Calculus 3 Lecture 14.3: Double Integrals over POLAR REGIONS

Calculus 3 Lecture 14.3: Double Integrals over POLAR REGIONS: How to perform Double Integrals over regions using Polar Coordinates/Equations. How to translate Rectangular Double integrals into Polar Double integrals.

[learningleopard]

Ignore this. It's for myself but use it if you find it useful. :D
Intro to double integrals over polar regions~ 0:00
Volume over polar region examples~ 22:45
Ex. 1~ 23:55
Ex. 2~ 42:15
Ex. 3~ 53:50
Ex. 4~ 1:03:00
Ex. 5~ 1:23:41
Side note about theta not always being from 0 to 2pi~ 1:34:51
Example of polar region where theta is not from 0 to 2pi~ 1:38:00
Explanation of how to determine theta bounds carefully~ 1:46:10
Volume between two surfaces~ 1:59:04
How area can be represented by volume~ 2:37:17
Ex. 1- (Area of region bounded by one polar function)~ 2:42:17 (choosing theta bounds~ 2:47:16)
Ex. 2- (Area of region bounded by two polar functions)~ 2:53:28
More volumes in polar form~ 3:01:03 (choosing theta bounds~ 3:07:59)
Volume using polar coordinates on a rectangular region~ 3:16:19 (used when function (integrand) inside is difficult)

[usarmy]

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[siddheshss]

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[bronation]

I pay money to take multi and just watching Professor Leonard's lectures for free online. This man deserves a portion of every university's tuition for teaching the entire nation's students upper division math.

[malloryakikonoramiller]

I will literally set up a kickstarter campaign for Professor Leonard to upload Dif Eq videos...who's with me?! :D

[frankq]

Honestly this professor teaches multi variable so much better than my professor at duke. But i guess its because we are trying to cover the same thing by less than half of the time

[garrett.]

Shoutout to everyone out there with me paying university tuition just to end up doing all of the best learning through this guy.

[alexgu]

Professor Leonard. omg, today I had my exam on this chapter. I went through all your lectures. Did your problems over and over. And today that i had my exam, I feel I was able to do all the problems. I feel confident. I dont know my grade yet. But thank you so so so much.I feel like i learned with you. Youre the best!

[bbd]

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[Peter_]

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Seriously.

[monsterjonster]

I need to send this man flowers and a package of tight t-shirts. Saving my ass Cal I-Cal III. Much love <3

[mattrhoades]

1:46:15 Anyone else agree that the Theta Limits are -pi/2 to pi/2 instead of 0 to pi. It does work out to same answer of 9*pi

[TheSetegn]

This professor is amazing.I impressed with his way of explanation. I clapped my hand whenever he explains things in simpler terms. I learn not only maths but also how to teach math artistically. Thanks so much professor for offering us for free.

[Jared-Cruz]

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[lupekale]

I love how he says that he wants us to solve for the integral on our own and then he picks up his marker and solves the problem for us. Leonard, you are amazing! THANK YOU!

[Adrian]

13:38 "Take your ZONE-IN pills... I don't even know what those are" He tried playing off like he doesn't know what aderall is

[Tuggernutz]

I hope these videos last forever, I cannot express the amount of gratitude i have for you making these videos and the impact they have. You have answered all the questions I had that my teacher was unable to convey clearly to me. Thank you so much for these videos!

[epistemophilicmetalhead]

x=r*cos(theta) and y=r*sin(theta). r first, then theta. dA is gonna be r*dr*d(theta)
circle involved? use polar.
43:00
50:40
***1:05:00 (sum of squares)
***1:22:10
be careful with theta. 0-2pi doesn't always give you the area of the circle exactly once
***1:39:00
1:59:00 => to find volume between two curves f1&f2, you gotta find area trapped between them. this can be determined if you know where they intersect. f1(one on top) - f2(one below) [sub a point in the relevant region and find out which one has greater value]
2:15:40
<3 volume = area when h=1
2:42:45
2:53:47
3:03:07
***3:16:40 (in bounds for inner and outer rectangular coordinates, sub polar coordinates for x and y and you get new bounds)

[thepontlessproject]

Anyone else listening at 1.5-2 speed to try to get through more lectures faster

[xwounded]

I honestly don't know why I'm watching this, I'm majoring in computer science I have nothing to do with this but his way of explaining grabbed my attention tbh.
Good luck to anyone who takes calculus 🙏🙏