of watching this guy teach us new tricks. Thank you!
extremely happy for you dude
Man I’m 33 pursuing a degree in physics. I’m in Cal 3 right now and it’s nice to know I’m not the only older person trying to do something like this so late. 🤙🏼
@@gp873 never too late for anything bro, life is full of opportunities and you cant get every 1 all the time
ur real motivation for everyone
thats sick sir good for you!
I keep getting ads from a guy with a heavy accent asking if the Math video from 1996 is REALLY helping.
1: It's math. It's not like it drastically changes.
2: CZcams was created in 2005, so, no, the mythical 1996 mathematics videos aren't helping.
3: The video your ad is on right now is a mathematics video posted in 2016.
4: Yes, it is helping immensely as a matter of fact.
Very glad my videos are helping :)
Professor Leonard are you gonna ever do differential equations?
I just can’t stand them disrespecting Professor Leonard like that! Yeah I don’t need math help Professor Leonard has it handled!
It's math. It's not like it ever changes! :)
I’m getting the same ads but they say “from 2006” not 1996, they’re just marketing at different segments lmao
If these students can't stay awake for Professor Leonard, they'd be in full-on comas with my Multivariable professor
This comment made my day!
To be fair, it's a 3 hour lecture.
Mallory Akiko Nora Miller ☺️☺️☺️☺️☺️☺️☺️☺️ you said it right
Actually, it does last 3 hours because sometime he would use up his 3 hours of time in the last video/section. You know this when sometimes his cloth from the last video is the same at the beginning of the following video. Until 3 hours pass, he cuts the video wear new cloth meaning is the next day.
Same here, mine did all of this (including polar coordinates) in 2 hours, and he looks angry all the time, mutters and barely interacts with the class. So boring. Leonard is like a God in comparison
This is the first time I've commented on a video and I believe I speak for a lot of people who watch your videos, that many if not all really appreciate what you do. From the passion and knowledge you possess in teaching this course, you're really able to target students weaknesses by not only providing a complete coverage of the course theory but also little tips and tricks along the way that I know comes from years of experience. I'm beyond thankful that you're able to teach beyond your classroom and hope you can take feedback like this to motivate you to keep going.
Thanks very much! And yes, it does motivate me :)
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@@ProfessorLeonard I know this reply was 5 years ago, and the video was posted 7 years ago, but, you are the best calculus professor in the world. I pay a tutor 85$ an hour and yet you still manage to explain everything better than them. Thank you so much for your amazing lectures. You put so much effort and care to your teaching delivery methods. I'm truly grateful
@@chinmayaranebennur4117same goes as me ! I should have paid my tuition fee to professor Leonard instead of my university lecturer. Man I really wish he got to live the best life he deserves, what a great man!🙏🙏🙏
I don't know what the demographics of Prof Leonard's channel subscribers are, but I'm 32, was a graphic designer for almost 10 years and my last academic math lecture was 15 years ago. Remorse for not studying math caught up with me suddenly ~2 years ago and since then I have been investing most of my spare time in learning math from the ground up from Khan Academy and, starting from December 2017, from Professor Leonard.
Now the funny part is that Prof Leonard made such a strong impression on me, that inspired by his phenomenal eloquence in teaching, last month I quit my job (for real!) just to give myself a few months to properly watch all his videos (and trust me, people have a hard time wrapping their head around someone quitting their job in order to study math). Hopefully at the end of this journey I'll be able to pretend that somehow I received the education I dream of having received when I was young.
Thanks Prof Leonard!
Wow thats really awesome. Nice job man.
Horhew I wish you the best of luck man
How's it going for you now, man? I'm interested to hear!
@@Sai1ence I’m curious as well
You are awesome!
I am 31, graduated in humanities and always intensely disliked maths, but I also have a fascination for astronomy and cosmology. At 30 I decided I'll give maths another try. Started with pre-algebra on Khan Academy, found Pf. Leonard a few months ago. Taking notes of every single video - this is currently my 196th page of notes. This is awesome and one of the most incredible thing that ever happened to me.
Thank you professor Leonard.
More than half the people in my lecture don't show up to class and they just watch Professor Leonard instead
Its what I started doing in my current class lol
same
saaame
Almost all my math teachers have been those super-formal and boring types who have stood and mumbled theorems and proofs throughout the entire lectures and hardly given any example problems and never talked to the students.
Context: Integrating under regions. What is R, how to find R, and how to evaluate when not given R (how to find)
2:06 check f(x,y) is a surface.
3:10 doesn't matter which order you find under the region dx, or dy, still yields same area.
where R is the Rectangular Region, which remember is based on the change in X and Y which both have intervals. Thus.
a
3:01:05 Change of Order of Integration
I was told you're some kind of god
Good looking out homie!
Good job homie, good annotation skils
Thank god that I finally found a professor that doesn't assume that everyone in a calc iii lecture already understands how to set these integrals up... thanks for the great video!
If you were my lecture, I wouldn't even miss a single period of yours. Prof L you are the best and your videos a very helpful.
Professor Leonard your teachings impress me
Best calc teacher right here.
I would just like to say thank you for providing a resource like this. I was able to go from getting a 52% on my first exam to getting a 99% on my second (no joke). Hopefully this encourages some of you.
Thanks again!
Great job!
I took a few years off after doing terribly at college the first time. I started going back to college in the fall and now I am about to ace Calc III because of your videos. Thank you so much!
Great Job!! Keep up the good work :)
Hi. I just learned that i passed my calculus resit exam and now i will graduate. Thank you so much, i coulnt do without these videos.
I've never been this awake for a math class in my life, you're the best math prof!
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You should just be cloned and teach calc1-3 in every school world wide and all kids will understand and learn to the full potential oooooooooooooooooooooor they could just watch you channel :^)
but cloning would be cool, infinite supermans
2:33:10 Someone decides to play clash of clans. Busted.
Mateo Gonzalez yaaas I was looking for this comment!!!!
that was clash royal lol
@@imafraidyoumightbeinthegan3742 in 2016, clash of clans was much bigger than clash royale
@@vantaylor9533 The first note and instrument was from the Clash Royal opening.
it was clash royale xD
Usually I can't really watch long videos because I feel like I'm in a hurry but I feel so happy to watch this even though I'm doing last minute study. I understand so much more than the textbooks and my lecturers and I feel so interactive, responding and all. I look so crazy saying "yes", laughing and nodding my head to your videos but I'm so grateful to have a lecturer like you.
I don't know that you'll ever see this, but I just have to add to the many comments here saying how much you are helping me. My current Calc 3 professor has absolutely illegible handwriting and goes through the material too quickly for me to properly learn it.
At the time of writing, this video was uploaded 7 years ago, but it still continues to help students like me, and we all greatly appreciate it
Thank you sir. Spent exactly 6 hours taking notes with you. If anyone is just watching without taking notes I highly recommend taking notes, I've tried both and I found that I grasp the idea much better when I'm taking notes rather than just watching.
i did that for all calc 2 and i passed it with 99%
@@porque6815 really, a 99? You aced pretty much every exam? Holy W
It doubled the time to watch the lecture
I am a Yemeni student studying in China. I am very thankful to you Professor , your
videos helped me to be among the best in the class.
Professor Leonard, I just wanted to say thank you for doing these videos. I'm in Calculus III now, and I find your videos extremely helpful!
When he asks the class "raise your hand if you understand this" I put my hand up as if I was in class, and I answer his questions out loud. Anyone else?
+Deasert Fox i am also guilty
hahaha I'm also doing that :D
guilty
Yup
head nod if you understand what's happening here
I just wanted to say thank you for being a wonderful person and sharing your knowledge in such an articulate caring way. You are an amazing professor and have taught me everything I know about calc 1, calc 2, and now calc 3. I’m so so thankful for you and what you have done for me and many others. Keep up the amazing work, with your teacher this world will become a better place for all of us to enjoy.
Hey King Leonard could you film a linear algebra series one day?
And differential equations please!
+1
just keep waiting...
and waiting...
*waits and cries about differentials next semester without our youtube professor*
Your videos have honestly helped me SOO MUCH through my calculus 2 and 3 college classes. I love that you do not move on until you can tell your students are understanding. It is very difficult for me to keep up with my quarter system lectures so watching you're videos before doing my homework has been a great supplement. Thank you!
Please keep making videos!
Due to the pandemic we are doing online lectures as any other Uni, but the Calculus Class just isn't woeking for me personally. My professor did not explain how to set up the intergralls either, rather just gave it and expected us to simply know how to do it. When i asked them how to do it they gave me a very vague answer that didn't help at all. Thank your professor Leonard for uploading these videos back in 2016, you are helping me so much right now.
Thank You Professor Leonard! The way you explained the order of variables just made everything click! Our hero saves the day once again!!!
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That is the key teaching about your teaching is targeting and repeating the key concepts and again, so many repeat of the same KEY concepts that lead to the solution.
At a particular point going through your video, I believe if I was taught like this I would have had first class instead of second class upper.
I hope your students really understand the seriousness of how GOOD your classes are and they should all have at least 70% and above in your classes. I am really serious about this comment because it takes a SUPERMAN to explain the way you do.
keep safe Prof.
Love the way you teach! These lectures compelled me to write comment. All maths teacher should be like you!!!
I really thought I was an idiot for not understanding calc 3, but then I realized that my professor is not super great. You break down every concept in digestible chunks so well. Thank you!!!
Remote learning 2020-2021, never thought I would miss math classes so such. Thank you for making it seem almost like we're all in the room as well.
This is my first time commenting on a CZcams video. I personally thank Professor Leonard for all the effort he put in to teach this course in an excellent way that students could understand. Thanks again!
Math is fun ONLY if you have a great professor to teach it to make it clear. I wish I could meet you in person to say: thank you! Really helped more than I can express. Even after my Calc 3 class is done, I think I just want to rewatch all of your Calc 3 vids to catch the ah-ha moment that I've missed throughout the duration of my class at university. Thanks Professor Leonard for sharing your class with the rest of us!
I'm totally envious of these students. The enthusiasm and vibe with which Professor Leonard teaches is contagious. But, I'm grateful that he has provided this content to help others learn (and also I'm inspired to keep going to the gym as well (if you know what I mean) 🤣 )
Came back to say, it took 2 days to go through this and I actually feel like I've gained a good grasp of this subject. So much more confident; thank you!
As a math major, I just want to thank you so much for providing us free educational math videos. They’ve helped me so much. I was able to understand everything clearly and concisely. I’ve gotten the highest scores on all my exams so far and I’m going to get an A my calc 3 class because of you. So grateful for professor Leonard 🙏🏼
barely ever touched multivariable calculus in my life, 1hr 40mins in and i understand everything you explain. great teacher
Professor Leonard I cannot express how grateful I am to you, your videos really help me during my semester when I couldn't understand anything in my own class
Prof Leonard is literally the best calc lecturer I've ever come across! I'm an Engineering student from South Africa and these videos are pretty much what's keeping my calc grade afloat!!
Why is this guy such a life saver he really saved my life today men o men one day i would like to meet him!!!!
Absolutely Fantastic. The best Maths Lecturer EVER. Can't wait for your video on Linear or advanced Algebra. I honestly don't know how to thank you for all your effort and passion for teaching us this beautiful science. Thank you, Sir.
Honestly best Professor I have ever met online. I really felt like I was in the class. Great Job Sir!!
Professor Leonard thank you! I am only making it through Calc III because of you! Most of my classmates watch your videos too.
Professor Leonard you are an outstanding teacher! You have an uncanny ability to really help all of us in hard math and actually make it easy. Thanks a lot!
Handsome, Charismatic, Brilliant. Thank you so much professor Leonard for all you share with us. You've successfully gotten me through my Computer Engineering Bachelors. We need more people like you in this world.
Professor,
Your videos got me through calc 3 in SP2017 after about a 10 year hiatus from calculus. Last night I watched your double integral videos to prepare for a STAT 410 quiz today. The prof tried to mislead by setting up the integral in such a way that we weren't always integrating between the same two functions! Switched that up right away! Thanks for making sense of calc!
I feel like even if you're comfortable with the material, watching your videos will add so many golden tidbits that would otherwise go overlooked. Love the stuff!
What a chivalrous, gentile presentation of this material. In these covid19 times where we are isolated and having to teach ourselves; Sir, I solute you.
I try to watch the ads for their whole duration to support you professor. I think everybody should! You do a great job!!
Why in the world would anyone call it "poor notation" to explicitly write out the variables for the upper and lower bounds in the integrals?
That's PROPER notation!
It makes things as clear as possible, instead of being vague and annoying.
I actually can’t get over how much sense you make😭🥺😭 tempted to show this to my lecturer so she can take notes 💀
Once again, Prof Leonard, you have translated my instructor's condescending ego-stroke of a 50-minute lecture into a concise and accessible explanation. Bravo, sir.
Thank you for demystifying double integrals for us! By 28:00 into this video, I think I understand it well enough now to get my homework done. I am so grateful for this presenter's skill and style of presentation. He made it easy to understand.
I went to class, never understood anything, our teachers proves stuff with really dry proofs, then this guy explains perfectly. I started skiping class and watching all of leonard's videos. Now I love math and I also aced my first cal 3 exam. Thank you Leonard!
Amazing teacher, very much appreciated. Keep up the good work Professor Leonard.
Dr. Leonard, I just watched this full video and then sat down to do my double integral homework, and I just have to say thank you so so much! I even just had a 19 part problem asking for the bounds of the two integrals that you would get if you went in the x direction and the bounds of the one integral you get if you do the y direction first and I got every single part right the first try. You care so much, thank you!
OMG HOW ARE YOU SO GOOD?? THIS IS THE BEST MATH VIDEO I HAVE EVER SEEN, THANK YOU SO MUCH
i want to take the time and say thank you very much for your videos professor Leonard! i am currently taking calculus 3 and i have to say that i am learning more about vectors, partial derivatives, and now double integrals than my professor whom is teaching my class. you do an outstanding job explaining the information from the fundamental principals and thats what i enjoy most about your lectures. i can see that you truly care about your students. i wish my university had ten more like you! i appreciate your hard work, keep up the good work. i hope in the near future you can upload more lectures covering topics in Linear Algebra and Differential Equations.
Your colored line example was very helpful in conceptualizing how to set up integrals!
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I did nothing understand in class but now I feel confident. You're so clear when you are teaching. You answer my questions that are in my head when you teaching from distant. Thanks sir
You are THE BEST teacher that I have ever listened to, bless you prof and we really love you
if i didnt have my math exam in 1 hour this 3 hour video would single handedly save my gps. i will be watching EVERYTHING you have done for calc 3 and really hope it will hlep me learn and survive math this semester. thnak you
You are a fabulous teacher! Your explanations are the clearest I have ever seen.
The best calculus SERIES EVER CREATED!!!
I don't comment on videos often or ever really, but I just wanted to thank you for uploading your lectures. Your explanations are clear and make sense. Thank you again so much for uploading these videos.
I've been lost for days! I didn't know what to integrate first or which direction until he mentioned pic the one that does not change functions. I appreciate this!
I don't usually comment on videos but for you..you're the best Professor Leonard. You make maths so enjoyable !!!!
Thank you so much!
Your videos help us more than the real time lectures of professors at our universities. :)
when Professor Leonard says to his class "hey hey stop writing look at me for a sec", I feel extremely compelled to stop writing as well
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if one variable is dependent on the other, that's gonna be the inner variable [to realise that, draw the region]
if both variables lie in a constant range (one number to another), the inner variable will be the one wrt to which it's easier to evaluate the integral the first time
if you aren't clear on which one should be the lower and upper bound for the dependent variable, draw the region
2:39:52
in problems, replace the third variable (usually z) by f cause that's your function
sometimes you will have to forcefully change bounds cause you can't integrate easily [dx dy]
{going along dy is travelling parallel to y axis}
1:27:00 - 1:28:00
He took 1 min to explain what I didn't get in last whole lecture
Wow wow !! How brilliantly you explained ! Thank you for sharing these videos and save us from confusion
Thank you so much professor, you've made me love and understand Calculus III. You explain with such dedication and attention to details. Your classes are awesome!
You're the best professor on calculus!! Thanks for do what you do!
hi prof, you are the best one teaching calc.. we are watching you from UAE, Dubai
Thank you so much
Thanks for saving my calculus Professor Leonard, it wouldnt have been possible without you xD
Dude, professor Leonard you are awesome man. Your videos really supplement my calculus 3 class and help me fully understand the material. Been watching your stuff since Calculus 1
Because I wanted to get an AA in calculus, I'm in summer school and already got 100 and 97 from the first two exams and now studying for the final one. You're awesome Professor Leanord. Cannot wait for your diff class in the fall semester :)
I hold a PhD in plant genetics, and this video gave me already twice as much of all the years in the Univeristy.
Your lecture are amazing!! I'm able to teach my friends and actually explain in detail, thank you 👍🏽👍🏽👍🏽
Fabulous teacher. Thank you Professor Leonard!
I am simply amazed how you teach with so simplicity. You are my real superhero
I'm taking Calculus 3 right now. My professor does a decent job of teaching, but he lacks the visual detail that you give in your videos. I put off watching many of your lectures because of their length (I always play at 1.5 speed lol), but I was having a really tough time with double integrals. This really helped me understand how to set up the integrals. I can do integrals no problem. But setting up these integrals was so confusing to me because I had no visual understanding of what was happening. Thanks for this, and hopefully I can save my grade and pass Calc 3 this semester with your help! I especially look forward to watching your lectures on triple integrals in spherical regions. My professor just went over that and I was completely lost lol
I literally LOVE YOU. I am preparing my engineering exam in Rome, Italy.
lectures uploaded 6 years ago still these are the best lectures to learn calculus...............Very great and hard job Professor Leonard..
Thank you for making this so easy, I was struggling greatly prior to watching this.
this is the stuff...this is how an instructor should teach a double damn integrals...i was complaining about how can i learn them and i learned them in 3 hours...thank you prof. you are the best!!
Hey thanks for the help! Finally no longer struggling :) exam is tomorrow and you've done me such a huge favour
you have born to be a perfect teacher ever. ımtelling u that this teaching is talent!!!
sir you nailed it .....i have watched over 6 videos on double integrals but this one teaches us all stuff on Double integrals...Thank you so much to upload such a video...love from Pakistan ❣️
Hey Professor, I am glad that I found you🙏🏼
you're an incredible lecturer professor Leonard,,,, thanks for your lectures
I hope that you make videos for those sections during the next 5 weeks.
1-Vector Fields->Vector and Scalar Fields- Consevative Fields - Line integrals - Surface and surface integrals - Oriented Surfaces and Flux integrals.
2-Vector Calculus->Gradient, Divergence and Curl-Green's Theorem in the Plane - The Divergence Theorem in 3 space - Stocks's Theorem - Orthogonal Curvilinear Coordinates.
Thanks a lot :) Professor Leonard
+Josef X yep!
Professor Leonard, thank you for a powerful analysis of knowledge on How to Solve Double/Repeated/ Iterated Integrals in Multivariable Calculus. This material is difficult to comprehend , however from doing problems and examples drastically improve my overall understanding of the subject. Putting x and y equals on the limits of integration is something that should help all students and non students.
I realize I've been given the God sent gift of someone finally putting calculus 3 into Lamon's terms but I do have one more request: can someone PLEASE post time stamps to these videos because that would make navigating these videos so much easier.
You put my lecturer to shame, never properly understood Double Intergrals till I watched this! Thank you!
thanks professor, i wasn't understanding the changing of dy to dx and vice versa, now understand perfectly :)
Thanks man, you are the only reason for my B.
OMG i wish u were my lecturer, awesome, thanks so much for share ur knowledge with us its helping me a lot!!
Big up from Panama
Great explaination sir, really loved it.