Calculus 3 Lecture 14.1: INTRODUCTION to Double Integrals (Background Info)

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.

[abdullaalawadhi]

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!

[Fidonese]

"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.

[marbrydav]

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

[biscaynebuckets]

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

[mohammd]

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

[LightskinLordandSaviour]

some lecturers so good it makes you wanna teach people

[seoexperimentations]

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

[Mrkevi]

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

[azwadrahman]

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.

[khizarpasha]

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

[madisonharp]

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.

[marwa]

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

[vickrdable]

Why is he particularly witty during this lecture? I was laughing the whole time <3

[generativeresearch]

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.

[lukeauslender]

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

[mzukisimakaluza]

"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.

[blakehill]

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

[varrien]

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.

[shasterdhari]

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

[ZackSussmanMusic]

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