Linear Independent Functions - The Wronskian

This video provides a lesson on determining if two functions are linear independent using the Wronskian.
Site: mathispower4u.com

[@totallytechalicious]

I've been watching your videos since 2014 and it's 2023 now. I can't thank you enough for making this content available online. My math performance in class has been stellar with your help.

[@Mathispower4u]

Thank you for the comment. I am happy that I have been able to help you. That is exactly why I start this channel 13 years ago! 😃

[@ivyk5025]

You sir are a legend of math KZbin! Not only have I been getting 100's on all my exams up to calc 4 (I had to retake calc 1 due to disaster grades), but I am able to learn quickly and easily! To all of those taking calculus: you can trust this channel to teach math. Just speed run it on the bus or whatever!

[@dorianclare4681]

2021 and this video was still extremely helpful. Thank you.

[@linhdinhnguyenvy94]

Very nice videos! Finally I can understand the Wronskian. Also, which software did you use?

[@vidgami46]

Thank you so much for posting this. My professor is next to impossible to understand, and you cover the same material very clearly.

[@AegixDrakan]

OHHHHH so that's what a freakin' wronskian is! Man, my teacher's slides were useless. THIS tutorial right here actually made it clear. Thanks! And thanks for that last little quote on the final slide. Gives me the drive to keep banging my head against this wall made of Math until I manage to break it and hopefully pass this stinking course.

[@pintasingh95]

1hr before the exam, I'm glad I found this video

[@sweetgoblin]

I know its kinda late but....did your exam went well

[@keeler1160]

At first I was like man I really dont feel like watching a 12 min video. Then i just said F it, i'm gonna watch it. I got hooked man.

[@dubbemand]

I actually stopped smoking because this video was more addicting.

[@davidbober8506]

Beast video, was having a tough time understanding how to work these problems.

[@leolson3]

You have helped me tremendously both in calculus and differential equations. Thanks for all that you are doing.

[@Mathispower4u]

I am glad! Keep at it.

[@jib9058]

your videos about D.E help me a lot .Thank you so much sir

[@matteiser1954]

I watched a few videos on this topic and this one helped me the most. Thanks!

[@Mathispower4u]

I'm glad. Thank you for the comment.

[@Peter_1986]

Mathispower4u Your voice is pleasant to listen to as well. 8-)

[@Mathispower4u]

Laurelindo Thank you.

[@eson3092]

Thanks for your tutorial. It is very straightforward for me to understand the Wronskian in differential equations's application. Just wonder, is it possible to use 'first order of Wronskian equals to zero' to find the singular points in the designed domain?

[@JHponyland]

I was wondering if a function is odd and another is even does that mean they can not be multiples of one another? Meaning odd and even functions will always be linearly independent? I tested some examples out and so far I haven't been able to find a set. Although I really do like using the Wronskian but I was just curious I guess.

[@tuckertiger7859]

This is so well explained and clear!! Thanks a bunch

[@Brandon-sx7pu]

Sheesh, Explained it better than my math professor

[@enzokuhlemsotra6383]

Thank You very much sir you explained everything very clearly🙏God bless you.

[@Mathispower4u]

You are most welcome

[@trytolearnmathematics343]

Every video helpfull for me ,love from India

[@Mathispower4u]

Glad to be able to help!

[@SangramNiramale]

Thanks a lot for a very clear explanation with good examples.

[@chriswass1176]

what if you were not able to find a C1 and C2 that will make the equation zero?

[@The6Kidd9SiLENT]

Can this be used to determine whether or not given functions are solutions to a DE?

[@oscarr4570]

as my friend borat would say, VERYY NIIIIIIIIICE

[@jaskaransingh0304]

Amazing video. Thank you for your help.

[@mikechowmanho]

Good explanation ! Your lesson is very useful ! Support !

[@ltrinhmuseum]

You have four cases. Wronskian = 0 for all x, Wronskian = 0 for some x, Wronskian != 0 for all x, Wronskian != 0 for some x. These four cases can be confusing for someone who learns this concept the first time. For instance, to prove that a set of functions are linearly independent you only need to prove that for some x over an interval yields Wronskian = 0. Hence, it would be wrong to think that Wronskian has to be 0 for all x over an interval. This is a subtle point, but not knowing details can lead you astray.

[@chick3n71]

Wouldn’t it be the same to check whether the inner product of 2 functions on interval I is equal to 0?

[@samramehboob4839]

amazing explanation... its really helpful

[@eleazaralmazan4089]

Your videos are awesome!

[@carloibarreta3473]

How do I know what the value of Csub1 should I substitute?

[@IamPROUDece]

Hey! nice tutorial I learned a lot! what book are you using? I'd like to try other some examples.. Thanks!!!

[@IamPROUDece]

I mean exercises..

[@yuyuejiang3278]

Such a great video! Awesome.

[@RAW2404]

thank you it was very helpful🤞✌👌

[@recipento225]

good explanations.. can determine the constants in case of x , 5x , x^2....plzzz

[@isaacneterosmiddlefinger186]

your channel is awesome

[@kkamous7278]

Love u from Pakistan,,, Great vidio

[@NickTheHunter]

Thank you very much for this video! It helped a lot!

[@YatharthRai]

So much thanks! This helped a lot!

[@adityacapte]

Thanks a lot !! Really clear explanation of the topic ! :)

[@jamunarani8361]

Thank u sir good service

[@SamuelBassVEVO]

best videos, love the quote at the end too.

[@ScilexGuitar]

3:50 Cant you just choose like x = 1 and then calculate the determinant to find that W =/= 0 ?

[@NeverChange95]

Can C equal to x? or it can only be a constant and "e" to the power of.. ?

[@wanx891]

very helpful thank you sir

[@akshaydamle95]

Thanks a lot, solved my doubts :)

[@aasthasharma7161]

🤗☺️thank you so much sir

[@GuillermoValleCosmos]

Why if the Wronksian is 0, it does not mean thy are dependent?

[@DancingPianoist96]

Super helpful! thank you so much! :D

[@faraoncindyb.7955]

what do you mean by interval ?

[@sidharthgurjar7477]

can wronskian be used for infinite order matrix???

[@dubbemand]

Thank you!

[@TheMrmoste]

The best !! keep going

[@Ashtheawesome1]

Thanks champ helped a bunch :D

[@Mathispower4u]

Thanks for watching.

[@bad9boy9999]

you are the best

[@SARA-ud1ro]

that was helpful ..thank you

[@byron5306]

thanks very much

[@stonebridgehibr9714]

great. i enjoyed it

[@cucumber_999]

Is this part is a playlist?

[@Mathispower4u]

Hi, here are a couple more videos on the Wronskian: kzbin.info/www/bejne/hoCUqKeYga5sadU, kzbin.info/www/bejne/pJecYmWHntOrl9E. You can find all of my DE videos here: mathispower4u.com/diff-eq.php. Playlists are here: kzbin.infoplaylists?view=50&sort=dd&shelf_id=11

[@cucumber_999]

@@Mathispower4u oh thank you so much! The playlist version doesn’t have the word Wronskian in the name but I see it now under Second Order DE section. I’m not that far yet in the playlist but some of my practice problems mention it. P.S: You’ve been an ENORMOUS help for me in math, like jeez. I seriously hated math during highschool until I found you. Now I practically breezed through Calc 1-3 and am now on DE’. I have to say too that I saw SomeOrdianryGamer did a video on ‘deep web browsing’ and found your page, or a page that linked to your page I think! It was so cool looking. I suffered from some sort’ve frequency illusion as I had seen your page before that video and it excited me greatly seeing it again in a video from someone I watch a lot. That was when I really started to take notes on your classes. Again thank you for all this : ) and thanks for the reply! I have an assessment in a week!!

[@Mathispower4u]

@@cucumber_999 Glad I could help. Thanks for your response. It is appreciated. RightNow I am working on discrete math. Once that is complete I will be adding to the DE library. Unfortunately, it will probably be after you finish your class. I wish you continued success.

[@cucumber_999]

@@Mathispower4u I have specific notebooks for your classes so knowing that is good. I’ll have to add to it in the future then. Have a good day or night : )

[@xyzme1217]

Thanks

[@statisdt]

so wen can select any value for c1

[@maxbrat8087]

i think you messed up @5:15 shouldnt the middle terms have canceled?

[@Mathispower4u]

2x^2-(-2x^2)=2x^2+2x^2+4x^2

[@maxbrat8087]

ahh yes you were correct lol.

[@gdeao51]

2 VECTOR LINEARLY INDEPENDENT NEVER MADE UP A BASIS OF MATRIX 2X2 ? IS TRUE OR FALSE? WHY?

[@meetpatel2853]

thenks sir

[@karimkhan1312]

excelent -- very systametic

[@mohamedameri360]

I honestly came here for 3:23 - 3:26 part as I needed to know when to stop deriving, ha.

[@marekrimal2371]

What if there are more than 2 functions?

[@samramehboob4839]

Num of derivates depend upon num of functions... If three functions we will will till 2nd derivate Like in 2nd ODEs we just take 1st derivate

[@souvikroy9599]

@@samramehboob4839 I am stuck with a problem having 3 variables. Should partial derivative be used to find the wronskian??

[@cameronaminian9442]

thanks

[@AmeerHamza-cy6km]

does not works for : x,x-1,x+3

[@aridaymogaful]

thanksss allot

[@StoneZachary-y4k]

Jackson David Thomas Nancy Moore Edward

[@oscarobioha595]

LinearLY not linear independent

[@eugensunic]

TERRIFIC PRESENTATION

[@samanhemal1361]

thanks