Calculus 3 Lecture 14.1: INTRODUCTION to Double Integrals (Background Info)
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- เผยแพร่เมื่อ 12 ก.ย. 2024
- Calculus 3 Lecture 14.1: INTRODUCTION to Double Integrals (Background Info): A lesson on where double integrals come from, what they represent, and how to understand them.
As an engineering undergrad, I'm impressed with the passion and the effort that you put into your lectures, as well as the sequential procedure that you take and the tiny details that you consider. Keep it up Sir!
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"I would be (upset) unless I gave you at least, like, two examples of how to actually use this."
That right there is the sign of a good lecturer.
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Got a Calc III midterm in 2 days. -A Canadian boy
how did you go?
Ahh yes. And two years later it is still just as great. I have a test in a few days as well. Friday night with a sixer and some Leonard.
Wow so you resort to legal activities I see🧐 can't relate
Hands down one of the best profs on YT. We appreciate you, Leonard!
That's Prof.Leonard to you
Professor Leonard, you're the greatest teacher I've ever come across. The world need more people like you. Thank you.
I just understood one of the most important concepts in calculus, this teacher is literally the best there is!
Professor Leonard,
your passion to actually make sense of calculus and allow us to have a deep understanding of the concepts has set off the infinite number of lightbulbs in my head. Thank you for everything and without a shadow of a doubt you are the best calculus teacher I have ever come across whether it be on youtube or live.
As an undergrad math major in cal III, you have made so much sense out of something my professor over-complicates and refuses to elaborate on. I can't be more grateful. Thank you for sharing your teaching ability! It's hard to find teachers that are as dedicated and truly put the effort into helping students understand.
some lecturers so good it makes you wanna teach people
Does this guy ever rip his shirt and leave in the middle of class?
+Kevin Hinojosa Only on Thursdays.... hahaha, jk.
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+asdsa dasdad Well, use double integral to calculate it!
Lolz wow do you get stares?????
@@ProfessorLeonard today is THURSDAY!!!!!!!!!!!!!!!!!!!!
0:00 -calc 1 def of reimann sums
10:35 - calc 3 def of reimann sums
34:26 - fuibinis theorum
35:18 - example
47:11 - intro to integrating over non rectangular regions
The way this professor explains shows his extent of knowledge and grasp on the subject. And the simplicity with which he explains adds to the depth and that is simply beautiful. Respect.
Professor Leonard: saving one and all undergrad failing grades all around the world. Thank you! I've never seen anyone so passionate about math.
So i really enjoy math, and i'm currently working on my bachelors of education to become a math teacher (hopefully calc), and with you as my teacher I have aced calc 2 and i'm about to ace calc 3, so thank you so much for that, but that's not the reason for my comment.
I do not attend my university lecture and instead follow along with your videos playing at 2X speed. Works just fine for me, and i really love how you get super into the "main point" portions of lecture at the end of a long description. Well, because of this enthusiasm, at 26:55, you're about to finish the intro to double integrals, and you get really excited and make a comment on how squeaky your voice got, and wow was it hilarious at double the speed. Just wanted to say that because i had to pause for a while so i could stop laughing and pay attention again.
You're the man Mr. Leonard, I really appreciate all these and you're definitely someone i look up to when imagining my future teaching career.
- An aspiring calculus teacher
hows everything going in terms of being a calc teacher so far?
@@Jacob-kc9ct hows life in general
Why is he particularly witty during this lecture? I was laughing the whole time
Extra coffee that day ;)
Noticed a lot of the comments are old.. just wanted to let you know you're saving my Online Calc 3 grade in 2020! :)
"Listen carefully, I don't wanna lose you now you've seen too much. You have to learn all of it." hahaha this really injected some energy to the lesson.
Just to add : thanks very much for the commitment and efforts at making math , calculus , etc easier, more accessible, interesting and fun .
I avoided it in lower secondary,struggled but failed it in high school,struggled through it in college , but now thanks to instructors like you, I'm learning more math , better , and learning it easier .
Math is still very material and relevant to me and I need to have a stronger foundation and better recall -because I'm continuing in my lifelong learning in social science and more post-graduate programs.
Thanks again.
Incredible Professor Leonard! I love the calc 1 and 3 side-to-side comparisons (clearing up the confusion). Cannot thank you more for letting us understand the concepts of double integrals in less than 30 minutes!
I applaud you for your amazing teaching ability and passion for calculus! Thank you so much I actually understand double integrals now :D
I'm screwed for the final, but due to your lecture, I'm less screwed...
lol
What happened to you after 6 years 😂😂
@@Salamanca-joro LMAO I actually passed the final and now i’m an electrical engineer! Was working at Amazon AWS and now layed-off and prob gonna go back for my masters. So now I must rewatch and relearn this horror…
@@shasterdhari haha glad to hear that you are doing good! I am in my first year of college taking this at calculus 2 so I had to check on people in the comments after 8 years 😂! Wish me luck 🙌
I needed a calculus refresher, and this is AWESOME! I sort-of learned how to do double integrals long ago, but never this way. Thank you, Prof. Leonard!
I just finished math last semester wouldn't have gotten all A's without you Prof Leonard you're really the goat. Can't even put into words the impact these lessons had on me. Got mad respect for you and i rock my "professor Leonard believes in you shirt" with a lot of pride.
Lectures like this one make me more and more attracted by math. I have successfully understood the concept of integral and why it works thanks to you, Leonard!
Best of luck!
-CS undergrad
This dude legit has kermit the frog in his class. And apparently Kermit is the only one paying attention.
I thought of Stitch
I also thought of Adam Driver haha
You know, you look like Clark Kent but you really are Superman when doing these videos… your secret identity has been exposed! Thank you so very much for this! Greatly appreciated!😃😃😃
Lecture Content
(0:00) Calculus I Background Knowledge to Understand for Double Integrals [Theory]
(9:40- 36:00) Introduction to Double Integrals [Theory]
(36:00 - 47:00) Volume Under a Surface Bounded by a Rectangular Region (using finite m & n values) [Example]
(47:00 - 52:00) What About Non-Rectangular Regions? [Theory]
Prof Leonard can you upload the assignment and notes of course.
Damn that would have been amazing..
Professor Leonard, thank you for an awesome video/lecture on the Introduction to Double Integrals in Multivariable Calculus. The theory and background on Double Integrals are helpful for a full interpretation and understanding. From watching this short video, I understand Double Integrals and its development in Calculus. Many problems in Electromagnetics Theory use Double Integrals.
I mean your lectures are just amazing but my freaking uni is giving us calculus 1,2and3in the same semester and I swear to god i am not kidding
And tomorrow is the final like literally the shittest uni on earth
That's crazy!!
same 0:
I'm loving this timing, just in time for me to brush up on the last few bits before finals begin. I hope to possibly see a little bit on triple integrals and separable differential equations just so I can see how you go through it. Cheers Superman, you're the best
I've totally been converted. 10 videos ago, I was dreading watching all these videos to catch up on my poor maths. Now, at 11:30 when he says "Thats cool!" I couldn't be more excited with him!
Hi! Sir I am Jawad from Pakistan. I really like your way of teaching. It's really very great. You explain every topic very well. God bless you Sir.
Hmmmmm, no math background needed to follow Prof. Leonard Calculus 3 Double Integrals Course. He is that good!
The embodiment of a Calc god. I cry not having such a math driven professor who motivates students in calculus. If only there were a professor Leonard for Physics 2 😭.
I wish I have Professor Leonard as my Calc 3 Professor. I'm failing calc 3 now as my university professor sucks at explaining anything.
Thank you Prof Leonard,
- CS Major Undergrad
you are THE PROFESSOR
The intro to this video is so good, I want to cry right now at how he makes the hardest part of early calculus ACTUALLY MAKE SENSE. #mindblown
hands down one of the best lectures i have ever heard. explaying everything very easily!
I gotta say I never actually got the explanation of dividing up the interval into infintesimal slices and taking the limit of those until calc III
so happy you have these videos up, this was my favorite undergrad math class
I have watched your video for two years, and for the first time your student asked for a question. You are amazing!!!!!!!!!!!!!!
Thank you so much for your clarity in describing these lectures. I am currently in this course at another university and our lectures are about 16 minutes long - just a few sample problems. It's not enough information for me. Thank you for describing the theory and connections so that I can visualize the math. Fantastic! Thank you for sharing your talents!
Professor Johhny Bravo. Best ever
Most videos tell you how to do a double integral but not why it works. This covered it beautifully. Thank you very much!
PROFESSOR LEONARD IS PROBABLY THE BEST CALCULUS TEACHER IN THE WORLD. YOU DO A FANTASTIC JOB AND THAT IS AN UNDERSTATEMENT.
I will do anything you want me to. You helped me a lot, I couldn't have gotten my assoicate degree in math without you. Now I'm working towards a B.A. in Computer Science, thanks a lot for everything.
Greate teching man.. you are so good to explain thing to ur students.. Im envying them really... wish your were my teacher at university :(
crazy how he got me past precalc, calc 1 , calc 2 and now calc 3
Whatta character!!! A most excellent teacher! Wished I had him during my calculus classes way back when ~
How splendidly you have explained the quintessence of ∫ and dx !
You've explained the "kernel of integration and derivation" and what it "actually" represents!
Thank you~
You really are great! You helping me so much in preparing my calculus exam. A lot of love from Rome, Italy! :D
Damn, that made beautifully perfect sense, compared to my current professor using slideshows and shot gunning the whole solution and using a mouse cursor to explain things. Thank you for understanding your craft so well that you’re able to break it down into something that actually makes sense even while still using abstract concepts of arbitrary points and infinitely small deltas of x and y. I feel like I have a better grasp on not only double integrals, but just integrals in general. Thank you for being an excellent teacher sir. It’s 1 in the morning, so I’ll finish the rest of this video tomorrow lol.
Wow, I passed calc 1 and I thought I knew what integration was, but I had no idea. I had to watch a lecture on double integrals to really understand intergration.
my mind has been blown
One of the most underrated channel's on TH-cam
Hey! Thanks for your classes and help a lot. Are you going to upload the next double integral videos? You are the best!
got my first college calc 3 exam in the morning. Thanks for the help, prof.
I solely learn from the textbook, but this lecture was spot on! Bravo!
Thank you so much! I am taking cal 3. You are the best professor !
thank you again leonard!!! i made a 20 on my first exam before i started watching your videos. On my most recent I made a 100
I just stopped the video to comment. This is just a fantastic explanation... Hands down. Excellent professor! Europe engineering student here!
IM a 4th year engineering student and this is the first time i know where the integration came from or even what it is
This is the essence of Math!! Bravo et merci beaucoup!!
You saved a suicide of an engineering student coz of math !
Finals again, so glad Professor Leonard still has lectures that I need
sir I was never, able understand what double integral actually meant, sir u made it clear sir u r living god on this earth for me thanks a lot.
Thank you very much for the videos. You are amazing at teaching. Im skipping my own lectures and study off of your videos! thank you again.
you are the Xavier of the ∆X-men. saving the world one lecture at a time
Really it helped me a lot bro
Simply awesome sir,
U derivated that from its root,
I mean points .
I think it is what we should know before getting into integration.
Fantastic sir
amazing and surprising. I wonder your, my dear professor
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great teacher with great teaching skill
Havent started calc 3 yet but i feel after watching all these lectures its going to be a piece of cake :>
Professor Leonard is a legend!!
You made my day. Thank you professor. Lots of love.
IS ANYONE GOING TO TALK ABOUT HOW HE CRACKED HIS KNUCKLES AT 29:03??? THAT WAS SICK!!!
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wrong button pressed. We as human are prone to err
tyler romero Dog?
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Did Superman get a day job?
This teacher does not want to leave students behind - I am shouting out tghe answers - sometimes the wrong ones. So many teachers don't care or don't know how to do this!
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Thank you very much professor Leonard, Very helpful for me, Super Math Pro!
Big fun to learn from Prof. Leonard. Thanks! )
sir your teaching techniques are great I understood everything😇thank u
thanks to you I never care about my math2011 lecture and you will carry me to A range
Very important Fubini theorem 34:18
The more I integrate the more excited I get !
Hey Leonard, do you have any channel on workouts? M a lifter too... u r awesome!!!
What is the success rate of your class? How many students take this course, and how many pass with a C or better? I'd like to know because you're a great professor, and I want to see if it shows in the statistics
+potato psoas
Actually it depends a lot on the teacher as well, because a good teacher will be much better at helping the students, which obviously would make it easier for them to pass that course.
Big Thanks Professor Leonard.
This is a really great video. Thanks again.
This is the ATHLEANX of Calculus
Thank you very much for this....I had this being solved without knowing the reason behind solving it....
who wouldn't pay attention with this legend as their professor?
Cool, calm and collected. 😎
Hello, Prof Leonard!
What type of book are you using for Calculus? Thanks in advance.
Jimmy Stewart's Calculus Book, subtitled "Early Transcendentals".