Using the LAMBERT W FUNCTION find ALL solutions! / ( W_0 and W_-1)
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- Опубліковано 10 лип 2024
- In this video we are going to solve 2 equations using the Lambert W Function. The goal is to find all real solutions using the lambert w function. You will learn how to determine how many solutions should you get considering just the lambert w function. (without the graph)
For the Lambert W function, go to: • What is the Lambert W ...
For the Application of the Lambert W Function got to: • Application of the Lam...
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Timecodes
0:00 - Intro
0:10 - introduction
2:52 - explaining two ways of solving the equation solve x^2=2^x,solve
3:02 - solving x^2=2^x for x greater than 0
5:52 - explaining how many solutions should we get using just the lambert W Function
8:59 - explaining all possible solution for x greater than 0 , for both branches W_0 and W_-1
10:57 - how to get expression for x considering the branch W_-1
15:30 - solving for x is less than 0
21:50 - solving the equation 2^x = 10x
24:50 - begging for subscribers :D
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For the Lambert W function, go to: www.youtube.com/watch?v=nY7Y0...
For the Application of the Lambert W Function got to: ua-cam.com/video/whgoDbcSClY/v-deo.html
Have a great day!
Hi Ivana!
Thanks a lot for this video and taking my comment. 😊
Please maintain the best quality that you have in your videos. I pray that you get atleast 1 million subscribers very soon!
Guess who has made the simplest and the best explanation video series on Lambert-W function?! :)
hi friends. hi teacher
We know that W(xlnx) = lnx
And how about *W[(lnx)/x]* ?
Is there some "formula" in this case?
For example
We know W(17ln17) = ln17
But to find/calculate W[(ln17)/17], can we find an exact value, a perfect value, without using approximations, without using things like Wolfram Alpha?
these are nice videos, i remember searching lambert W function videos on youtube only a few years ago and finding very little information about it, but yours and a few other channels quite recently have posted very good about it. much appreciated! keep it up
Yes it's true, more and more channels have been posting it, which I find very good. Thank you for watching and for nice words.
Very nice. Thanks!
Congrats for 1k subs!
Thank you for being here on this channel and for the support ❤
Cool, thanks for explaning how to solve different equations :D also good way to remind myself of wolfram functionalities :)
Thank you for watching 👀🙏
Thank you. I was trying to solve this problem yesterday for fun. Never even heard of Lambert W function before Wolfram Alpha gave me an answer. Thanks for the good explanation.
You are very welcome. I'm glad this video helped you.
thanx a lot very good explanation
Ottima spiegazione!
Grazie Ivana.
Grazie a te ripasso tanti concetti di matematica e fisica e imparo un pò l'inglese.
Grazie Stefano!
thank you
A very nice lesson! OnceI was a mathematics teacher in an Italian high school but I never taught the Lambert function (which I barely knew). Is it normal to teach these things in the USA? Thanks for the reply.
Really is sincerelly amazing;the clear of your way of teaching, thanks you.
Is very clear the way of your english; im from Argentina and mostly tutorials of other teachers in you tube,are very dfficult to understand for me;here we uses spanish,only,so to the difficulties natural of maths;it is added the difficulties of idiom,because of this ;i say thanks for all,mrs teacher.
Helo,professor;coul you teach us. To solve solutions ;the teory of root matrix of matrix?
Thanks you for all!!
Have a good yerar.!
Nice video with easy to understand explanation. Please whenever I punch my question in Wolfram alpha I get Even.
I would like to add the solutions of the case a^x=x ^n ,with a>0 and n>0 : x1=Exp[-W[-ln [a] /n] , x2= Exp[- W[-1 ,-ln [a]/n] ]
x3= - Exp[-W[ln[a]/n] .More than 2 solutions may arise if n is an even number.
Good
Thank you for this really helpful and precious content. During my research I contact a problem in the form of { A+Bx^C+DLn(Ex+F)=0} This probably should be solved by Lambert W Function. But I couldn't transform it into a solvable form of Lambert Function. My question is that, can the equations in the general form of {A+Bx^C+DLn(Ex^F+G)=0} be solved by Lambert W function? Thank you in advance for your response🙏
How do you know, that only the W_0 and W_(-1) have to be considered?
First of all, Thanks for a Perfect and detailed video!
But the only missing part here is:
How to calculate the W_-1, with formula/series?
I know there is a series for W_0.
But i didnt find any proper answer for W_-1 🥺
I'd be happy if you upload a video with a solution for finding the numerical value of
W_-1 🙏🏻
With the repeated series: Xnew = Xn - f(Xn)/f'(Xn) you will find the respective x value which is closest to your guess ,so the series should worm for all solutions ,you just have to start with different guessed values.
w(a)=x
you want to find x
x*e^x=a
x*e^x-a=0
use the newtonian formula to find x, itll give you w(a), the starting x value for the sequence will be relevant to which branch you will obtain the result of
there is no series for it btw
Thanks! Can you please share what are the real life applications of Lambert W function??
Finding the answer to an equation.
@@WomenCallYouMoid I think you have misunderstood or perhaps purposely ignored what hufeza 1991 meant. I reckon what he/she was asking for was examples of where the Lambert W function is useful in solving equations which arise in fields such as physics, engineering, finance, economics, sociology, evolutionary theory etc. rather than just in mathematics itself. I also would be interested to know the answer to the way I have interpreted hufeza's question especially if there are applications in physics.
I thought I left a comment but I don't see it, maybe it was removed. My question is that at 15:36 for x
🙏🎆🙏
1:51
Also waiting for 1000 subs so we celebrate :D
Heheh yees 🥳
hi friends. hi teacher
We know that W(xlnx) = lnx
And how about *W[(lnx)/x]* ?
Is there some "formula" in this case?
For example
We know W(17ln17) = ln17
But to find/calculate W[(ln17)/17], can we find an exact value, a perfect value, without using approximations, without using things like Wolfram Alpha?
Only 2 and 4 I guess in turns of integers
3 real values. For both branches, W_0 and W_-1, and for x>0 and for x < 0. (Bc of x^2)
Please when you are talking to the audience don’t hide the board thank you
Your hair is blocking the board
0:19 I’m sorry, but I don’t think you’ll ever get 1000! subs :((( (i think like a real mathematician, I’m sorry)
The one who tells the truth must not be silenced 😷🥺😃
You're right. ;P
[Geek alert ahead!] For 1000! (1000 factorial) subscribers, each and every atom in the universe has to somehow create approx 10^2488 Google accounts and subscribe. That seems very hard...
lol
@@adityakumargupta9730 that comparison is very good. thanks!
@@adityakumargupta9730These are rookie numbers. :)