Calculus 3 Lecture 13.7: Finding Tangent Planes and Normal Lines to Surfaces
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- Опубліковано 15 гру 2024
- Calculus 3 Lecture 13.7: Finding Tangent Planes and Normal Lines to Surfaces: How to find a tangent plane and/or a normal line to any surface (multivariable function) at a point. This is based on the ability to find the gradient of a function.
If I learned one thing from watching these lectures it's that the right siders need to step up their game.
u mean the students in the audience?
Yeah, that's what he means. Particularly the ones that the Professor calls the "right-siders", who are on the right side of the classroom.
Right is right. #Right-sideExceptionalism
That does means they are dumm. They goone through calc 1 to 3 . Means some guys dont pay attention in class but they are god damm well prepared in exam and have capacity bring higher grade then the people who are active in the class
The reason Leonard is so good isn't because he teaches the math, it's the fact he teaches the intuition. Thanks Prof Leonard
True quotes
There are many reasons for why professor Leonard is great;
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I am a computational chemist/physicist. But I am also a private instructor. The two challenges I enjoy facing and resolving are research and making things understandable to the point where they become second nature to the student. I am humbled by this presentation. I know that I am looking at a historic presentation. I am very sensitive! It's only once in a a very long time that we see a presentation that in of itself is a wonder and a masterpiece. This is one of them!
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0:00 Tangent planes to a surface at a point
29:20 Example 1
52:16 Example 2
1:02:22 Planes and Lines
1:06:40 Example 3
1:15:30 Example 4
1:24:35 example 5 Not completed
1:27:30 Example 6
1:35:25 Example 7
Thank you
thank you !!
Wdym by example 5 nt cmplt
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I watched this whole lecture and had everything worked out. Started solving problems on my assignment until they started talking about linear approximations. I went and started studying my schools resources and now I'm confused.
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Reading the textbook about tangent plane to the level surface didn't make sense to me, but this sticked to me instantly. Thank you again for saving me Professor Leonard!
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Professor Leonard ,thank you for an excellent video/lecture on Finding Tangent Planes/Normal Lines to Surfaces in Calculus. This is another well explained lecture that I really understand from start to finish. This material also takes practice for a solid improvement and deep understanding.
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multivar professor at uni made this look a lot more confusing than it actually was ! thank you so much professor leonard for explaining this so crisply! really appreciate it
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exercise start at 41:33. for people want to do some difficult exercises, begin at 1:24:47
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Hello Professor! I have been watching your videos since high school and find them tremendously helpful as you clearly explain the concepts and logic behind the steps. I self-studied AP Calculus BC and your Calculus 2 videos were integral to achieving a 5, the highest score! Currently, I'm taking Calculus 3 in university and rely heavily on your videos. However, your Calculus 3 videos do come out after an exam. Do you upload the videos right after your lectures or a few weeks after? If it's the latter, would it be possible to upload them sooner? If you can't, it's completely understandable. However, if you can, It would be most greatly appreciated! -Best regards, a sleep-deprived university freshman
P.S. As of 4/7/16, my class finished covering double integrals and began triple integrals. I thought that fact might be helpful as a reference to how far ahead or behind your class is compared to another class.
+- Kim Hi there! The videos are uploaded as soon as they are created. I try to complete them as quick as I can, but they do take a few days to edit together. Trust me, I'm holding nothing back from you guys. Best of luck!
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when he asked, " did I explain this well enough for you to understand?"
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I have been wondering how in the world the gradient which is just the partial derivatives produces a normal vector to the function for weeks now, and now I finally get it. thank you.
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I improvised a way to find normal lines a few years ago, which involved finding the partial derivatives along the x/y-coordinates, then creating lines through a common point, and then using the vector product to find the normal line - I guess that that method works as well, although the method in this video is certainly a lot faster.
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Those 2 dislikes are from other professors...
+German Grammar
Yeah, and those professors probably thought that he wasn't dry and formal enough or something.
Too much humour, to much intuition. Disliked.
Et cetera.
Laurelindo which is unfortunately a trashy outdated mentality to think about it
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27:38 if you're on a point of the level curve where the tangent line points to the center, and so gives you a gradient in a complete different direction than the center, how's that the fastest way to the center?
"Hello, yes, no?..."
"YESS! D:
watching him at a higher speed makes him look even more excited about math
1:41:45 POV you now understand the math concept
1:34:23 Shouldn't be there a negative one at the denominator in that normal line equation?
To me, the most intuitive way to find a normal plane is to simply find the 2 partial derivatives so that I get the 2 lines that touch the point, and then I use those lines to find the normal vector to that point by using the cross product.
Thanks to you, if I cannot get math2011 this semester, I will cry!
As you are going to carry me to A!
Shouldn't r'(t) give you a tangent vector and not just the slope of the tangent vector? @19:38
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Brilliant explanation ,so intuitive thank u professor
Do you cover linear approximation?
Thank you so much. Very intuitive explanations!
Waiting a lecture on differential equation
just keep waiting
Fredde He probably already mastered it, needn’t wait anymore.
Well it needs its own course not a lecture
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At 1:27:45, I found it easier to make it tan z - y/x = 0.
I yawned right at 46:05.
I felt like he was staring into my soul.
lol I got bored from all the easy exercises, so I made one of my own:
f(x,y,z,u) = logbase(x^(y^(z(^||w||^v)))) where w is a vector function defined by and v = ||w(v)|| / the family of spheres (x^2+y^2+z^2).
1- kill me
2- find the tangent plane of f(x,y,z,u) = -5 at a point of your choice, and the tangent line as well.
its actually quite easy, the implicit functions cancel out during the deriving process.
0:00 - 33:00 = Tangent Planes "Proofs"
Love you
At 29:12 the normal line will completely miss the summit as r(s) travels up or down.
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For the last two questions at 1:31, why do you move the z variable and make the gradient in terms of i,j,k? Wouldn't you just turn z variable into f(x,y) instead and treat the gradient in terms of i and j? This was done in the last word problem you did in section 13.6 (last question of this video). Seems like a contradiction.
In that case, you would get the level curve in 2D and not the 3D surface itself.
In the last question of video 13.6 , the function was in 3D in that case gradient must be in 2D . In the last problem of this lecture, it is an equation of a level surface which is in 3D but the actual function which we have to pretend is in 4D, as professor said that the gradient must be one dimesion lower than the function therefore gradient for this question must be in 3D.
In 13.6 question, "function" was given.
But in this problem "equation of level surface" was given we had to pretend that a function exists in 4D.
thank you for your question I was confused myself after reading your comment but I figured it out after thinking for a while.
You really are the superman of math! :D Thanks so much for sharing these! A million times better than how my book does it, which is in an extremely abstract way that I just couldn't follow and grasp properly. Do you accept donations?
Also, could you put the subject in the titles of your statistics videos? Just like in these videos. It's a lot easier to find what you're looking for that way :) (I'm going to cover them for a re-exam during the summer and don't need to repeat everything)
are you going to go over differentiability in several variables, iam really having a hard time trying to grasp the idea, it would be awesome if you did !!
prof leonard im on a section in my calc 3 class called tangent planes and linear approximation is this video based on that section?
Professor, at 13:23 You said it is two things being multiplies and the added together, it looks like a dot product and used that, what about product rule for differentiation?
Awesome lecture!
Keep it up pls your help is great for us
why did we not do an example where we dot the gradient with the derivative of r(t)
Hello Professor many thanks for all your great efforts. Is there a way we can get the lectures notes beside the videos. Thanks again
hi, I was wodering for example 2, is the gradient a normal to a bunch of level surfaces or level curves? What I got from it was that when in 4-D and the gradient is taken which gives a normal vector, it gives the normal to a bunch of level surfaces. When in 3-D and the gradient is taken, we would get normals to level curves.
WLOG, that we were first given a 3-D surface the we cheated to get a function in 4-D and same for 2-D.
Clarify, please.
professor really superman
If we know the two partials fx and fy and we could turn these into direction vectors we could do a cross product to get the normal. Therefore how do we get the direction vectors from the slopes which are scalars? How could on do this in 2D - ie turn dy/dx into a direction vector? Tony Johannebsurg
Hi Professor, do you have a plan to talk about contour integration?
I want ask you ?! this lecture are the same of ( EXTREMA OF FUNCTION OF SEVERAL VARIABLES ) . because this is the next lecture in my book which is 13.7 .. thanks
Thank you very much professor :)
n4m: left at 51:35 (example 2)
for ex 1: check tangent & normal lines (4 me)
1:16:00 left (ex 4)
THANK YOU SO MUCH !