Calculus 3 Lecture 13.9: Constrained Optimization with LaGrange Multipliers

[@johnathonsnipes8132]

3 minutes in and this guy already healed my lack of intuition of level curves.

[@pdog44450]

forget calculus, this dude should upload his workout routine

[@phenotypealpha]

Probably uses calculus to design his routine ;p

[@Peter_1986]

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.

[@narutouzumakix9201]

that's pretty interesting actually

[@hamstrung22]

@@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.

[@diegol4452]

that'd be biceps 100000 series 10000 reps

[@aubreeswart2206]

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. 😂😭💚

[@danieljulian4676]

You haven't learned too much if you could have learned twice as much in half the time.

[@rwharrington87]

Congrats on 900K subscribers. I don't know how long I've been subbed to your channel for, but I don't even think it had 100k at the time. The (psudo) proof of the lecture quality is in the pudding. You've taken me all the way from an intermediate algebra review, through statistics, precalculus, and all of calculus up to this point. May the journey continue onward and upward.

[@skylerpretto1221]

Hands down the most intuitive explanation of Lagrange multipliers I've ever heard!

[@KhadijaAlshemeili]

If you are familiar with the concept Examples will strat at 22:18 Good luck with your exam! And wish me luck too!

[@abhigyanpraveen7590]

Good luck bro

[@serpent3348]

Sending luck from the future to the past!

[@ejp7360]

There's a special place in heaven for people like this guy.

[@rachelrigsbee6650]

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!!

[@victorkotov7502]

best teaching style for ADHD students!

[@sneha.........]

I did my engineering 7years ago....came to b5rush my concepts...all I can say is I love this guy...

[@EvaSlash]

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.

[@danieljulian4676]

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.

[@vvictorg123]

@@danieljulian4676 its his literal job bruh lmao

[@Mikebigmike94]

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.

[@danieljulian4676]

@@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.

[@Mikebigmike94]

@@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.

[@alvinarevalo9378]

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

[@elisiandchrissy]

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

[@brendancleaver93]

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.

[@zion030]

8 years later and I'm using these videos to help me through class because my professor is rushing very fast through things and gets pissed when we ask questions or don't understand. Professor Leondard is so easy to understand and i love that i can rewind/rewatch parts if I don't get it at first.

[@Chemasaurus]

The excitement at 5:16 is the energy we need in a calc 3 lecture

[@starryecliipse]

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!!

[@vaidehichennubhotla7887]

superman teaching calculus!! This is the most awesome lecture I have ever had in Calculus. Thank you very much professor.

[@MaxRollison]

45:50 Was a great example for understanding for anyone needing to learn Lagrange Multipliers. Explained well too

[@anangelsdiaries]

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!

[@georgesadler7830]

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.

[@swordoflorn]

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.

[@hocho1717]

Im in the same boat my friend. I currently do go to class and watch this instead. we will see how it goes

[@silentheister]

@@hocho1717 howd it go?

[@noahaguilar8766]

@@hocho1717 yeah how'd it go?

[@hocho1717]

@@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!

[@regularlyirregular8876]

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.

[@pedroinacio_maths]

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

[@UROOZFATIMA190]

Love his passion and incredible ENTHUSIASM for teaching maths.

[@strange6973]

I think Johnny Bravo just taught me constrained optimisation... Is this what pure joy feels like?

[@Alley00Cat]

Thank god I can rewind. I tend to blink

[@kscottvarga9606]

It's for comments like these that have me reading em.

[@eliya3424]

😂 Funny and original

[@rashedkhaled7375]

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

[@jovanni_ch]

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

[@Avi00124]

does monster help?

[@nouman8639]

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)

[@f_add_mebowshot5677]

bro explains in a way that a toddler would understand🔥🔥

[@canman5060]

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 !

[@ibrahimelosta7422]

44:38 z=1/4 when landa = -1 not z=-1/4

[@iceverything2000]

Its true but his answer is still correct.

[@austing.8682]

[@biscaynebuckets]

I caught that too but still gives you the correct answer haha

[@betaalphapsi9103]

no you get -1 for f which is NOT a minimum

[@zaidradwan4000]

It can be either positive or negative

[@معندعاس]

أحسنت يا غلام ...........اسلوب جيد لتعليم

[@drewski91]

Professor, you are the best teacher of calculus i have ever seen

[@thebossification101]

Great explanations and extremely engaging. My hat goes off to you Professor Leonard.

[@MuhammadAmmar-i4k]

The best channel for calculus

[@Himawari_.]

Thank You so much sir. I really appreciate your lectures. No professor able to teach like you. So humble teacher. tq

[@davidg3298]

0:50- The idea 6:25- Level Curves 11:53- Constrained Optimization 45:41- Hard Problem

[@nikolas_ohler]

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!

[@aleynadoven]

I got AA from my calc 3 class thanks to you and ur videos , thank you so so much

[@kevvonkev]

DUDE HES THE BEST!!! He has helped me gain to much insight and intuition!

[@juanvilla5613]

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

[@zaidradwan4000]

You are very active and enthusiastic doctor

[@leohuo4263]

If my professor gone through the theory behind lagrange multipliers, it would have made constrained optimisation much easier to understand

[@Demonface54]

Honestly, if any of my teachers had the enthusiasm that you do for teaching, i would be doing a lot better in class.

[@leensameer6805]

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 🙏🏼💙

[@tiagocoelho7642]

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 :)

[@imamalam4971]

Wouldn't it be the best thing ever of Prof L covered ODE AND PDE

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Prof. Leonard, you are the GREATEST!

[@dahe1352]

this dude is jacked

[@elle694]

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. :)

[@Iceage31580]

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.

[@danielleg6915]

I love his passion for the math and for teaching!

[@SirTrollingham]

For the problem given at 52:00 I've found an easier way to solve the system of equations. Since y = 2x(λ-1) and x = 2y(λ-1) we can solve for λ and set both equations equal to each other, giving y/2x + 1 = λ = x/2y + 1. Subtract 1 from both sides to give y/2x = x/2y and then cross multiply to have 2y^2 = 2x^2, which simplifies into y^2 = x^2. You can then plug that back into x^2 + y^2 = 8 and solve to get x = ± 2 and y = ± 2.

[@alexmaclellan1983]

Very useful as I get ready for my comprehensive exam. Much appreciated, Prof. Leonard!

[@GueVonez]

Those first 10mins pumped me up so much

[@Akash-rs2yp]

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

[@whateverchannel92]

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

[@nickcooley2857]

LOVE IT, BUY THAT MAN A BEER!

[@shani2114]

Thank you, Prof... I have the exam in 2 hours... Great Help...

[@manstuckinabox3679]

Hello prof, 53:35, just devide by x, that's what I did, same result without burdening my attention towards checking x=0's validity.

[@alextsvetkov3211]

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

[@matthewzarate9116]

28:34 "I need job security, find something else to do!" lmao

[@rebeccanery_]

Amazing class! Please never stop teaching!

[@EeDymonNij]

45:00 shouldn't z=1/4 instead of z= -1/4 (for lambda = -1)? ..

[@21mejia25]

Yes

[@nalviduro3832]

You deserve a medal.

[@RohanDutt31]

11 dislikes coming from your angry calc 3 profs who can't teach!

[@mukulyadav31]

Im in college and learning calc. It is nothing compared to the level of education these kids are getting.

[@mthokozisisiphiwe7655]

wow that was awesome i love the energy you have Sir salute

[@JM-ty6uq]

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?

[@KhadijaAlshemeili]

1.25 speed will help you a lot if you have an exam in the couple 2 days don't waste your time to watch the video and do some practicing exercises! good luck! & wish me luck too ;)

[@anniedrew4440]

If Professor Leonard taught my calc class, I'd have perfect attendance

[@viveknsharma]

Sir is absolutely amazing... I bow to him...

[@ademolaadebowale2723]

Definitely going to need to practice this a lot more. The systems of equations always mess with me and leave me scratching my head.

[@khaloscar]

Prof Leonard saving my grades

[@Peter_1986]

I have to try this method for that box problem at the end of the previous video.

[@rileymenter6095]

"Solve for Lamba" 28:44 that was all I needed

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I enjoy my holidays by watching your lectures..💓

[@haniehsoleimani6096]

Just perfect. Now I know the idea behind it:)) Great help. Thank you so much.

[@15997359]

U are real blessing sir, thank you so much for all u videos🙏🙏🙏🙏

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I watch all the adds to support the video

[@robertleo3561]

You are an incredible teacher

[@marouanemaachou7875]

So passionate , keep it coming !!

[@JesusMartinez-bw4bv]

11:16 - Examples Start

[@KhadijaAlshemeili]

no :)

[@markpascual100]

"i need job security. ya'll find something else to do" cracks me up

[@queenstrategy904]

This guy is spectacular

[@wonjunlee5413]

Your lecture is super easy to understand and really funny. I envy your students

[@ammarsiddiqui4329]

Need that Superman-esq wkout routine!!!!!!!!!!

[@graceless000]

at 45:00 I'm pretty sure the z for lambda = -1 is supposed to be z= 1/4 not -1/4. I checked.

[@aaliyahjackson3623]

yea it supposed to be positive

[@JuiceBoxBoiii]

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.

[@mariasako5408]

What a great teacher!

[@elvistekito9622]

Great Video ! 😀

[@rwharrington87]

54:00 you can make the algebra much less of a pain in the ass if you just solve for lambda after setting the components of the gradients equal and solving for x and y. You get y/(2x+1) = lambda in one equation and x/(2y+1) = lambda in the other. Since both of them equal lambda, x and y must be equal.

[@BruceWayne1996-1]

brilliant explanation, you are amazing.

[@sivadasanet7966]

Thank you Professor. It helped a lot...

[@SuperiorWare]

This channel is SUPERB! 60FPS WE MEET AGAIN!

[@agusssia111]

Amazing lectures, great help for me, thank you :)

[@audymashal2214]

great professor you are a genus

[@hageldave]

Hi there, great video! I really liked your explanation of level curves and how they need to be tangential at the optimum .. until I realized that this is not true when dealing with multiple constraints. When the level curves of two equality constraints intersect at a single point (non tangential), then this point is the only feasible one and the level curve of the objective function cannot be tangential to both of them. Most likely it isnt tangential to neither of both, BUT the sum of the scaled gradients of the constraints is equal to that of the objective. Unfortunately I cannot think about the sum of constraint level curve gradients in an intuitive way to further stick with this geometric explanation. However this made me understand L2 regularization in linear regression :)

[@hamidgholami2683]

You are more than great

[@jackbirnbaum4379]

excellent presentation