There are some teachers that show you how smart they are. And there are teachers the teach you how to solve. You are the perfect example the latter one.
You are cool. My dad was a math and science teacher for over 40 years (a great benefit for me). He instilled in me a love of math. I'm glad I found your channel. It's time to reclaim my lost working years now that I'm retired.
@rutamupadhye1828 this doesn't work. I first tried it on desmos and quickly realized that there are no solutions just differentiating both sides. A quick search on math stack exchange tells me that this is because to be able to differentiate both sides, both sides have to be functions, and not just this equivalence that we have here. If we do so we can clearly see that for f(x)=2^x+x and g(x)=5, f(x) is not equal to g(x) for all x. We can still use differentiation to solve this problem though, as we can find an approximation as accurate as we're willing to calculate with Newton's method (heh, that's the name of the channel). To apply it, we can define a function, f(x)=2^x+x-5 (its roots are the solutions to the problem), and find its derivative f'(x)=ln(2)2^x+1. Newton's method is iterative, and the next step in the approximation (c_n) is written in terms of the previous approximation (c_[n-1]) as c_n=c_[n-1]-(f(c_[n-1]))/(f'(c_[n-1])) (admittedly this looks overly complex in plaintext but look it but to get a better idea). It starts with an initial guess, and each successive iteration approximately doubles the precision. This gives us a value of about 1.71562073328.
It is giving the wrong answer. And in India we have learnt to never differentiate an equation. Although, we can differentiate identities. But, I am not sure of this.@@rutamupadhye1828
First semester of Mech Engineering, a professor gave us a task to solve an equation to find the ideal chord length for an airplane wing. He didn't tell us the equation was unsolvable via elementary functions, essentially the point was having students crack heads at it until figuring out they couldn't solve it analytically and needed to use some numerical method, a valuable lesson going into engineering. Instead I did some research online and found the Lambert W function and managed to solve the equation with it. I'm not sure if he was impressed or mad that I avoided the main point of the exercise, but I did get a 10.
@@raghavkumarsingh4222 Oh, this was like 10 years ago. I've since graduated, got a Master's, etc. I did my Bachelor's at a federal university in Brazil. Good luck on your studies, I've had quite a few colleagues and friends from India when doing my Master's, great people.
I'm a Principal Scientist in mathematics and theoretical computer science (mainly) and still enjoy your videos. I'm not a teacher (unless you count the odd PhD), so I really admire your skill at teaching, which is something I don't really have. My wife is giggling, teasing me about - erhem - watching another guy solving him some sexy little equation. 😊
Thank you. For me, Lambert was a VERY brief aside in a larger lecture, so I quickly forgot all about it, and probably could have used it on multiple occasions. The same thing happened with the Convolution theorem. A professor said "Oh, by the way, this is the convolution theorem," wrote it in a corner of the chalkboard, and went on with the rest of the lecture. Years later, I was doing a proof for a class, and no matter what I tried, I couldn't make it work. So I worked forward from the question, worked backwards from the answer, and found a peculiar equation ay the place where the two met. So I included that equation in my proof without knowing what it was. I went to the appropriate lecture about that homework problem when the professor went over that particular proof. When he got to the mysterious equation needed to make the proof work, he said "convolution theorem" and suddenly I was able to remember that very brief aside in that calculus lecture and got mad that its mention was so brief.
I like your way of presenting in a confidential tone, the tone of someone telling a story. You know how to bring us into your world where mathematics would be a game. Don't change anything. Thank you.
I have to say that I have tried to watch several videos on this topic from prominent UA-camrs. You are the only one that actually managed to explain it to me. Thanks for a great video.
I am 31. I have no business watching these videos but I find these videos so peaceful plus I get to learn such cool things! I have always been in love with Maths (but unfortunately never had a teacher who could make it learning this fun!). Love from India. God bless you.
MERCI. J'ai bientôt 80 ans, retraité d'une fonction médicale, donc culture mathématique sommaire, je passe mon temps à “ potasser “ des maths, ainsi grâce à des transmetteurs comme vous, je m'instruis en prenant grand plaisir ; j'adore les maths ! MERCI. G.B
Finally a clear explanation of how a mixed linear and exponential equation is solved algebraically in exact form with a special function I had not heard of before.
I'm a french mathematical teacher, but i didn't know this function. Thanks for your very pedagogical explanation of this equation's technics of resolution !
Your enunciation and pace of delivery is just right for my brain to clearly process the information (comfortably) before embracing the next step in the problem process.
Sir, you are really an amazing and exciting teacher. You also speak very clear making it understandable for those who are not native in English like me. All I want to say is that I hope I had only one teacher like you during my 30 years of education. Keep going and good luck.
Dearest creator of enlightening content, your elucidation of the Lambert W function is truly captivating. Your brilliance shines brighter than the morning star itself. Gratitude for sharing your knowledge and igniting the flames of curiosity within us all. Stay celestial in your pursuits!
Tellement apaisant, et souriant ! Merci pour cette démonstration et pour vos explications que je comprends (l'anglais n'est pas ma langue naturelle). Vous prenez la peine de parler lentement pour que nous puissions intégrer vos propos. Vous êtes vraiment une très bon professeur capable d'enseigner à quelqu'un qui n'a jamais fait de mathématiques de ce niveau depuis plus de 50 ans. Le prix Nobel de pédagogie s'impose !
I am an Indian and i am really obsessed by your teaching ....... you have that art to teach and make things clear to us . i show my gratitude respectively.❤❤❤🎉🎉😊😊😊😊 you have 1 more subscriber 🎉🎉🎉🎉
Great job for an introduction to the Lambert W function. It is important to point out though, that unlike logs, the Lambert W function is multi-valued between [-1/e, 0). Therefore, you have to be careful when using it.
Merci infiniment, votre cours est très pédagogique et je commence enfin à saisir la fonction de Lambert, même si je dois m'accrocher parce que mon anglais n'est pas parfait, votre est diction claire...j'ai 70 ans et les math me passionnent. Merci. Thank you very much, your course is very educational and I finally begin to grasp the function of Lambert, even if I have to hang on because my English is not perfect, your diction is clear... I’m 70 years old and I am passionate about math. Thank you.
My friend, I am your viewer from Turkey. Even though my English is not good, I understand the language more or less and I understand your operations very well. Thank you very much indeed ❤
I came here for the maths, but to my great delight I discovered there was more enjoyment to be had; the way you speak is mesmerizing, and I really wish there was a Windows font with your beautiful handwriting.
You will learn about it when you learn quadratic equations in school. So, something like x + 5 = 0 is easy, right? x = -5. But what if you have something like x^2 + x = 5? That you can solve using quadratic equations. This will be useful if you have something like 2^x = 5. You know the answer is between 2 and 3, but what is it, exactly?
A natural Teacher as you is gold for the Student Body, You know your field extremely well. You taught me in 5 minutes what 10 other teachers tried and failed to do. Thank You Sir.
I have never subscribed faster to a UA-cam channel. Was already familiar with the Lambert function, but this was the most engaging math video I can think of to watch. Massively looking forward to checking out the rest of the channel. Thank you!
You are an excellent teacher. All explanations of this I could find online were incredibly hard to understand, but you explained this with elegance and simplicity. Wonderful job.
Yeah! After studying another similar equation, I just ground this out successfully after a few false starts along the way. Two years of college math through calculus, linear algebra, and differential equations and I never was taught the Lambert W function. Nice to expand my horizons.
Your videos are wonderful! I appreciate your enthusiasm and the clarity with which you explain things. And, as I am sure you know, the symbol you like to call "flower" is really the stylized Greek letter phi.
Boy I watch a lot of math guys on youtube, and lots of them are really nice, too. but I just love to listen to you. I would've loved to have you had as my math teacher. you are one of those where I just listen and I just understand, the sign of a great teacher.
You are really cool! Only in you i made myself to understand “W function”. With your cool presentation and nice instructions, makes me understand it. Keep it up Nice Guy!
Prime Newtons, your tutorials are excellent and i enjoy watching them. This specific Lambert W Function is new to me and i am learning it from you. Excellent video , professional details explanation. Thanks.
You are not only teaching mathematics, u r smiling mathematics, gesturing mathematics, breathing mathematics, may b sleeping and eating mathematics too,....superb
Congratulations, a very clear explanation of the Lambert function. Just one small criticism: in my opinion it needs to be emphasised that we are in general here dealing with irrational numbers which cannot be written exactly as decimals. So for example ln2 is only approximately 0.693. It is for this reason that in pure mathematics it is preferable to leave the answer as ln2.
For cases where 2^x + x = N where both N and x are positive integers, the simplest solution is to convert N to binary. For any x > 2, 2^x will always the most significant binary digit and x the sum of the remaining binary digits =1. I shall have to learn why the Lambert W function works. At 71, its been over 50 years since I learned the expansion for e. Until I work through the derivation of the expansion using calculus I doubt I will properly understand Lambert W.
Thank you. That was a good one. I stumbled on your video after watching another video on the Lambert W function. I do say that functions like this are sometimes more difficult than some problems encountered in the Calculus because of the depth of manipulation and rewriting involved to get everything arranged in the correct format of the Lambert W function. Your teaching methods and style of delivery are impeccable and peerless. I have already subscribed and would be very happy to participate as a member of your community. Cheers. P.S. Hibiscus 🌺 is a tropical flowering plant whose flowers come in different colours (white, green, yellow, pink, etc.). The red Hibiscus is especially renowned for its culinary use in making the sorrel drink or the Hibiscus tea (called 'Zobo' in Nigeria 🇳🇬). Cheers.
I recently stumbled upon this product logarithm and was able to solve simple things like x^x = 2, but this particular one defied me (or rather: I messed it up a bit). Luckily you took me by the hand and led me to the promised land. Seems like the W function has some power in it 😊. Thanks for the lecture!
I saw a similar equation like this when I was learning about diodes & transistors. I had to guess a solution by repeatedly putting different x’s on the equation, but this seems like a whole new perspective to solve!! I really love your explanation!!
Really interesting how, when I saw your video, I solved it myself first, and we rearranged it in different ways! I exponentiated both sides with base 2 and then multiplied both sides by ln2, getting the required form, and so 2^x ln2 = W(32 ln2). I had no idea there were different ways to solve these equations using Lambert W.
I did a different shortcut, multiplying both sides by e^-ln2 in order to remove it from the left hand side rather than adding it to the "input" of the productlog haha
Initially i was skeptical about this video question and solution.... You have missed the odd step, but - you have a wonderful demeanour and excellent board work and communication skills....
Best video on this topic I have seen. Very excellent job! Note: I actually have a masters in EE and have had math up through 700 level, so this is just me going back and refreshing my memory on the W fn after seeing a youtube video suggesting an algebra problem I should have been able to solve quickly and realized I had forgot how Lambert fn works. Most of the videos don't explain it as clearly as you did. This was a perfect quick refresh. Am I odd that I go back and refresh my very old algebra skills in algebra when I have been using calculus to do my job for the last 40+ years? In all fairness, problems like this do not come up often in my line of work, however I use calculus everyday.
What the hell ??? What level math is this ??I had college Algebra Trigonometry and 4 semesters of calculus I had to slow down this video work this out on a pice of paper So I could better understand I never heard of this “W “ until today You did an excellent job of explaining it was just little to fast for my 66 year old brain to keep up So got a pice of paper and started to write down problem as you were doing it I believe in hands on doing math.This has to be an advanced college algebra course That you would take after college algebra Something I never took I am totally blown away I am definitely subscribing to your channel Totally impressive
Very nice! I knew about the Lambert W function but I don’t think I would have been able to express the equation in a form where it could be applied. Keep up the great work 👍👍👍
Subscribed, better than any, literally ANY lesson I've come up over yet. Mathematics is my favorite subject and I explore new functions/techniques and try to learn once I see those. I often find it quite frustrating to not get a proper explanation, searched throughout the whole internet. It gives me trouble to search for new things which actually teaches from the beginning of a topic. I've casually and randomly jumped upon this channel and I'm genuinely fascinated about how easy and clear, yet proper his lessons are! You've just earned a sub bro, keep it up ❤❤
Thank you for this! I was aware of the function before but couldn't really wrap my head around it. This has cleared things up for me. Much appreciated!
You've re-kindled my love of Math. I got sidetracked several decades ago but your calm teaching manner and clear solutions has given me new inspiration and a better way to spend some of my time in mental workouts :) There are many "smart' people, like some of my old Physics/Maths Profs...but few who could teach. Thanks very much.
There are some teachers that show you how smart they are. And there are teachers the teach you how to solve. You are the perfect example the latter one.
Thank you! Wish I deserve such magnanimity!
@PrimeNewtons outside of gta 5, i've never seen anyone use the word magnanimous (or magnanimity) lol.
Jokes aside, you deserve a lot more subs
And then there's teachers like mine who do neither 😂
0@@PrimeNewtons
You are cool. My dad was a math and science teacher for over 40 years (a great benefit for me). He instilled in me a love of math. I'm glad I found your channel. It's time to reclaim my lost working years now that I'm retired.
Ценный Й😅😮😮😮1
I am the one who integrates
Thank you walter white
What percentage of our genetics has to doe with medical health ?
I thought your dad was a chemistry teacher
The best thing is I learn Math from your videos without getting bored. Thats a mark of a great teacher.
Glad you think so!
You could also differentiate the eq and find it ig
@rutamupadhye1828 this doesn't work. I first tried it on desmos and quickly realized that there are no solutions just differentiating both sides. A quick search on math stack exchange tells me that this is because to be able to differentiate both sides, both sides have to be functions, and not just this equivalence that we have here. If we do so we can clearly see that for f(x)=2^x+x and g(x)=5, f(x) is not equal to g(x) for all x.
We can still use differentiation to solve this problem though, as we can find an approximation as accurate as we're willing to calculate with Newton's method (heh, that's the name of the channel). To apply it, we can define a function, f(x)=2^x+x-5 (its roots are the solutions to the problem), and find its derivative f'(x)=ln(2)2^x+1. Newton's method is iterative, and the next step in the approximation (c_n) is written in terms of the previous approximation (c_[n-1]) as c_n=c_[n-1]-(f(c_[n-1]))/(f'(c_[n-1])) (admittedly this looks overly complex in plaintext but look it but to get a better idea). It starts with an initial guess, and each successive iteration approximately doubles the precision. This gives us a value of about 1.71562073328.
It is giving the wrong answer. And in India we have learnt to never differentiate an equation. Although, we can differentiate identities. But, I am not sure of this.@@rutamupadhye1828
@@rutamupadhye1828 how when I'm doing it log is being undefined (log²(-1/ln2))
First semester of Mech Engineering, a professor gave us a task to solve an equation to find the ideal chord length for an airplane wing. He didn't tell us the equation was unsolvable via elementary functions, essentially the point was having students crack heads at it until figuring out they couldn't solve it analytically and needed to use some numerical method, a valuable lesson going into engineering. Instead I did some research online and found the Lambert W function and managed to solve the equation with it. I'm not sure if he was impressed or mad that I avoided the main point of the exercise, but I did get a 10.
May I know from which institute u are doing Mech Engg because Iam too in 1st sem ME ...from INDIA
@@raghavkumarsingh4222 Oh, this was like 10 years ago. I've since graduated, got a Master's, etc. I did my Bachelor's at a federal university in Brazil. Good luck on your studies, I've had quite a few colleagues and friends from India when doing my Master's, great people.
Out of 100?
Because every professor I know is going to go: "Hey, this guy is not supposed to know the Lambert W!"
10 out of 1000?
I used this at Lambda Lambda Lambda
I'm a Principal Scientist in mathematics and theoretical computer science (mainly) and still enjoy your videos. I'm not a teacher (unless you count the odd PhD), so I really admire your skill at teaching, which is something I don't really have.
My wife is giggling, teasing me about - erhem - watching another guy solving him some sexy little equation. 😊
I am honored. Thank you 😊
"Unless you count the odd PhD"
I wish to be able to use that phrase to describe my education someday
@@srig3649Same man. same.
Easily the best intro to the Lambert W on UA-cam.
yes
I totally agree!!!
bprp better
The chalk sound with your soft voice and clear hand writing almost gave me ASMR. 10/10
Thank you. For me, Lambert was a VERY brief aside in a larger lecture, so I quickly forgot all about it, and probably could have used it on multiple occasions.
The same thing happened with the Convolution theorem. A professor said "Oh, by the way, this is the convolution theorem," wrote it in a corner of the chalkboard, and went on with the rest of the lecture.
Years later, I was doing a proof for a class, and no matter what I tried, I couldn't make it work. So I worked forward from the question, worked backwards from the answer, and found a peculiar equation ay the place where the two met. So I included that equation in my proof without knowing what it was. I went to the appropriate lecture about that homework problem when the professor went over that particular proof. When he got to the mysterious equation needed to make the proof work, he said "convolution theorem" and suddenly I was able to remember that very brief aside in that calculus lecture and got mad that its mention was so brief.
I like your way of presenting in a confidential tone, the tone of someone telling a story. You know how to bring us into your world where mathematics would be a game. Don't change anything. Thank you.
I have to say that I have tried to watch several videos on this topic from prominent UA-camrs. You are the only one that actually managed to explain it to me. Thanks for a great video.
Excellent job of describing a use of the Lambert function... you are a great teacher !
I am 31. I have no business watching these videos but I find these videos so peaceful plus I get to learn such cool things! I have always been in love with Maths (but unfortunately never had a teacher who could make it learning this fun!).
Love from India. God bless you.
MERCI. J'ai bientôt 80 ans, retraité d'une fonction médicale, donc culture mathématique sommaire, je passe mon temps à “ potasser “ des maths, ainsi grâce à des transmetteurs comme vous, je m'instruis en prenant grand plaisir ; j'adore les maths ! MERCI. G.B
Finally a clear explanation of how a mixed linear and exponential equation is solved algebraically in exact form with a special function I had not heard of before.
I love your way of explaining, the expressions and light in your face when you come to the conclusions. Admirable!
So far the best mathematician I've come across
Such a clean and clear instruction without any intimidating math jargon or notation!
I'm a french mathematical teacher, but i didn't know this function. Thanks for your very pedagogical explanation of this equation's technics of resolution !
Lambert function should really be part of french culture
Your enunciation and pace of delivery is just right for my brain to clearly process the information (comfortably) before embracing the next step in the problem process.
Sir, you are really an amazing and exciting teacher. You also speak very clear making it understandable for those who are not native in English like me.
All I want to say is that I hope I had only one teacher like you during my 30 years of education.
Keep going and good luck.
As an old engineering math tutor i appreciate your expression .You really simplify the difficult problems.
I have watched a number of Lambert W function clips and done some problems but this one was very nicely explained. Step by step and methodical. Kudos
You are good Sir, both in teaching and knowledge.....I'm 75yrs and still learning.
This is the perfect level of math for me. I haven’t done this stuff for forty years, and it feels good to get back to it.
Your penmanship is amazing.
chalkmanship
Man, you have such a calming voice, it makes it really easy to listen to you and understand everything!
Dearest creator of enlightening content, your elucidation of the Lambert W function is truly captivating. Your brilliance shines brighter than the morning star itself. Gratitude for sharing your knowledge and igniting the flames of curiosity within us all. Stay celestial in your pursuits!
Tellement apaisant, et souriant ! Merci pour cette démonstration et pour vos explications que je comprends (l'anglais n'est pas ma langue naturelle). Vous prenez la peine de parler lentement pour que nous puissions intégrer vos propos. Vous êtes vraiment une très bon professeur capable d'enseigner à quelqu'un qui n'a jamais fait de mathématiques de ce niveau depuis plus de 50 ans. Le prix Nobel de pédagogie s'impose !
I am an Indian and i am really obsessed by your teaching ....... you have that art to teach and make things clear to us . i show my gratitude respectively.❤❤❤🎉🎉😊😊😊😊 you have 1 more subscriber 🎉🎉🎉🎉
Great job for an introduction to the Lambert W function. It is important to point out though, that unlike logs, the Lambert W function is multi-valued between [-1/e, 0). Therefore, you have to be careful when using it.
You speak with a remarkable clarity which rivals some of the best teachers i’ve had. Thank you for making these lessons.
OMG. Where have you been all my life. If I had you as a teacher i would have became an ingeneer.
One of the best math channels on youtube. Congrats and thank you for sharing your knowledge.
Wow, thanks!
@@PrimeNewtonsNot the op you replied to, but right back at ya, Thank You!! You're doing great things!
Although my english is limited, let me please to say you that : you are one of the best teachers i have ever seen .Good day to you.
Merci infiniment, votre cours est très pédagogique et je commence enfin à saisir la fonction de Lambert, même si je dois m'accrocher parce que mon anglais n'est pas parfait, votre est diction claire...j'ai 70 ans et les math me passionnent. Merci.
Thank you very much, your course is very educational and I finally begin to grasp the function of Lambert, even if I have to hang on because my English is not perfect, your diction is clear... I’m 70 years old and I am passionate about math. Thank you.
Man! You are good. An NBT - Natural Born Teacher!
The best and only video you need to grasp the Lambert W function!
My friend, I am your viewer from Turkey. Even though my English is not good, I understand the language more or less and I understand your operations very well. Thank you very much indeed ❤
Wow, thank you
I came here for the maths, but to my great delight I discovered there was more enjoyment to be had; the way you speak is mesmerizing, and I really wish there was a Windows font with your beautiful handwriting.
What a gentle and kind Tutor you are..so refreshing and inspiring ❤ thx deeply
Милый, приятный, умный диктор. Одно удовольствие смотреть и слушать!
Really soothing voice and friendly personality. Makes math very approachable.
I really like his style of teaching. Clear, slow and with passion
i dont know were these functions are used i am here for the vibe this man has
I used it the other day when calculating various downpayment values and their relationship on total interest amount over the course of said loan
@@TARSRobot those things went over my head I'm just 15 I don't understand it
You will learn about it when you learn quadratic equations in school.
So, something like x + 5 = 0 is easy, right? x = -5.
But what if you have something like x^2 + x = 5? That you can solve using quadratic equations.
This will be useful if you have something like 2^x = 5. You know the answer is between 2 and 3, but what is it, exactly?
@CST1992 hmmm my head is almost bursting thh🤣
Using quadratic equation looks almost impossible 😢
@@brokenamigo4880same here
A natural Teacher as you is gold for the Student Body, You know your field extremely well. You taught me in 5 minutes what 10 other teachers tried and failed to do. Thank You Sir.
His energy is contagious. It makes the video so lively
I have never subscribed faster to a UA-cam channel. Was already familiar with the Lambert function, but this was the most engaging math video I can think of to watch. Massively looking forward to checking out the rest of the channel. Thank you!
Welcome aboard!
Your cute smile makes everyone not only to love your videos but also to love Mathematics.. I appreciate your great work. Thank you..
That was a very nice explanation of the Lambert W function. I like your calm way of speaking and it was a well chosen example to calculate.
You are an excellent teacher. All explanations of this I could find online were incredibly hard to understand, but you explained this with elegance and simplicity. Wonderful job.
Yeah! After studying another similar equation, I just ground this out successfully after a few false starts along the way. Two years of college math through calculus, linear algebra, and differential equations and I never was taught the Lambert W function. Nice to expand my horizons.
Your smile gives me chills. I can easily enjoy and learn from your videos.😊
Your videos are wonderful! I appreciate your enthusiasm and the clarity with which you explain things. And, as I am sure you know, the symbol you like to call "flower" is really the stylized Greek letter phi.
Very impressive lecture indeed. The calmness with which you teach and the ideas that you put forth is really very appreciable.
Glad it was helpful!
Great treatment of an interesting function (that I had never heard of before). Excellent presentation style.
Boy I watch a lot of math guys on youtube, and lots of them are really nice, too. but I just love to listen to you. I would've loved to have you had as my math teacher. you are one of those where I just listen and I just understand, the sign of a great teacher.
I love the way you explain Mathematical Concepts!! You break down the complex into understandable points
You are really cool! Only in you i made myself to understand “W function”. With your cool presentation and nice instructions, makes me understand it. Keep it up Nice Guy!
Prime Newtons, your tutorials are excellent and i enjoy watching them. This specific Lambert W Function is new to me and i am learning it from you. Excellent video , professional details explanation. Thanks.
You are not only teaching mathematics, u r smiling mathematics, gesturing mathematics, breathing mathematics, may b sleeping and eating mathematics too,....superb
Beautiful lesson! Very clear and explanatory! Thank you very much, professor! Greetings from Italy.
Thanks you. This is the clearest description I've heard for LAMBERT W.
Your teaching technique is wonderful! Bravo! Take a bow, my good man!
Rick Ross Strech Marks...
I am extremely satisfied with all mathematical explanations! Congratulations！Not even a small default
Congratulations, a very clear explanation of the Lambert function. Just one small criticism: in my opinion it needs to be emphasised that we are in general here dealing with irrational numbers which cannot be written exactly as decimals. So for example ln2 is only approximately 0.693. It is for this reason that in pure mathematics it is preferable to leave the answer as ln2.
For cases where 2^x + x = N where both N and x are positive integers, the simplest solution is to convert N to binary. For any x > 2, 2^x will always the most significant binary digit and x the sum of the remaining binary digits =1.
I shall have to learn why the Lambert W function works. At 71, its been over 50 years since I learned the expansion for e. Until I work through the derivation of the expansion using calculus I doubt I will properly understand Lambert W.
Thank you. That was a good one. I stumbled on your video after watching another video on the Lambert W function. I do say that functions like this are sometimes more difficult than some problems encountered in the Calculus because of the depth of manipulation and rewriting involved to get everything arranged in the correct format of the Lambert W function.
Your teaching methods and style of delivery are impeccable and peerless. I have already subscribed and would be very happy to participate as a member of your community. Cheers.
P.S.
Hibiscus 🌺 is a tropical flowering plant whose flowers come in different colours (white, green, yellow, pink, etc.). The red Hibiscus is especially renowned for its culinary use in making the sorrel drink or the Hibiscus tea (called 'Zobo' in Nigeria 🇳🇬). Cheers.
I am a big zobo fan. Thanks for your kind words.
That was a great introduction to the W function!
Prime Newtons is a prime example of an extraordinary teacher.
I recently stumbled upon this product logarithm and was able to solve simple things like x^x = 2, but this particular one defied me (or rather: I messed it up a bit). Luckily you took me by the hand and led me to the promised land. Seems like the W function has some power in it 😊. Thanks for the lecture!
This is my first time on this channel. To be honest, this is really awesome!
Your enthusiasm is infectious.
I saw a similar equation like this when I was learning about diodes & transistors.
I had to guess a solution by repeatedly putting different x’s on the equation, but this seems like a whole new perspective to solve!!
I really love your explanation!!
Thanks for sharing
_"I had to guess a solution by repeatedly putting different x’s on the equation"_ Graph the equation to get the approximate (very close) value of x.
Thank you sir
You certainly have a really charming voice that helps comprehend this stuff without any distress
Really interesting how, when I saw your video, I solved it myself first, and we rearranged it in different ways! I exponentiated both sides with base 2 and then multiplied both sides by ln2, getting the required form, and so 2^x ln2 = W(32 ln2). I had no idea there were different ways to solve these equations using Lambert W.
whoa that's much faster - nice one!
I did a different shortcut, multiplying both sides by e^-ln2 in order to remove it from the left hand side rather than adding it to the "input" of the productlog haha
Man, this is magical.... greetings from brazil
Initially i was skeptical about this video question and solution....
You have missed the odd step, but - you have a wonderful demeanour and excellent board work and communication skills....
It blew my mind and you explained it in such a simple manner that I managed to solve every question after
At first i thought it cant be solved, but you made it look so easy. Thats mark of a quality teacher. Thankyou Sir.
Wow I literally learned so much in your video than a month of math school, seriously, thank you.
You are really good at teaching, slow ,careful and explains it pretty good. Keep it up.
It's been my pleasure to follow your cristal clear & relax way of solving the equation. Be luck with you.
Greetings from Warsaw
😅😅😅
everyone should have such a math teacher...thank you!
Best video on this topic I have seen. Very excellent job!
Note: I actually have a masters in EE and have had math up through 700 level, so this is just me going back and refreshing my memory on the W fn after seeing a youtube video suggesting an algebra problem I should have been able to solve quickly and realized I had forgot how Lambert fn works.
Most of the videos don't explain it as clearly as you did. This was a perfect quick refresh.
Am I odd that I go back and refresh my very old algebra skills in algebra when I have been using calculus to do my job for the last 40+ years?
In all fairness, problems like this do not come up often in my line of work, however I use calculus everyday.
What the hell ??? What level math is this ??I had college Algebra Trigonometry and 4 semesters of calculus I had to slow down this video work this out on a pice of paper So I could better understand I never heard of this “W “ until today You did an excellent job of explaining it was just little to fast for my 66 year old brain to keep up So got a pice of paper and started to write down problem as you were doing it I believe in hands on doing math.This has to be an advanced college algebra course That you would take after college algebra Something I never took I am totally blown away I am definitely subscribing to your channel Totally impressive
Excellent! Like Bill & Ted's adventure. Thanks also for the clearest chalkboard writing I've ever seen. I look forward to your other videos.
I love your intro, you make math seem like an exciting riddle
Great video and wonderful and gifted teacher. Impressive!
Excellent explanation!!!! Thanks soooo much!! A great introduction to the Lambert product function!!!
Very nice! I knew about the Lambert W function but I don’t think I would have been able to express the equation in a form where it could be applied. Keep up the great work 👍👍👍
I guess the main reason why it can be used in such a way is due to the function having a definite solution.
Subscribed, better than any, literally ANY lesson I've come up over yet.
Mathematics is my favorite subject and I explore new functions/techniques and try to learn once I see those. I often find it quite frustrating to not get a proper explanation, searched throughout the whole internet. It gives me trouble to search for new things which actually teaches from the beginning of a topic.
I've casually and randomly jumped upon this channel and I'm genuinely fascinated about how easy and clear, yet proper his lessons are!
You've just earned a sub bro, keep it up ❤❤
Thank you for this! I was aware of the function before but couldn't really wrap my head around it. This has cleared things up for me. Much appreciated!
You are so articulate and an excellent teacher thank you!
Wish I had a math teacher in school with this much charisma.❤❤❤
Ps.I am also wearing the same t shirt right now.😊😊
Thanks for your solid presentation and the focus on the purpose of each step; really well done.
I'm surprised that I learned this on the first try, You are a great teacher.
Your elaboration is crystal clear. good job and thx. .
All of us living in the mathematics community love you.
You've re-kindled my love of Math. I got sidetracked several decades ago but your calm teaching manner and clear solutions has given me new inspiration and a better way to spend some of my time in mental workouts :) There are many "smart' people, like some of my old Physics/Maths Profs...but few who could teach. Thanks very much.
You are a great teacher 👏
Glad you think so!
You are an excellent teacher. Would like to see you with an additional blackboard to be able to expand upon your presentation.
Great suggestion!