My Cal3 teacher from Ecuador is incompetent and we had to correct a dozen of mistakes for him in one single lecture. Thanks Christine, I have learned something from you finally!
thank you so much. if the courses from mit opencourseware are like this, i wish i could just take that for credit. these videos are sooooo much better than what i am getting right now. our teacher didn't even bother to teach us how to graph these equations by hand in precalc or now in calc 2, so it's nice to get an intuitive sense as to why limacons look like this.
You will obtain the same graph. If you graphed up to 8pi, you would essentially plot a bunch of points that you had already plotted in the first 4pi radians. If any of that was confusing please tell me and I will try to clarify!
love your delivery method, I am 43 now, and haven't heard chalk on a blackboard in a while, it was in high school (1995) that they started the transfer from black to white boards, and now they don't even use over head transparencies any more, a real shame, as you and your chalk is so asmr with a soft voice, a great companion, you would make an excelent teacher in your own right, not just a tutor. PS: I have Autism, so that it is not so weird, just like the tone, and the pace, I dropped maths in year 10, as they just got to algebra, had a horendous teacher, the staff there didn't know about autism, learning disabilities, even bullying!; so I can't understand half of this, but the formula re-arrangements I can, just, but would be nice for you to show HOW one uses these skills, as it looks all a lot of physics, lasers, etc. that would use this stuff, no wonder you need a high grade before you get taught this stuff.
This is an MIT class and I am not saying that there won't be any mistakes done by tutors. However, you should have to be much careful and/or think twice when criticizing and saying that there is something wrong with graphing and her solution. Anything she did in this video is absolutely correct. You should have to be aware of the importance of the period of a trigonometric function while graphing in polar coordinates.
The graph of r equals one plus cos(theta/2) and setting up the problem is beautiful, however placing the upper and lower limits on the integration continue to give me problems in Calculus. Thank you for the lecture.
My professor made the graph of r=1+Cos Theta . Which was basically the same on the outside with no inner curves i.e. A heart on its side with no curved line inside. I don't under stand why theta over two made the difference of an inner curve. I would think only the width would be affected. Can you draw a graph of r=1+Cos Theta? No need to fined the area. Thank you.
There was no reason to change the limits on the second integral to obtain the blue area. Not sure why she chose to do that, probably created confusion even though it gave the correct area. Otherwise a good lecture.
Great explanation. I think there is a little mistake from 17:25. She forgot to multiply the second integral with a factor two (to subtract the 2 smaller pink areas).
i dont think if she graphed it right.. :( she can't read the comments but at least anyone see this comment must try to do it on your own to know my point... there's given value of theta and just plug it in there...graph is different..correct me if im wrong
Good question. The issue in your understanding lies in that you're treating the bottom picture as if it were IN cartesian space, when in fact it's just a projection of polar space onto a cartesian frame of reference. The area accrued is positive.
Who the hell writes the dialogues? Cosine time function? Whoever is writing the commentary needs to do some math themselves. I've seen a number of mistakes on these videos.
Which equations governed mechanical barometer so we easily calculate energy sources by atmospheric pressure which is enough to cook food for 1000000 peoples 👅👅👅😃
![เป็นไปได้ไหม - WanMai [Teaser] | 05-12-24](http://i.ytimg.com/vi/P5Uto6e453w/mqdefault.jpg)
Wow... so much clarity and depth. I cant explain how much this has cleared up my confusion.
My Cal3 teacher from Ecuador is incompetent and we had to correct a dozen of mistakes for him in one single lecture. Thanks Christine, I have learned something from you finally!
everybody from that country is incompetent hahahaha
@@JJOSEMORALES perhaps like your parents were, at raising you.
omg, this is like the best maths explanation I have ever seen! Well done!
Absolutely
when I become an engineer coz of your teachings, I will never ever forget you ever
Thank you so much.
This world is a good place to be alive and educated.
I am grateful that I am a part of this good world :)
Watching in 2k24
Amazing class
thank you so much. if the courses from mit opencourseware are like this, i wish i could just take that for credit. these videos are sooooo much better than what i am getting right now. our teacher didn't even bother to teach us how to graph these equations by hand in precalc or now in calc 2, so it's nice to get an intuitive sense as to why limacons look like this.
Excellent presentation of a concept that often confuses my students. Well done! ;-)
Very excellent presentation Madam. All students are blessed to sit in your Classes. One time listening is sufficient for ever to remember.
You will obtain the same graph. If you graphed up to 8pi, you would essentially plot a bunch of points that you had already plotted in the first 4pi radians. If any of that was confusing please tell me and I will try to clarify!
love your delivery method, I am 43 now, and haven't heard chalk on a blackboard in a while, it was in high school (1995) that they started the transfer from black to white boards, and now they don't even use over head transparencies any more, a real shame, as you and your chalk is so asmr with a soft voice, a great companion, you would make an excelent teacher in your own right, not just a tutor.
PS: I have Autism, so that it is not so weird, just like the tone, and the pace, I dropped maths in year 10, as they just got to algebra, had a horendous teacher, the staff there didn't know about autism, learning disabilities, even bullying!; so I can't understand half of this, but the formula re-arrangements I can, just, but would be nice for you to show HOW one uses these skills, as it looks all a lot of physics, lasers, etc. that would use this stuff, no wonder you need a high grade before you get taught this stuff.
Is that a gigant chalk???? Nice explanation!!!
This is an MIT class and I am not saying that there won't be any mistakes done by tutors. However, you should have to be much careful and/or think twice when criticizing and saying that there is something wrong with graphing and her solution. Anything she did in this video is absolutely correct. You should have to be aware of the importance of the period of a trigonometric function while graphing in polar coordinates.
DMENC I almost had a stroke reading this
Excellent explanation.
The graph of r equals one plus cos(theta/2) and setting up the problem is beautiful, however placing the upper and lower limits on the integration continue to give me problems in Calculus. Thank you for the lecture.
great explanation
thankyou, i'm insomnia, and i can deep sleep after watch this video.
Thank you for this. So helpful😭
My professor made the graph of r=1+Cos Theta . Which was basically the same on the outside with no inner curves i.e. A heart on its side with no curved line inside. I don't under stand why theta over two made the difference of an inner curve. I would think only the width would be affected. Can you draw a graph of
r=1+Cos Theta? No need to fined the area. Thank you.
Thank you for your help.
Great, Christine.
thank you. the video was very helpful.
I like your videos. Thanks for posting them !
Isso foi lindo!
From Brazil.
Cool stuff. The basics!!
The blue stuff or the pink stuff? 😜
Also theta is a real number - a very important assumption
good explanation
She doesn't read these comments. This is MIT's youtube page
Thank you very much!!! Ah pretty graph! (=
There was no reason to change the limits on the second integral to obtain the blue area. Not sure why she chose to do that, probably created confusion even though it gave the correct area. Otherwise a good lecture.
Great explanation. I think there is a little mistake from 17:25. She forgot to multiply the second integral with a factor two (to subtract the 2 smaller pink areas).
the integral she subtracts is equal to the entire pink area, she multiplied it by two a little before 17:25 :)
I have NO idea f what I just saw, but it looks interesting no doubt!
Theta 4 pi not pi over 4 1:07
She's amazing!
When calculating the area of the blue, wouldn't you have to subtract 2 * the pink part? (integral of (1 + cos theta/2 )^2 from pi to 2pi)
It really helps me!!
useful. thanks
Thanks 🤩 😌👍
Fabulous.
Fabulous!
Thx!! It's very useful!
i dont think if she graphed it right.. :(
she can't read the comments but at least anyone see this comment must try to do it on your own to know my point... there's given value of theta and just plug it in there...graph is different..correct me if im wrong
Graph was correct, I think you might be mistaking polar with rectangular coordinates
12:34 , explain that bit to me please
How did she get to 2pi to 3 pi
Ask you a question where is the x-y plane related to r-theta??
y is everyone applauding her tuition. I kno she's smart n all...but i got a brain freeze as soon as question appeared! where's my dummy?!
what's a beautiful shape of this graph :)
Good
Nice.
If we integrate the area from A π to 3π, won't negative and positive area make zero as sum?
Can anyone clear my doubt?
Good question. The issue in your understanding lies in that you're treating the bottom picture as if it were IN cartesian space, when in fact it's just a projection of polar space onto a cartesian frame of reference. The area accrued is positive.
@@vivekpatel6530 thank you
yes, 4 pi, as many people can eat 1 meat pie, but not many can eat four!!
My head!
Thanks for the tutorials, but now i'm more confused. :(
my head!!!
Who the hell writes the dialogues? Cosine time function? Whoever is writing the commentary needs to do some math themselves. I've seen a number of mistakes on these videos.
Which equations governed mechanical barometer so we easily calculate energy sources by atmospheric pressure which is enough to cook food for 1000000 peoples 👅👅👅😃
Ok, is it normal I tottaly understand anything from all of this ahah wtf
Is That Elon Musk 🦋
Congrats, u just drow a panocha hahaha
i got a raspberry pi...python:)
I M ADDICTED TO GEOGRAPHY, MATH AND PHYSIC PLEASE TELL WHO AM I ?
MARGELLAN
I know all these kind of of problem because I am from India.
I am in 1st year of my college
Deux consin alphaallah resign emblem course devoid
so big chalks used in MIT, that is what makes them different
Too easy.