I've always thought of surfaces as being 3D. But in actual fact they are still 2D, living in 3D world. Learn something every day. Brilliant.
@NeelSandellISAWESOME5 ай бұрын
This isn't really a good way of thinking about it. These surfaces are just a map from 2D to 3D.
@worldclassmediocre92753 жыл бұрын
It baffles that you don't have more subscribers. Your work is very helpful
@DrTrefor3 жыл бұрын
Haha glad it helps:)
@actualBIAS4 ай бұрын
You know what? I'm stunned how much effort you've put into these playlists just for people like me. You did this on your own and you did this without any other reason than to teach people. Thank you so much. Without people like you this world would be a much darker place.
@tomatrix75253 жыл бұрын
I’ve taken Vector calc ages ago. I did well and finished fine, but felt our instructor always deprived his explanations of the intuition or logic. This is simply amazing
@DrTrefor3 жыл бұрын
Thank you!!
@andersongoncalves1933 жыл бұрын
This is simply the best explanation I have encountered. Bravo!
@DrTrefor3 жыл бұрын
Wow, thanks!
@raajdhanwani20273 жыл бұрын
Oh My God! How Brilliant is this explanation!
@Deepak-pi9xx3 жыл бұрын
First 4 minutes cleared my so many doubts. Thank you Trefor
@irenepadre33522 жыл бұрын
simply the best calc prof out there! thank u dr. trefor!!
@shivkarj14563 жыл бұрын
The animations really help in visualizing surfaces. Thank you so much!
@guifzas3 жыл бұрын
I really want to thanks you for this videos, you increase my knwoledge in vector calculus and I love it! you are the best
@DrTrefor3 жыл бұрын
Happy to hear that!
@briandwi2504 Жыл бұрын
Very nice image of the meaning of parameterization at the end of the video. Such elegance in thought.
@vkjmathstuition12183 жыл бұрын
Wonderful!!! You have exposed the explanations which remain hidden: 2D surface to 3D surface parameterisation.
@joonahulkkonen83463 жыл бұрын
Just what I needed for this week’s assignment! Thanks!
@DrTrefor3 жыл бұрын
perfect timing!
@Numerically_Stable2 жыл бұрын
Highly insightful, keep up the good work. Cheers!
@bensonchou98652 жыл бұрын
This really helped a lot! Our professor didnt teach much and it was really confusing before this video!!
@xandiczr124449 ай бұрын
THOSE VIDEOS ARE INCREDIBLES! Gave me a lot of great insights I''ve never had!
@pedrogaleano67223 жыл бұрын
If you read this, you've helped me a lot. Thank you!!!
@DrTrefor3 жыл бұрын
Glad I could help!
@siwasoontreerat61252 жыл бұрын
Best explanation ever. I am very appreciated your work.
@DrTrefor2 жыл бұрын
Thank you so much!!
@adibamaisha71348 ай бұрын
binging the entire playlist calculus exam in 3 hours 😅💜
@hikmatullahpakhtoon36943 жыл бұрын
Beautifully explained.
@DrTrefor3 жыл бұрын
Thank you 🙂
@user-hg8sz7fh8n Жыл бұрын
brilliant visualization and demonstration!
@awwab1094 Жыл бұрын
I really really appreciate you thanks man 🌹❤️
@DrTrefor Жыл бұрын
It's my pleasure!
@carlosraventosprieto2065 Жыл бұрын
i really loved that last point of view! It would have been nice if you put some points in the r-theta axes and see where is it on the x-y-z space nice video!!
@continnum_radhe-radhe2 жыл бұрын
Thank you very much sir 🔥🔥🔥
@adiljan13053 жыл бұрын
sir how do you make such things in a simpler way. Your method and techniques of teaching are really wonderful. Always feel amazing at your vector calculus video notification.
@DrTrefor3 жыл бұрын
So nice of you to say!
@dominicellis18673 жыл бұрын
Wow I get how cones are the fundamental shape of implicit quadratic functions it’s just a circle that has a height that stretches the radius by that height I guess that’s why space time is a cone
@sergiolucas382 жыл бұрын
Great video :)
@anujmishra68343 жыл бұрын
Great work sir, thanks
@himanshu__3703 жыл бұрын
Really cool video 🔥🔥🔥🔥
@DrTrefor3 жыл бұрын
Glad you liked it!
@hlp69523 жыл бұрын
thank you so much!
@visualgebra3 жыл бұрын
Thank you for this topic dear Professor !
@DrTrefor3 жыл бұрын
You’re most welcome!
@sudiptaroyarts38613 жыл бұрын
You are awesome sir I get very help from this video ❤❤❤ I am also physics undergrad student 1st year
@DrTrefor3 жыл бұрын
Thank you so much!
@sudiptaroyarts38613 жыл бұрын
Mention not sir
@ogunsadebenjaminadeiyin27293 жыл бұрын
You're called blessed, brother. Trust me, by Prof's videos, you'll love Physics, especially Electromagnetism. I'm a physics grad.
@beabee2562 жыл бұрын
Is there a good practice problem manuel that you can recommend for vector calculus (with full solutions)? Stewart only has the final answers and that doesn’t help much… 😞
@derickblacidocontreras29143 жыл бұрын
Dr Trefor, could you make a video about extended Green´s Theorem, please? Thanks in advance
@ogunsadebenjaminadeiyin27293 жыл бұрын
Super
@DrTrefor3 жыл бұрын
Thanks!
@leadtoexemplify3 жыл бұрын
r is not z-height right? r is the projection length of the point. did I miss? Thanks for the video. Finally I understand the intuition behind parameterization. never too late to learn it properly
@Darkev773 жыл бұрын
Why were you not my professor in uni :(
@DrTrefor3 жыл бұрын
haha if only!
@ogunsadebenjaminadeiyin27293 жыл бұрын
😂
@wilurbean3 жыл бұрын
This seems like, and I haven't watched forward yet, like we're gonna smash that line integral into 2D or 3D and use Jacobians.
@ironheart4442 жыл бұрын
Thanks for the explanation, it is really good and your videos are really helping! Also, one question: if you were given a parametric surface, i.e. the equation only r(r, theta), what would be your approach in trying to find the shape of this surface? Let's say that you are asked to draw the curve and it is not an impossible one hahaha
@j.o.59573 жыл бұрын
Question to myself: so it seems that we can parameterize anything to turn it into what's essentially a square (or perhaps a cube if you're looking for volume). That would be a natural parameterization. I can see how we find that for this concrete example. But is there a general formula for this? And what would that look like? I know there is cylindrical coordinates and spherical coordinates, but these seem hard to find. Looking forwards to finding out if there's an answer to this, how to select a natural parameterization.
@DrTrefor3 жыл бұрын
Broadly speaking, a useful parametrization is one that captures naturally symmetries in the constraints of a system.
@j.o.59573 жыл бұрын
@@DrTrefor Interesting, I'll think a bit about that, thank you
@chandankar50323 жыл бұрын
So...Here we gotta choose the parameterisation such a way ,so that we can see how the surface is sektched by r(t) in xy plane and z axis individually. Is there anything more to it ,why we did that parametrisation ? Edit: Also why we need two parameters in 3D in the first place ? So that if we hide one parameter it gives the curve in XY pane and hiding the other gives the Z axis component ,right ?
@claris48072 жыл бұрын
In the cone example, I think the phi corner (top corner with the z-axis) should also be taken into consideration, as r runs from 0 to 3. For me the a cone consist of piled circles (disks) arranged from small to large. By taking the top corner into consideration the latter is fixed. So why not using three parameters (r, theta, phi) instead of two (r, theta)?
@cantorbernoulli44072 жыл бұрын
Hi dr. Trefor first of all thanks for the video, i got a guestion is there a specific way of who we find the parametric equation of a function?
@masoncamera2732 жыл бұрын
How would you take the gradient of a vector function with r(u,v) when it has three components of only two variables?
@alexanderwhittemore1491 Жыл бұрын
Why did we need to introduce two variables u and v, instead of just leaving the variable t?
@sejalpotbhare32383 жыл бұрын
Sir if we are given some vector function f(x,y,z) and a surface in xy plane which is bounded by x^2+y^2=z^2 and the plane z=4 ....then what will be the double integral of f.n dS?
@luphiax42393 жыл бұрын
In which video have you explained cylindrical coordinates as you said?
@UtkarshRuhela3 жыл бұрын
Why do we need two parameters exactly to describe a surface in 3D? Why not 1 or 3 parameters?
@DrTrefor3 жыл бұрын
It’s sort of a definition. We call a 2D surface an object described by two parameters
@arielfuxman88683 жыл бұрын
3:55 can the bound of u be dependant on the value of v?
@DrTrefor3 жыл бұрын
Yup that is fine. It gets messier when it is nonrectanular in the uv space, but certainly not imposible. It's just like integrating over a nonrectangular region in the xy plane.
@midhunskumar17292 жыл бұрын
Could you pls do class on Laplace and Fourier transforms
@DrTrefor2 жыл бұрын
Have a whole playlist on laplace transforms:)
@mahmudalam4412 жыл бұрын
Dear Dr. Trefor, your presentation is nice and clear. May I ask you, how do you make the animations? I am a Ph. D. student of Mathematics, want to learn this animation. I would be happy if you please reply to my comments. Can I contact you via email? Thanks
@benking69083 жыл бұрын
Shouldn't the limits of theta be exclusive of 2 Pi, so that you don't double count it with zero? In the video it says less than or equal to 2 Pi.
@DrTrefor3 жыл бұрын
This is going to be more relevant when we actually use these descriptions, but we often want to be able to describe the boundaries of a region. Take the simple unit circle which we paameterize with theta between 0 and 2 pi inclusive. Now it has two defined endpoints, one starting at 0 and one ending at 2pi and can do an integral from 0 to 2pi. If we used strictly less than 2pi, then it no longer has two endpoints.
@Festus20222 жыл бұрын
why do you say you're describing a 2 dimensional surface, when a cone is a 3 dimensional structure? Not sure what you mean by a 2D cone embedded in 3D.
@DrTrefor2 жыл бұрын
It’s similar to the surface of the earth. We can only walk two directions, north/south or East/west. Yes there is a third direction up into the air but if constrained to the earth we can’t access it, so “2 degrees of freedom embedded in 3D”
@Festus20222 жыл бұрын
@@DrTrefor thank you! I like your videos
@jordanleyva457 Жыл бұрын
jordan leyva here
@Somebodyherefornow2 жыл бұрын
x^(2/3)+y^(3/2)=1
@blugreen993 ай бұрын
No chalk and blackboard with all its distracting handwriting and obscurity of text and diagrams by lecturers body and arms. Excellent use of 3d effectsand color in clear diagrams.!.