Calculus 3 Lecture 13.9: Constrained Optimization with LaGrange Multipliers
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- čas přidán 6. 07. 2024
- Calculus 3 Lecture 13.9: Constrained Optimization with LaGrange Multipliers: How to use the Gradient and LaGrange Multipliers to perform Optimization, with constraints, on Multivariable Functions.
forget calculus, this dude should upload his workout routine
Probably uses calculus to design his routine ;p
I have actually made up a unit for weightlifting, which I call "Arnold".
It's simply the product of the number of sets, the number of reps, and the weight in kilograms.
So for example if you lift 20 kg and do 3×8 sets and reps, then you lift 480 Arnold, or, I guess, "480 Ar".
It seems to me that any sets, reps and weights that have the same value for Arnold give roughly the same effect.
that's pretty interesting actually
@@Peter_1986 Interesting, but flawed. Doing 3x5 100kg BP would give you 1500 Ar, and doing 30x5 10kg BP will also give you 1500 Ar. You definitely aren't going to make any progress doing the latter tho. Hypertrophy works at the 8-12 rep range generally. Strength gains at the 3-5 rep range. You're not putting enough stress for hypertrophy, nor enough weight for strength gains. Might see some minimal results, but you know for sure you'd gain with the former.
that'd be biceps 100000 series 10000 reps
26:37 - “I don’t wanna lose you now; you’ve learned too much.” The way he said that so seriously is so funny and sweet at the same time omg. 😂😭💚
You haven't learned too much if you could have learned twice as much in half the time.
best teaching style for ADHD students!
3 minutes in and this guy already healed my lack of intuition of level curves.
Hands down the most intuitive explanation of Lagrange multipliers I've ever heard!
Thank god I can rewind. I tend to blink
It's for comments like these that have me reading em.
😂 Funny and original
I don't understand why calc teachers will sometimes just teach you plug and chug. Understanding the underlying concept is so important. Thank you so much for this video!!
There's a special place in heaven for people like this guy.
The excitement at 5:16 is the energy we need in a calc 3 lecture
His excitement from 6:30-8:30 is why I love math so much: it's a beautiful thing when everything falls into place so perfectly.
If you are familiar with the concept
Examples will strat at 22:18
Good luck with your exam! And wish me luck too!
Good luck bro
I did my engineering 7years ago....came to b5rush my concepts...all I can say is I love this guy...
Honestly hands down the best at teaching this, not only do you love what you do, but helps others love math as well. Thank you for not making any assumed knowledge but breaking it all down for the students. Really helped me understand
This video saved my life, I missed my lecture on lagrange multipliers because I was sick and the textbook was no help at all... this video explained things super clearly and I understand lagrange multipliers now, thank you SO MUCH!!
superman teaching calculus!! This is the most awesome lecture I have ever had in Calculus. Thank you very much professor.
You are a good teacher. The professor I had just blew threw everything without even seeming to care if we learned or not. There was absolutely no care or anything in his method of teaching, unlike yours.
I think you're probably the one who should care whether you learn or not. Don't give the instructor responsibility for pouring knowledge into your thick head.
@@danieljulian4676 its his literal job bruh lmao
I agree we should all take a little responsibility but for one, there's no need for the insults and 2, people pay vast sums of money to be educated by some of the best in the world, not to have a book worth a few quid thrown at them and say there you go. those sort of people shouldn't be teachers. they just want an easy wage with zero passion.
@@Mikebigmike94 fair enough, mike. I will add that one can pay a lot of money to take a degree at a research university and as you say, get pretty poor classroom experience. Even at universities that are second rank, but still use the "publish or perish" model for their faculty ladder. There are only a very few elite universities for the entire planet. The lectures we're watching here are being presented in a community-college environment. The comment to which I responded is just a crass complaint from someone who gave no substantive comment on the teaching methods. It's hard to tell whether Gib Gob is a thoughtful student or a numbskull. I decided it was the latter. If you look in the comment threads for lecture videos on this platform, it is not uncommon for someone to say pretty much the same thing as Gib Gob. What Professor Leonard is doing largely consists of working examples on the whiteboard. I have no idea what kind of problems these students will be prepared to tackle once they have strayed outside the framework of the examples. I see very little in the way of mathematical background, and a hard focus on the results of the theorems. There are many other video lectures on Calc 3 to be found, particularly the ones from MIT Open Courseware. The exercises presented there are much more difficult than the formulaic application of results we see here.
@@danieljulian4676 well these students also follow along with a university level textbook and achieve the same degree as any other university, there’s a few articles/videos explaining these “elite” or top universities are not what they seem. Most degree holders end up on the same salary and are still very highly employable. If somebody wants to become an expert on calculus or whatever other topic you can do so by years of studying textbooks in your own time if you have the passion. But while you’re an undergraduate, it doesn’t have to be the most difficult thing in the world. Knowing the concepts and being able to solve most of the textbook problems should be enough.
Btw I’ve found most of these communities college professors can explain concepts a lot better than other universities, like MIT. A lot of the time the latter seem to just put on a “show” of how fast and how good they are at going through concepts/problems without caring if students understand.
Excellent lesson.
You do a great job of not just showing how to solve the problems you present, but showing where it all connects together.
Thanks
Love his passion and incredible ENTHUSIASM for teaching maths.
45:50 Was a great example for understanding for anyone needing to learn Lagrange Multipliers. Explained well too
I can't believe I'm paying someone hundreds of dollars to teach me calc 3 when I can learn it far easier for free online from you.
Im in the same boat my friend. I currently do go to class and watch this instead. we will see how it goes
@@hocho1717 howd it go?
@@hocho1717 yeah how'd it go?
@@noahaguilar8766 failed the first time. Took it again and did extremely well! If you are in the same boat, don't give up like I did the first time haha!
I'm paying hundreds of dollars to do online homework with no instruction from my professor in this required course when I could be learning about my actual major.
Great explanations and extremely engaging. My hat goes off to you Professor Leonard.
Thank you very much for such a profound and at the same time comprehensive explanation. Was stuck with this concept for a while and wanted to understand the logic behind the concept and not just memorize the formula.
Thank you!
Thank you so much Professor I was near to be hopeless about the Lagrange multipliers but with you , you've explained it like a piece of cake . Sending greetings from Kuwait
Professor Leonard ,thank you for a short and in depth video/lecture on Constrained Optimization with LaGrange Multipliers in Multivariable Calculus. This topic is simple to follow, however, the algebra can get messy in order to find correct solutions.
I think Johnny Bravo just taught me constrained optimisation... Is this what pure joy feels like?
you're the best math teacher EVERRRRR and I'm from Canada your method of teaching is the best I ever experienced in my life thank you very much
Very useful as I get ready for my comprehensive exam. Much appreciated, Prof. Leonard!
Proff. Tomorrow is my calculus final exam hope so I will be manage to get A+ grade just because of you. Your attempt for class participation is really great. As Einstein said, " Education is not the learning of fact but the training of the mind to think". You are doing same. (Thank Proff)
44:38 z=1/4 when landa = -1 not z=-1/4
Its true but his answer is still correct.
I caught that too but still gives you the correct answer haha
no you get -1 for f which is NOT a minimum
It can be either positive or negative
I think there's a mistake at 44:38 since the second z should have been positive. The result is correct though. Thanks a ton for this video Prof Leonard, carrying me through my Calc 3!
أحسنت يا غلام ...........اسلوب جيد لتعليم
been watching ur vids since calc 2 really helped me for finals.. spent countless monster and rockstar fueled all nighters studying my weak points with ur vids.. taking calc3 over the summer and watching ur lectures after my lecture really helps me understand my notes and homework... you're the best.. I'm hopeful for differential equations lectures next xD
does monster help?
You are a great teacher, always motivated and concerned if the students are understanding the fundamentals of the subject in question before they actually start solving problems...
Thank you for your lectures, its because of you I will pass Calculus 3 :)
Those first 10mins pumped me up so much
Professor, you are the best teacher of calculus i have ever seen
Amazing class! Please never stop teaching!
You are very active and enthusiastic doctor
I love his passion for the math and for teaching!
this dude is jacked
Prof. Leonard, you are the GREATEST!
Thank You so much sir. I really appreciate your lectures. No professor able to teach like you. So humble teacher. tq
Congratulation. You've made LaGrange Mulitpliers a lot more understandable than LaGrange made for himself ! He didn't have much confidence when he started this !
Thank you very much for your great efforts .... And I hope you will put Arabic subtitles in all your videos...
You are an amazing person 🙏🏼💙
Just perfect. Now I know the idea behind it:)) Great help. Thank you so much.
I got AA from my calc 3 class thanks to you and ur videos , thank you so so much
DUDE HES THE BEST!!! He has helped me gain to much insight and intuition!
LOVE IT, BUY THAT MAN A BEER!
The best channel for calculus
Honestly, if any of my teachers had the enthusiasm that you do for teaching, i would be doing a lot better in class.
wow that was awesome i love the energy you have Sir salute
Wouldn't it be the best thing ever of Prof L covered ODE AND PDE
Sir is absolutely amazing... I bow to him...
Thank you, Prof... I have the exam in 2 hours... Great Help...
So passionate , keep it coming !!
"i need job security. ya'll find something else to do" cracks me up
Also, does anyone know if he uploads his class notes anywhere?
Definitely going to need to practice this a lot more. The systems of equations always mess with me and leave me scratching my head.
28:34 "I need job security, find something else to do!" lmao
For the last example, you could also set ‘ 2x+y = lamda2x and 2y+x = lamda2y ‘ equal to lamda and then set them equal to each other and once you simplify you end up with x^2=y^2 so that way you solve directly for x nd y
Amazing lectures, great help for me, thank you :)
Wow! Good work Jhonny Bravo!
Hi Professor Leonard! I think the "z" in 43:19 should be equal to ¼ instead of -¼ though the answer is still the same. :)
1+2+1 = 4lambda^2 then 4 = 4lambda^2 divide 4 from both sides you get, 1 = lambda^2 and finally you take a root from both sides therefore lambda equals plus or minus 1. I got confused too, and did the math.
I enjoy my holidays by watching your lectures..💓
U are real blessing sir, thank you so much for all u videos🙏🙏🙏🙏
great lecture. I did not blink once :)
What a great teacher!
Thank you very much! You're the best
This channel is SUPERB! 60FPS WE MEET AGAIN!
You deserve a medal.
If Professor Leonard taught my calc class, I'd have perfect attendance
great explanation. Thank you!
great professor
you are a genus
I have to try this method for that box problem at the end of the previous video.
Thank you Professor. It helped a lot...
Your lecture is super easy to understand and really funny.
I envy your students
45:00 shouldn't z=1/4 instead of z= -1/4 (for lambda = -1)? ..
Yes
for the last example, couldnt you have just gone back to your g(x,y) equation and used the x^2+y^2=0 to find x=y as a substitution? or is there a reason that i cant do that
I m looking forward to kkt conditions or inequality constrained optimisation ... haven't you make a lecture for it ?
Oh my god. I get it. I’m literally on my midterm and we only have chapter 16 of James Stewart left to cover LMAO. I just got it. I love this thank you
brilliant sir ! thank you very much
brilliant explanation, you are amazing.
You are an incredible teacher
This is an amazing video but I have a doubt, I am not able to understand why taking the gradient produces the normal. The gradient is the rate of change in a specific direction, so how did it become normal to the curves? Thank you.
Professor Leonard, why don’t you just x/4x for finding lambda in last example. It gives lamda-1- = neg or pos 1/2. Does making this cause a miscalculation?
do gradients have to be same direction or negative scalar works too ?
33:30 How can you conclude a maximum? I did the second derivative test to get D(x,y) = -1, so I got a saddle point.
I took the directional derivative of f in the direction of the normal n = (2,3), and got a value greater than zero telling us that the function is increasing in that direction. Wouldn't that mean that (3/2,1) is a minimum?
excellent presentation
0:50- The idea
6:25- Level Curves
11:53- Constrained Optimization
45:41- Hard Problem
have to say YOU ARE AWESOME!
This guy is spectacular
11 dislikes coming from your angry calc 3 profs who can't teach!
hi professor ...
I hope you continue the constrained optimisation and teach the KKT inequality constraint problems asap
My question may be strange but I have no one to ask this can you tell me a Lagrange algorithm to find a minimum arbitrary volume within another volume which can contain it by maximum of it inside it or minimum of it out side 🙏🙏🙏
"Solve for Lamba" 28:44 that was all I needed
If my professor gone through the theory behind lagrange multipliers, it would have made constrained optimisation much easier to understand
what should we do when there are multiple constraints. ?
From the original equalities you can see that y/(2x)=(Lambda-1)=x/(2y). Then, 2y^2 = 2x^2 and x^2=y^2 which avoids using substitution. Also Thank you so much for the videos, I rather watching them than reading the book
Hello sir can you please make a video on constraint optimization with inequality constraints...
god this really saved me for my test tomorrow
In the last problem, with the two equations we get after taking gradient and equating, from both the equations, we can calculate the value of lambda and equate that, that will directly give us x^2 = y^2