Lambert W Function Intuition

In this video I start building some intuition for the Lambert W function by plotting it in comparison to its inverse.
For more videos in this series, visit:
• Lambert W Function

[@jamesmccamish3901]

You do a great job of simplifying things as much as they can be. Much appreciated.

[@marpin6162]

You deserve more subscribers.

[@physicsandmathlectures3289]

Thank you!

[@MrAksupriatna]

I agree, so that why I subscribe

[@alijoueizadeh2896]

Thank you for your precious time.

[@peternolan814]

Hello,
A day has passed since I watched this video having commented yesterday what's below. Today is May 12 2021.
Say I have a value for x some number. Then I can write:
(some number) = yexpy
I was thinking that the whole problem with the Lambert W Function is that this equation cannot be solved for y and yet there is some other number for y such that this equation is true.
So glancing at what I wrote below I can calculate a value and get some number for in my case:
Number 2 = Exp(1 -4at/c)
by selecting a value for t and entering values for the constants a and c.
I then can write:
Number 2 = yexpy
such that the value of y that satisfies this equation is:
y = W(Number 2)
the value of the Lambert W Function. This then, in my case, will yield the speed of the particle.
I think I might understand it all a bit better now,
All the best and many thanks,
Peter Nolan. Ph.D.(physics). Dublin. Ireland.
Hello,
Your account of The Lambert W Function is very good indeed. The graph is most excellent.
I'm interested in this differential equation:
dv/dt = a((1 -2v/c)/(1 - v/c))
such that v is zero when t is zero and a and c are constants.
According to Wolfram's Mathematica the solution is:
v(t) = 1/2(c -cProductLog(E^(1 - 4at/c)))
or:
v(t) = 1/2(c - cW(E^(1 - 4at/c)))
where W is The Lambert W Function and where E is "e" the base of natural logarithms. I'm struggling a bit however. I'm hoping that since t varies from zero to infinity I can select any t and calculate the value of:
E^(1 - 4at/c)
but how then do I calculate the value of y = W(x) where x = E^(1 - 4at/c)?
I'm sorry to be confused.
All the best and many thanks,
Peter Nolan. Ph.D.(physics). Dublin. Ireland. I'm 67yo.

[@hectortroncoso322]

Lets see,if i take x and aply into the function :X . e^ X so i obtain Y.
If i take now this Y,under certain conditions supposed acomplished;i want to know how to operate with the operation to be back to Y.
Thanks.

[@jamesmorton5017]

This is a good trick and sound manipulation. What is lacking is how to transform your scalar W(64ln2)/ln2 into a numerical value. What is the function of W?

[@CaptainBlackthorn]

Great video

[@physicsandmathlectures3289]

Glad you enjoyed it!

[@NXT_LVL_DVL]

The inverse of a function is just the reflection with respect to the line y = x . let's try it with polynomials and trigonometric functions or any other functions other than exponential

[@user-mo1dh1xf2k]

Решено измерение скорости имея координаты X1,X2,Y W-функция Ламберта вместо Евклидова пространства