Application of the Lambert W Function (Part 2)
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- Опубліковано 8 вер 2024
- In this Video I am going to show you how to apply the Lambert W Function. I am explaining the basic tool when it comes to application of the Lambert W Function. Watching this Video you will be ably to recognize and solve some basic problems using the Lambert W Function.
For the Lambert W Function Introduction go to: • What is the Lambert W ...
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Guys just to point out, the solution at the end is positive, x = 0.309. If you didn't know a negative times a negative is a positive 😁
I apologize for the mistake made due to lack of concentration.
Conclusion: when you study take breaks and drink coffee for better concentration :)
Thanks Ya Bec for noticing and reporting 🙂
x=0.309
x=0.756
That's (-0.5)•(-0.619061) = 0.30953 approx.
Respect
There's another positive x solution, x=W_-1_(-1/3), which is about 0.756. W can be nasty with its multiple values. This other solution also can be checked with graphing 6x and e^2x. And I wish UA-cam made easier commenting math functions... 🙂
Yes, as -1/3 is a value between -1/e and 0, product log function will have 2 real solutions, one per branch, W0 and W-1.
Seems "Those who can, do; those who can’t, teach." It is quite easy to see that 6x is not a tangent to e^2x, so the equation has either 2 or 0 solutions.
Got interested in the Lambert function recently. Your explanation of it is the best I have seen online so thank you and keep up the good work. David Lyttle
Thank you David, it really means a lot.
Thank you! I watched both videos and finally understand how this works!!
Thanks a lot.
Thank you. Elegant and clear. I'm a new subscriber 🙌👍
The clearest explanation I have seen.
You should put a light diffuser in front of light to reduce glare on greenboard. Stay safe
Great video....Love and respect from India!!🇮🇳🇮🇳🇮🇳🇮🇳
Thank you, I appreciate it 🙏
@@intellecta2686 alwys most wlcm mam,,keep shining! 🤟🤟
Wow, I have learned another way to solve for x. Thanks.
Haha. I tried so hard to follow along. You are so much better at math than me. ☺️ enjoyed your video. Keep them coming 👍
Heheh this is not very common math, there are not many people who use this, mostly programmers. It's totally normal for you to look complicated :)
hi, if i dont want to use wolfram, how do i compute W(-1/3) munally..
You cannot do that since the Lambert function has no analytical solution!
@@gregorymirsky8707 but you can numerically but that is what wolfram does....
As a result of the solution of this problem: When we look at the Wolfram table, which of the values W(-1/3 ) = -1.512135 and -0.619061 will we accept as the solution to our problem? You got the value - 0.619061. From where ? I couldn't understand this. Also, can you give me information about the application (used on phones or computers) where I can obtain the Wolfram table, which is the most used in solving such problems. Thank you.
I wish you successful work. Kind regards.
Man the Lambert W function is so cool, I wish it was real.
Thank you!
Please use good chalk on the board
Excelente. Explicas muy bien.
It's really difficult to pay attention to this with such beauty in front of the board. ;)
but -1/3 >-1/e then 2 solutions, I think x≈0.309 x ≈0.756. How is it possible calculate Lambert function if I haven't Wolframe? Thanks
A smile once in a whiles would be most becoming .. 😁
Thank you for making this video. Very well explained . What it does not do is to explain the product log function i.e. what exactly is it etc...
Please make more math videos, I particularly liked your historical excursion i.e. what does w mean and where did it come from etc.
Thank you for the comment. I appreciate it. I will definitely be making more math videos, more often than I have so far.
Since solution x = -0.3, and so 6*x is also negative, but e^(x) > 0, and so initial equation is not fulfilled, because then: 6 * (-0.3 ) = e^(-0.6) would need to be true
What is W(-1/3) it just came out of nowhere and we should go to wolfram to answer that question?
Also, the solution, is it the only solution or is it good enough to just supply the one solution if we can get it?
Very clear presentation.
Ottimo video!
good ideas, Lambert W is a confusing function but its getting a bit clearer😔
とても分かりやすかったです
ところで、先生の動画は複素平面への理解を大変助けると思います
Thanks
very easy for me........
If you graph this two functions you can see that they touch each other twice, therefore there are two solutions for this equation. What's the second solution?
Lambert W_(-1)(1/3)/-2 is the other solution
Oh yeah, the solution of 6x =e^(2x) helps me to have a better life.
it's those with a disinterest to learning like you who constantly complain about not knowing
Beautiful explanation from a beautiful lady.
thank you for making good video
last answer mean x=+~~~?! ^^
thank you teacher
One more solution x=0.75622.Comes from the -1 branch of Lambert W function.
Wrong solution..6x=e^(2x) , x=-0.3... negatife solution.impossibble
Please watch my video ua-cam.com/video/nY7Y01oH0z8/v-deo.html. Here I explained that x must be ≥ −1/e. That means you can have a negative solution but it must be greater than or equal to −1/e.
@@intellecta2686 i watched it..but that problem solution must be positive
Ooo that, you are right haha didn't even notice that mistake. Thank you for noticing. Have to pin it. I thought you mean it's not allowed to have negative solutions. But yeah, it is positive 👍
@@intellecta2686 Yes, you should pin that reply. I skipped ahead and wondered why my sign was wrong. Not.
@@intellecta2686normally 2 solutions but you have the only 1
It is almost impossible to see what you write on the board. Maybe it is because of the light and chalk you use.
True. First video with new lights + new chalk.
X=0.309 (positive)
X is positive
Must have TWO solutions?
Correct
I find rather two solutions namely x approx 0.309 or x approx 0.756. Why did you get only one solution? Wolfram even seems to say, that for each integer n there is a solution as given by -0.5*W_n(-1/3). But you chose not to talk about those solutions as defined by the parameter n. Why is that?
Please solve the integration of sqrt of cosec(x)
elliptical integral
Thnk you for explanation
But how can I calculate-1/2W(-1/3)
You can watch this video, I explained everything ua-cam.com/video/hu8oXMFDNQk/v-deo.html
l,ecriture est invisible à cause de l,éclairage
👍❤
The Reflection from the board is distracting.
Pls always make your chalky bold
ok
Dear teacher! Please change your chalk. fade!
W is just an approximation like log. Nothing special about it. Now it is better if you use a computer numerically solving such equations, you do it at the end anyway by calculating W.
Your writing is not visible, because of the color of your chalk..
Je vous remercie beaucoup de tes leçons,je voudrais te dire que l'écriture n'apparaît pas bien merci
I did not understand ua-cam.com/video/whgoDbcSClY/v-deo.html
why is it equal to x
What is your Name?