How to Parametrize a Curve

[@hannananan9427]

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!

[@clashroyalecontent9645]

🤓

[@Manny123-y3j]

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!

[@clashroyalecontent9645]

🤓

[@alexwill6900]

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

[@clashroyalecontent9645]

🤓

[@siphilipe]

Definition of great teacher: Is the one who makes complicated stuff easy. And you are. Thanks!

[@bgreene3674]

Wow. This seemed so complicated in class, but you made it easy-peasy. Thank you so much!

[@clashroyalecontent9645]

🤓

[@FINSuojeluskunta]

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.

[@fireflylectures]

🤙🏻

[@TheWojtek619]

Thank you very much - exactly what I was looking for - clear and concise!

[@ΆνφαΝόμπα]

I was literally struggling with this for few months. Thanks a lot for cleaning this up🙂

[@kunasheelan2189]

The most easiest explanation so far. Thank you so much.

[@David_F97]

Should have showed parametrization of more complicated functions.

[@nataaalia]

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.

[@SdtGvn]

Perfect👏 the more straightforward and the more elegant

[@Cyrus_II]

Thank you. You're a legend. You solved my problem without even making it half way through the vid

[@tljstewart]

@:33 "there are lots of rights answers" Perfect. This fact is overlooked and understated too often.

[@douchelip]

Thank you for the simple explanation.

[@savannahconlin6865]

This practically saved my life.

[@clashroyalecontent9645]

Holy shit bro this was the fucking easiest damn thing to do thank you so fucking much bro

[@ammar7609]

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?

[@soumyajitsarkar2372]

Amazing and very well explained :)) Thank you Sir and lots of love from India :)

[@chongochishimba6207]

Done deal...was facing problems on parameterization thanks

[@mefatoum1979]

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

[@Entertanium101]

Very helpful video

[@MrBlash93]

Amazing Video! You really helped me. Thank you!

[@fireflylectures]

Blas, you are very welcome!

[@Brenovisk7]

Thank you! Finally understood parametric equations

[@rayannzakhia9372]

This was really useful

[@lambrospasaliadis6286]

yep, u did for the simple functions, but VERY GOOD WORK!

[@omarshaaban1887]

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!

[@Secondbloodbrother]

Thank you very much! So simple but so helpful!

[@harmsyamial5392]

thank you so much

[@cool_huip_]

Thank you sir

[@alvinlepik5265]

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.

[@fireflylectures]

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".

[@alvinlepik5265]

Cheers for the suggestion, I've been trying to find out more about parametrization in general. (Y)

[@rajendramisir3530]

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.

[@andreaLA222]

Thanks for the video!

[@iangomez7190]

thank you!

[@AyushBhattfe]

Thanks a lot Sir! Great explanation!

[@freemindfreemind9865]

that explanation is just great!!! thx a lot

[@fireflylectures]

Djimy Slot - No problem :)

[@luiszmaciasvalade5807]

Muchas gracias... excelente explicacion

[@fireflylectures]

Luis zMacias Valade De nada!

[@sarahrichardson8624]

thanks dude you rock! im bout to patrametrihosdfnos my ass off

[@comet1062]

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)?

[@ravidarji]

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

[@tasintahmid8559]

Thanks a lot

[@Live_with_rahulG]

Great lecture!!! Thanks sir for solving my problem.😎😎

[@sergiomanzetti1021]

Missing a t on 12 at 4.28, it should be 2t^2+12t+19. Except for that, excellent session!

[@ezrawyschogrod3468]

great video!

[@fireflylectures]

Ezra Wyschogrod - Thanks! :)

[@pedroneto8991]

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.

[@billwindsor4224]

Great, clear explanation, sir - thank you!

[@felipecampos94]

very useful dude, thx a lot

[@fireflylectures]

felipecampos94 - No problem, glad to help!

[@maris6848]

thank you right to the point

[@jamesdodrill384]

i was curious on how it changes direction. helps out. thanks

[@EmpyreanLightASMR]

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.

[@JossinJax]

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?

[@aniketmukherjee4392]

Sir what kind of utility i get it from??

[@alinagonzalez4129]

very helpful

[@Randomguy-vl6gi]

What you did is just substitute

[@alinagonzalez4129]

Had no idea what was going on in class until I saw this

[@TFGValce]

thanks a lot man! really helped :) keep up the good work

[@fireflylectures]

Chris Tan - Will do! :)

[@vishgudur7742]

Can the x equation when you are parametrizing be anything?

[@TheTristan890]

right on point, thanks

[@harleyjean6287]

really struggled with this thank you !

[@skills4089]

U made it simple❤❤❤

[@SuperJg007]

Worth watching!

[@lucianoqueiroz2710]

Thank you. at 4:17 3^2×2 = 18.

[@hassamrajpoot8397]

Would there be a way in which we can't paremeterize an equation?

[@Gipsy4u]

Good stuff, Thaanks

[@thesage1096]

thanks

[@fireflylectures]

Naruto Uzumaki - You're welcome! :)

[@robinschneider8183]

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!!

[@DarkLava2007]

What about parameterizing a curve where it isn't a function? maybe xy^2=1?

[@user-gp8tp1di4h]

You're the best

[@HiTeaJJJ]

thx

[@tyan4380]

tnx!

[@B.A.Gondal]

awesome dude....subscribed :)

[@fireflylectures]

Asymptote - Sweet! :)

[@user-tt3vp1uw6o]

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

[@ramzanjoura4292]

Does every curve have parametric equations? Please answer and explained with example

[@missempoi1976]

y= 2(-t)square+1 =2tsqaure+1? Where’s the negative gone? sorry I don’t get it T_T

[@KitKat5151]

how do you do your video like this? with yourself in the corner?

[@fireflylectures]

Hi Kathryyn McIntosh , Google "green screen" or "chroma key".

[@michelandrew2226]

A more visual approach would be better.

[@fireflylectures]

@Mis Sempoi -- (-t)^2 = (-t)(-t) = t^2 (since -1*-1=1). Hope that helps.

[@harshitkumar1144]

i know more

[@SawyerHinson]

most useless video ever

[@LateNightRituals]

thx