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!

"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.

Nothing like cracking open a cold one and watching some Professor Leonard.... Ahhhh. Got a Calc III midterm in 2 days. -A Canadian boy

Hands down one of the best profs on YT. We appreciate you, Leonard!

Professor Leonard, you're the greatest teacher I've ever come across. The world need more people like you. Thank you.

some lecturers so good it makes you wanna teach people

I just understood one of the most important concepts in calculus, this teacher is literally the best there is!

Does this guy ever rip his shirt and leave in the middle of class?

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.

Professor Leonard: saving one and all undergrad failing grades all around the world. Thank you! I've never seen anyone so passionate about math.

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.

Why is he particularly witty during this lecture? I was laughing the whole time

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!

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.

Noticed a lot of the comments are old.. just wanted to let you know you're saving my Online Calc 3 grade in 2020! :)

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!

"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.

I applaud you for your amazing teaching ability and passion for calculus! Thank you so much I actually understand double integrals now :D

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.

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

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

This dude legit has kermit the frog in his class. And apparently Kermit is the only one paying attention.

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

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

I'm screwed for the final, but due to your lecture, I'm less screwed...

hands down one of the best lectures i have ever heard. explaying everything very easily!

Whatta character!!! A most excellent teacher! Wished I had him during my calculus classes way back when ~

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.

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!

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!😃😃😃

Most videos tell you how to do a double integral but not why it works. This covered it beautifully. Thank you very much!

I have watched your video for two years, and for the first time your student asked for a question. You are amazing!!!!!!!!!!!!!!

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 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

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~

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!

Hmmmmm, no math background needed to follow Prof. Leonard Calculus 3 Double Integrals Course. He is that good!

got my first college calc 3 exam in the morning. Thanks for the help, prof.

You really are great! You helping me so much in preparing my calculus exam. A lot of love from Rome, Italy! :D

Thank you so much! I am taking cal 3. You are the best professor !

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

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.

you are THE PROFESSOR

This is the essence of Math!! Bravo et merci beaucoup!!

Professor Johhny Bravo. Best ever

Finals again, so glad Professor Leonard still has lectures that I need

I solely learn from the textbook, but this lecture was spot on! Bravo!

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.

انت مبدع يا ليونارد

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

PROFESSOR LEONARD IS PROBABLY THE BEST CALCULUS TEACHER IN THE WORLD. YOU DO A FANTASTIC JOB AND THAT IS AN UNDERSTATEMENT.

Big fun to learn from Prof. Leonard. Thanks! )

thank you Prof Leonard! you are a life saver

Thank you very much professor Leonard, Very helpful for me, Super Math Pro!

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.

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.

I love this guy.... You are saving my life...

This is a really great video. Thanks again.

professor leonard..i love you..you really simplified maths for me

crazy how he got me past precalc, calc 1 , calc 2 and now calc 3

Havent started calc 3 yet but i feel after watching all these lectures its going to be a piece of cake :>

This guy deserves a medal💗

One of the most underrated channel's on KZfaq

You made my day. Thank you professor. Lots of love.

amazing and surprising. I wonder your, my dear professor

you are a gift from the math gods

Thank you very much for this....I had this being solved without knowing the reason behind solving it....

sir your teaching techniques are great I understood everything😇thank u

great teacher with great teaching skill

Greate teching man.. you are so good to explain thing to ur students.. Im envying them really... wish your were my teacher at university :(

Hey! Thanks for your classes and help a lot. Are you going to upload the next double integral videos? You are the best!

Big Thanks Professor Leonard.

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

You are a blessing. Thank you

thanks to you I never care about my math2011 lecture and you will carry me to A range

my mind has been blown

IM a 4th year engineering student and this is the first time i know where the integration came from or even what it is

Thank you very much for the video!

GOOD JOB!

Prof Leonard can you upload the assignment and notes of course.

Professor Leonard is a legend!!

Really it helped me a lot bro

Awesome, thanks Leonard!

The more I integrate the more excited I get !

you are the Xavier of the ∆X-men. saving the world one lecture at a time

Thank you so much Prof!

Fantastic professor.

This dude is the best!

Thank you Mr Professor...:)

Cool, calm and collected. 😎

i love this class!

Damn this guy is good and thanks (From INDIA).

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]

I just stopped the video to comment. This is just a fantastic explanation... Hands down. Excellent professor! Europe engineering student here!

You are awesome man

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

IS ANYONE GOING TO TALK ABOUT HOW HE CRACKED HIS KNUCKLES AT 29:03??? THAT WAS SICK!!!

please upload more videos i have been struggling with my second year calculus without your videos,can we have double over polar as well.