Calculus 3 Lecture 14.3: Double Integrals over POLAR REGIONS
Vložit
- čas přidán 20. 04. 2016
- 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.
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)
Thank you so much I did not want to spend hours skimming for one part
On
L'n'I'll ô.o'l''l'
O'
O'
"some of you guys arent even watching" these kids taking the legend for granted :(
maybe some students love to study in relax mode rather than in class
These lessons may be long, but they are such high quality. People pay money to get these lessons elsewhere. Thank you so much for making these lessons available for everyone! you saved my grade in cal 3.
there is an ad starts like "are you searching youtube for math help? from 2008 videos reeaaaaallyy?" and I was like bitch this is professor leonard, 2008 or 3008 doesn't matter for him, ppl will talk about this legend for generations :D
shin akuma I got annoyed by that ad as well.
These lessons are long because they are incorrect. The extra r makes it physically impossible for a double integral to return an area^2. I wish professor Leonard would not continue to try to justify this misinformation. I am used to seeing stuff that is wrong and figuring it out from getting my degree in Biochemistry.
These lessons are long because they are incorrect. The extra r makes it physically impossible for a double integral to return an area^2. I wish professor Leonard would not continue to try to justify this misinformation. I am used to seeing stuff that is wrong and figuring it out from doing research for my degree in Biochemistry.
@@TheFarmanimalfriend what? look up the actual proof of polar integration and you'll still see the extra r.
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.
Not just the nation, the entire world.
Even here in India, even understandable of a 15 yr old like me.
T
AGREE!!!
Ubiobboiobjbjob Hhhhh ohjjjjjj I’m so excited about you guys so I don’t
Iiiiiio I uuu. 😊ao
I will literally set up a kickstarter campaign for Professor Leonard to upload Dif Eq videos...who's with me?! :D
I will be starting diff eq next semester... Lets make it happen!!
agreed!!
I'd chip in :)
make it so
You can support him on Patreon. He needs a two thousand dollars per month goal to make it happen -
www.patreon.com/ProfessorLeonard
Shoutout to everyone out there with me paying university tuition just to end up doing all of the best learning through this guy.
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
Still, this lecture is so helpful to me.
same problem here!! great professor, but we only get 3 hours a week...
I need to send this man flowers and a package of tight t-shirts. Saving my ass Cal I-Cal III. Much love
tight tee shirts ahahahah
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!
update on your grade !!!
@@EmilioLopezFlores he prolly doesnt remember hahaha it was 3 years ago
Congrats🎉
I swear, these lectures are good enough to allow you to pass an exam even without reading the course book.
Seriously.
i passed all my calc 3 exams by high grades by these lectures, amazing
@@mariagevorgyan1470 That's awesome.
exactly, what i said
got an 82 on my calc 3 test
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!
I am gonna download each of professor Leonard videos and store them for my children so if anything goes wrong with youtube in future my children don't have to suffer from maths because of some teacher at school.
You would do better to remember this
That's smart AF
@@epistemophilicmetalhead9454 loooool
@@epistemophilicmetalhead9454 already did
@@bbd9106
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
hahaha
LMAO 🤣
watching the video on ritalin :D
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!
Just want to say Professor Leonard, your calc lectures got me through some really rough spots in my undergrad math classes. You’re a gift, and your lectures are clear, to the point, and made what made no sense in class somehow just click after watching you teach the same topics. God Bless you!
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.
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
That's what I wrote prior to watching his explanation. I haven't confirmed that it's equivalent yet.
yea that also works too
@@yinkak3921 Isn't that what it _should_ be, though?
It seems very weird to integrate over a quadrant where the region doesn't even exist - that goes completely against pretty much all other double integrals that I have ever seen.
@@Peter_1986 in polar coordinates when r is negative, the point get's flipped so for example if theta = pi and r = 2cos(theta) then r = -2. since r is negative we flip it so the point actually ends up (2,0) which is on the region. He talked about how to plot points in polar coordinates in his calc 2 playlist so you might want to watch that
yeah it works and later in the video in a similar example he used -pi/2 to pi/2 instead of 0 to pi
This guy is like a nerdy jock and its awesome. He will beat you up and do your homework. keep it i^2 Prof.
Anyone else listening at 1.5-2 speed to try to get through more lectures faster
Yes. The whole thing is easy. I just slow down when he wants to prove something.
that's the only way to watch CZcams Math videos.
Is that beneficial
I did but I noticed that when you really take the time and understand what he says instead of just doing the exercises, you will learn in a much meaningful way. I advise you to stop doing that guys
@@kozukioden2406 theirs objective is to crack exam, not to become lecturer, but as a student one must give full attention atleast to what he says, pondering on his points is far away.
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 🙏🙏
Wow this is a super good lecture. I remember learning this stuff years and years ago before youtube and not being able to watch lectures online. You had 1 instructor the office and lectures they had and whatever textbooks you could get. This guy's awesome. I remember Cylindrical coordinate systems blowing my mind at one time but this guy really helps break down every step. It's refreshing to see such a well crafted lecture. Not sure why youtube thinks I need a calculus lecture but I really enjoyed the refer class and will gladly watch this and other lectures. Wish this was a thing 20 years ago.
High quality teaching! I like that you really make sure the students understand every aspect of the subject and not just plug in numbers! 3 and a half hours goodies!
Freedom of information is fucking fantastic. This marks a primary shift in the delivery of education. My lecturer is awful - so here I am watching someone on youtube who I completely get. I feel sorry for those who had to teach themselves this from text books.
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
after watching any video of Prof.L, I'm compelled to say: Wow! that was the best lecture on the topic. i need a prof.L for my Quantum mechanics class now.
My god, what an amazing teacher. No wonder I never understood a single thing about calculus from my teachers!. Hope I can become as good at explaining as you are (I'm teaching programming at first year university courses).
Its a long section but every minute is worth the watch, lots of good info. Whats really sad is the last 2 videos are roughly 7 hours. My professor spent one class of 50 min to go over both sections. Then he sends everyone an email saying he is disappointed with everyone when the average test grade is 50-60% and that we need to do more homework.
I wish every teacher and professor out there had your same passion! Thanks to you I have aced Calc 1-3! Thanks!
not gonna lie, you're very handsome
Then you have a twisted understanding of beauty
What's wrong with you m8?
@@marbrydav9698 well he is good looking. Its just fact.
@@AndyU96 no u
No homo
I never ever comment here, but words can barely express my feelings of gratitude. Brilliant, brilliant videos! Thank you so much for what you are doing. I wish there were more teachers like you. You are absolutely amazing.
Thanks to you Professor Leonard, I improved greatly on my most recent exam after watching your Calc 3 videos
Thank you for this Professor Leonard! With the recent jump to digital classes, my math professors already difficult lecture style has become even more difficult but your videos are helping me get through it. Thank you for saving my grade this semester ^^
Wow... I am having fun learning Calc from you. That's a first! haha
Holy moly wish I found this man earlier in my semester, so much makes so much sense now. 10/10 watch these long but amazing videos
THANK YOU! Like honestly this kind of help and teaching should never be taken into granted.
Professor Leonard.. Thanks from the depth of my heart for such fabulous lectures. I have never seen teacher like you before. Lot of blessings for you from India ❣
You're the reason I've gotten A's my past two midterms. My tuition should honestly go to you!
I fell asleep watching something completely unrelated and woke to this. Not mad. 10/10 will save this for later.
شكرا
thank you
gracias
Danke
grazie
merci
Professor Leonard thank you for another monster and lengthy video/lecture on Double Integrals over Polar Regions. This is a mammoth amount of material for any Math/Engineering students to absorb , however deep pattern recognition and practice wili help in all levels. From reviewing this topic and taking notes, I will rewatch this video for a clear understanding of the material.
You are an absolutely jaw dropping genius of a teacher!
I appreciate how you placed your adds. Thank you for this smart move!
thanks for being my professor during covid when my calc 3 professor doesnt hold any lectures and points us to you and khan academy for learning :) it really is a blessing
Nearly DONE!!! Professor Leonard enriched my vacation! I love multivariable calculus!
We appreciate you, Professor Leonard! Thank you.
Thanks Prof Leonard, I am seriously ahead because of you.
Watch me crush the final exam on 5/27/2022.
I want to thank you so much! so lost in class but i came across your video and I understand! This got me so motivated right now, God bless you.
the coolest professor. thank you so much. i will never get bored in your class. you release energy that makes things really interesting. wish I had cal classes with you
These lecture videos are pure gold, thanks alot Professor Leonard
This guy has some real teaching talent, though the content was simple I saw complete video.
The setup at 1:46:02 is technically correct, but the integral makes more sense if you integrate theta from -(pi/2) to (pi/2).... they give the same result, and I feel this is far more intuitive geometrically.
Thank you very much Prof; you really know how to make my academic life easier.Next week I will be sitting for my examination on this concept, I'm now ready all because of you.
I liked the Pirate Joke ...Professor Leonard has helped me through my Associate Degree and my UnderGrad ...So thank you for your Commitment in ensuring we get this Complex theorems ..and if anyone has information on where he teaches i would like to enroll there for my Post Grad Studies ...feel free to hit me up
Thanks heaps for professor Leonard's lessons, I really appreicate it and they help a lot! Though at 2:47:27, when theta goes from 0 to pi, the result of the double integral is 9pi/4.
BEST PROFESSOR EVER. Thank you for all you do!
This "Super Man" has a super brain that he can explain D.I. so so so detailed !!! Amazing, and he had upload all of this amazing lecture online free!, This super hero saved my life.
Thank you so much professor leonard, you explain so well, I always learn so much from watching your videos :) Great effort and perfect explanation!!
Thank you, with tears in my eyes, thank you
I was really struggling on this topic. And I searched about this before my quiz, hoping to get some sample questions related to this topic. But lucky me got whole lecture that too in free of cost. I paid thousands of dollar in my university and did not understand anything but this video made this topic really easy for me. Kuddos to Professor Leonard. And I would like to thank him from bottom of my heart. Thanks for this video!!
Thank you so much Professor
Teachers like you made me fall in love with maths
Keep up the good work
Interesting. I'm doing Calculus 3 and i'm 11. I'm also a contortionist and I find Calculus super easy. I've moved on to Stokes Theorem and Navier Stokes equation and Schrodingers equation and Gauss Theorem and Newtons theorem and Greens theorem. I love math. I'm also doing Triginometry and Calculus.
prof you have made my life easier.thanks oncemore
2:48:36 Why would you go from 0 to pi anyway? The angle goes from -pi/2 to pi/2 and using those bounds gives the correct answer.
Omg thank you i didnt understand why either...
Can i know why thougj im confused
@@ozurking4748 So, it happened that the surface was symmetrical along that axis, but it wasn't determined by the area of the region. I hope that is clear enough.
Wouldn't integrating with the bounds -π/2 to π/2 give us zero? since π/2 to 0 and 0 to -π/2 are on opposite sides of the x-axis? Correct me if I'm wrong (four years later)
23:00 Start ex 1
42:10 Ex 2 Between z=x^2-y^2 and cylinder
54:30 Ex 3 (Good one)
1:03:00 Ex 4
1:24:00 Ex 5
Superman is teaching me calculus.
You are AWESOME SAUCE!!! You make math GREAT AGAIN! Thank you for not being boring!
i still cant believe these lessons are free. bless this man
came here after being stuck in a problem but I knew where to came, you never disappoints thank you Prof
Professor Leonard I'm so grateful to you, thanks a lot ♡
Thank you so much for your dedication to quality education videos. Your approach to teaching helped open the door for me to go back to school and succeed. I cannot thank you enough good sir.
You know what’s crazy I fell asleep while watching a Star Wars battlefront 2 review by the act man and wake up to calculus lessons
Hello professor Leonard can you do "differential equations". I like how you explain the problems and you covered everything which helps a lot. I just like to know more math. Just what I learn in class is not enough for me. And thank you for all of ur videos
One of the most sensible videos on double integration
Cheeersss! I was just waiting for the new video.... Thank you Mr professor.:)...:)
Great explanation, thanks Prof. Leonard.
professor, you are the Best in Cal3
thank you a lot prof. Leonard for your greatly and funny lectures ,I really understood many of topics of calculus3.
Professor Leonard , you are the best one
Please do differential equations Professor Leonard!
1:12:00, I always used to mess up the shifted circle limits, they seem so easy now! big thanks prof
Thanku so much for this videos sir!!....saved my calculus...got the whole stuff in my head in one go!!..thanku so much!!
HANDS DOWN THE BEST CAL TEACHER!!!!
r^2=2r cos {θ}, r=2 cos (θ), i got it now thanks Leonard 👍👍👍
13:30
they're called Adderal.
big thanks may god bless you and ur family
Simply awesome... Thank you very much :).
I just wish I watched ur videos earlier not 4 days prior to my finals :(
2 days before the exam and I still have so many videos left. I’m watching them at 2X speed.
These videos at 1.5x are so entertaining and still understandable as review. so glad i have mtn dew.
i watch at 2x
2x at excercised and 1.5x at concepts
I'm 99% sure Professor Leonard made a little mistake explaining that you cannot go from 0 to pi on the area integral at 2:48:40 . He specifically said it himself on 1:57:00 that doing that is okay because the negative will cause the integration to "flip" onto the side that is part of the region. Also, I tried the integration that goes from 0 to pi myself and on the integration calculator and still got the same answer; 9pi/4.
Yeah I noticed that too. But maybe he just wanted to make a point about exploiting symmetry.
that was a long journey but an amazing one
THANK YOU for saving my life!!
Imagine if we had a Professor Leonard for all of our courses
My dream
Thank you so much, hope you upload Differential Equations videos by next year.
Minute 2:49:00
Here and in the previous example, i would take the angle between -pi/2 and pi/2...the minus will turn the area below the x-axis from negative to positive.
Superb explanations!! Thank you!
It makes verry sense in a one unique style it is to see that your s practical manner instad of a theories manner
How did I fall asleep to videos about old video games and wake up to calculus lectures??
Easily one of your best introductions
35:21 for anyone who didnt understand where did 1/1 came from..........for x axis 0 + 2 / 2 which is 1 for Rkx.........0 + 2 / 2 which is 1 for Rky......tan theta = (Rkx / Rky) tanm inverse of that value will give you the starting angle
i wish i could "like" your videos 1000 times!