I've had really hard time understanding parametrization for a long time. But watching this video cleared it up, and now I finally understand how to do it. Thank you so much!
Dude, this is so darn simple and easy to understand. My instructor never actually took the time to talk any of this out, and your video helps so much. Thank you!
I have watched dozens of videos from various people and I really like how you broke it down. I actually feel like I understand parametrization or whatever its called lol
This channel is growing on me. You tackle some complicated topics that (at least my) homework and "teachers" (had to get a jab in) refuse to explain and the book doesn't say a peep about it.
OMG THANK YOU. I had a quiz as practice for my upcoming midterm, and I got every single one of the parametrizations wrong because I just didn't know how to do it, and now with your video, I found out it was quite simple.
The examples are in explicit form, that's why x = Ct works. Simple implicit forms such as x^2 + y^2 - 1 = 0 can be tackled trigonometrically. What will you do when your curve is in implicit form and with arbitrary polynomials.
That is a great question. You are correct that the examples above are explicit functions. Parametrizing implicit curves is not typically done in Calc II/III (the basis of these videos) beyond simple curves such as the unit circle you mentioned. Parametrizing general implicit curves is considerably more difficult (and in some cases is impossible). For more in depth reading, google a paper by Christoph Hoffman at Purdue called "Conversion Methods Between Parametric and Implicit Curves and Surfaces".
Thanks Alvin for making this point. And thanks Firefly Lectures for showing how to parametrize explicit curves and explaining the differences between parametrizing the same curve using various methods.
I mean, it makes sense on paper, but the minute you graph it in the calculator (parametric), the graphs do come out looking different. So that part I don't get.
Can you suggest me a theoretical textbook about this subject matter? I've read "Leithold" and "James Stewart": they don't explain how to do the parameterization, they just use it. By the way: good video.
Wait, I thought one of the major pros to parameterizing was that you can define curves such as circles since Y was dependent on T rather than X. Wouldn't we lose that benefit by making X=T?
Hey guys, I need help. The function x=z^2 +1 is given. Now I want to parametrize it. In the solution they use the "simple parametrization of a curve" and compute x(t)= (t^2 +1/0/t). I can't comprehend this. Thanks in advance for your help!!
I've had really hard time understanding parametrization for a long time. But watching this video cleared it up, and now I finally understand how to do it. Thank you so much!
🤓
Dude, this is so darn simple and easy to understand. My instructor never actually took the time to talk any of this out, and your video helps so much. Thank you!
🤓
I have watched dozens of videos from various people and I really like how you broke it down. I actually feel like I understand parametrization or whatever its called lol
🤓
Definition of great teacher: Is the one who makes complicated stuff easy. And you are. Thanks!
Should have showed parametrization of more complicated functions.
Wow. This seemed so complicated in class, but you made it easy-peasy. Thank you so much!
🤓
The most easiest explanation so far. Thank you so much.
This is a very intuitive video, thank you
This channel is growing on me. You tackle some complicated topics that (at least my) homework and "teachers" (had to get a jab in) refuse to explain and the book doesn't say a peep about it.
🤙🏻
I was literally struggling with this for few months. Thanks a lot for cleaning this up🙂
OMG THANK YOU. I had a quiz as practice for my upcoming midterm, and I got every single one of the parametrizations wrong because I just didn't know how to do it, and now with your video, I found out it was quite simple.
Thank you. You're a legend. You solved my problem without even making it half way through the vid
Thank you very much - exactly what I was looking for - clear and concise!
Amazing and very well explained :))
Thank you Sir and lots of love from India :)
Holy shit bro this was the fucking easiest damn thing to do thank you so fucking much bro
Perfect👏 the more straightforward and the more elegant
Thank you for the simple explanation.
This practically saved my life.
Amazing Video! You really helped me. Thank you!
Blas, you are very welcome!
Thank you! Finally understood parametric equations
i was curious on how it changes direction. helps out. thanks
The examples are in explicit form, that's why x = Ct works. Simple implicit forms such as x^2 + y^2 - 1 = 0 can be tackled trigonometrically. What will you do when your curve is in implicit form and with arbitrary polynomials.
That is a great question. You are correct that the examples above are explicit functions. Parametrizing implicit curves is not typically done in Calc II/III (the basis of these videos) beyond simple curves such as the unit circle you mentioned. Parametrizing general implicit curves is considerably more difficult (and in some cases is impossible). For more in depth reading, google a paper by Christoph Hoffman at Purdue called "Conversion Methods Between Parametric and Implicit Curves and Surfaces".
Cheers for the suggestion, I've been trying to find out more about parametrization in general. (Y)
Thanks Alvin for making this point. And thanks Firefly Lectures for showing how to parametrize explicit curves and explaining the differences between parametrizing the same curve using various methods.
thank you sir your videos helped me a lot...... but i have a question if i want to improve my skills in math from where should i start?
thank you so much
Thank you very much!
So simple but so helpful!
@:33 "there are lots of rights answers" Perfect. This fact is overlooked and understated too often.
Done deal...was facing problems on parameterization thanks
Thank you for this video!
How are you using your handwriting? S-pen or something? Or what's the app called?
Thank you in advance!
thank you right to the point
yep, u did for the simple functions, but VERY GOOD WORK!
Very helpful video
Thank you sir
Thank you. at 4:17 3^2×2 = 18.
thank you!
Can you parameterise y=f(x,y)? where it is not possible to get rearrange to y=f(x), although you can get f(y)=f(x)?
i found smtg similar than this in my calculus textbook but i didnt understand how and why they chose x to be "t" ; now i do thank you
Thanks a lot Sir! Great explanation!
Muchas gracias... excelente explicacion
Luis zMacias Valade De nada!
that explanation is just great!!! thx a lot
Djimy Slot - No problem :)
I mean, it makes sense on paper, but the minute you graph it in the calculator (parametric), the graphs do come out looking different. So that part I don't get.
Thanks a lot
Thanks for the video!
Great, clear explanation, sir - thank you!
Great lecture!!! Thanks sir for solving my problem.😎😎
This was really useful
What you did is just substitute
right on point, thanks
thanks a lot man! really helped :) keep up the good work
Chris Tan - Will do! :)
thanks dude you rock! im bout to patrametrihosdfnos my ass off
Can you suggest me a theoretical textbook about this subject matter? I've read "Leithold" and "James Stewart": they don't explain how to do the parameterization, they just use it. By the way: good video.
very useful dude, thx a lot
felipecampos94 - No problem, glad to help!
Wait, I thought one of the major pros to parameterizing was that you can define curves such as circles since Y was dependent on T rather than X. Wouldn't we lose that benefit by making X=T?
great video!
Ezra Wyschogrod - Thanks! :)
really struggled with this thank you !
Had no idea what was going on in class until I saw this
Sir what kind of utility i get it from??
Find a parametrization of the portion of parabola
y = ax² + c
from
(−1,a + c)
to
(1, a + c) .
Hey mister, can you solve this for me ? Please
Can the x equation when you are parametrizing be anything?
Missing a t on 12 at 4.28, it should be 2t^2+12t+19. Except for that, excellent session!
What about parameterizing a curve where it isn't a function? maybe xy^2=1?
thanks
Naruto Uzumaki - You're welcome! :)
Good stuff, Thaanks
very helpful
@Mis Sempoi -- (-t)^2 = (-t)(-t) = t^2 (since -1*-1=1). Hope that helps.
Would there be a way in which we can't paremeterize an equation?
Worth watching!
thx
how do you do your video like this? with yourself in the corner?
Hi Kathryyn McIntosh , Google "green screen" or "chroma key".
U made it simple❤❤❤
Hey guys,
I need help.
The function x=z^2 +1 is given. Now I want to parametrize it. In the solution they use the "simple parametrization of a curve" and compute x(t)= (t^2 +1/0/t).
I can't comprehend this.
Thanks in advance for your help!!
tnx!
awesome dude....subscribed :)
Asymptote - Sweet! :)
You're the best
Yes, this is HOW you do it, but please explain WHY I should do it. Why would y = 2t^2 + 1 be simpler than y = 2x^2 + 1, it's basically the same shit
y= 2(-t)square+1
=2tsqaure+1?
Where’s the negative gone? sorry I don’t get it T_T
A more visual approach would be better.
Does every curve have parametric equations?
Please answer and explained with example
i know more
most useless video ever
thx