Calculus 3 Lecture 13.8: Finding Extrema of Functions of 2 Variables (Max and Min)
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- เผยแพร่เมื่อ 21 ก.ย. 2024
- Calculus 3 Lecture 13.8: Finding Extrema of Functions of 2 Variables (Max and Min): How to find Relative (Local) and Absolute Extrema of 2 Variable Functions. Optimization is also discussed.
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Born too early to explore the Universe, born too late to explore the world. But born at the perfect time to explore calculus 3 with Professor Leonard.
I like that way of thinking.
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I mean technically only 42% of the world has been explored
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Einstein said if you couldn't explain something clearly, you didn't really understand it.
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Thank You Professor Leonard
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I get it now why Professor's lectures are so effective and why people really understand them. For example, a lecture is 3 Hours Long. He would spend 1 Hour 'Defining things', 1 Hour 'Doing Examples', and 1 Hour 'Repeating' the important points. This leaves no room for confusion. A solid 3 in 1 Package with a lot of mathematical humor. Thank You very much Sir for your Efforts.
3:38 critical points. 5:53 inflection points = concavity. 19:44 saddle point. 22:07 inflection point example. Summary 25:38. 29:01 connection between calculus 1 and 2. 32:32 second derivative test. How many second partial derivatives: 34:38.at 37:15 four possible outcomes. Example 1 at 46:55. 57:59 fxy. 1:04 "Tricky Systems."
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@@Danny-zb1ze BROO I said the same thing , God blessss you
Thank you mate!
I can only understand the topic if i see the examples so sometimes i go straight to the examples , thank you man i appreciate it
0:00 Introduction
32:32 Second Derivative Test
46:50 Example 1
1:04:22 Tricky Systems
1:25:14 Example 2
1:51:37 Example 3
2:02:44 Important Note
2:05:54 Absolute Max and Min
2:10:00 Example 4
2:53:55 Example 5
3:07:57 Example 6
3:25:40 Example 7 (Optimization)
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@@porque6815 You guys too? YIKERS LMFAO
mine did 1 example that took 15minutes and that was it " it simple just follow formula "
My math teacher from last year just stood and talked in a monotonous voice the whole time, and it was extremely obvious that it was all pure routine for him.
It felt almost as if he was talking to himself.
Absolute MAX and MIN starts at 2:05:53
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Hey Professor Leonard,
I don't know if you read these or not, but I really admire your passion for teaching and you are REALLY good at it (& you're funny as hell too (albeit in a corny way no offense)). I know you'll never get to know me, but you've helped me so much in this class (as I am sure you did with thousands of others) and I hope you realize the impact you are making on students across the world. Thank you man!
Thanks very much for taking the time to write this!! I do read them, and they mean a lot to me :) I'm certainly happy you have found value in these videos!
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@@lunaeaqua4339
Actually now when I think about it, Michel Van Biezen is probably even better.
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and he really helped me out a lot when I studied physics topics such as Thermodynamics and Interference/Diffraction, among other things.
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you probably won't see this comment since the video is a year old but holy s**t I LOVE you right now. Im going to ace my test thanks to you. thank you so much for uploading the lecture you taught the lesson in a very easy to understand manner and went through it thoroughly step by step. YOU ROCK!!!
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...OR maybe I just have mediocre faculty at my college?
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Leonard: today we will be looking at double integrals, first, do you guys remember how to add? alright, let's do a quick review.
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For me, that's the best part. I'm taking calc 3 eight years after I took calc 2, so the review of the basics really helps refresh and solidify!
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Lo escribo en español porque me la re banco. Profesor Leonard sus clases han de ser lo mejor que hay de calculo en todo internet. Le estoy muy agradecido por su aporte y su buena disposicion para los videos. Saludos y espero se encuentre bien mi pana.
professor your lectures are remarkably well and you discuss every concept in a very good way and if you add subtitles in your video then your videos become the best math videos on youtube.
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22:41 "You guys know about horses?" made me literally laugh out loud
3:26:00 "60% of the time, it works all the time" killed me on the Anchorman reference
3:38 hour :P
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At 3:22:30 where you are restricted by a circle you can also substitude for x = cos t and y= sin t between -pi
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Wasn’t planning on watching the whole thing to the end but those first 30 mins really got me hooked! Wow you’re a great professor ❤
Professor Leonard, thank you for an exceptional video/lecture on Finding Extrema of Functions of Two Variables. This lengthy lecture is a tremendous amount of mathematical tools and information for any student to absorb in Multivariable Calculus. From watching this lecture, I found this topic highly problematic, however, I will rewatch this video for a deep analysis and understanding. This information was also part of Calculus One that is, finding Max and Min values.
Thanks for these full length lectures. You are extremely easy to follow and thorough, which I appreciate in a math class
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A BIG THANKS TO YOU SIR .HONESTLY WITHOUT YOU ME AND MY MATES!!! WE NOTHING TO CALCULUS
Best lecture on this topic being an teacher i used to watch professor leonard lectures and teaching techniques too thanks alot professor Leonard
Before you watch his whole lifesaving video, please go to 1:33:23, then back to the start and enjoy!
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Great teacher! You explain much more clear than my professor.
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Never thought I'd see the day when Leonard would teach algebra in Calculus
Nonetheless, an amazing lecture
1:48:42 But wait Leonard that doesn't give you a substitution...."Yea it do.......listen! Yea it do" lmao had me cracking up in the library hahahaha. Thanks once again professor Leonard there's no way I would be able to survive my calc 3 course without you!
I have watched literal days worth of these lectures and I have never heard him inflect his voice this way. This was weirdly entertaining. 3:01:30
I wanna hear the concavity song! lol
Thank you Professor Leonard. This is going to save my Calc 3 grade. I really appreciate these videos!
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Are you going to be recording a class on differential equations?
He now has lots of videos on Differential Equations available. :)
@@Peter_1986 do they cover the entire course?
@@trevor6711
Not sure, but apparently he is still working on them, even though he already has a bunch of long videos uploaded, so they should cover quite a lot.
I definitely know that they cover all the most common ODEs, such as separation of variables, linear ODEs, substitution methods, Bernoulli's ODE and so on.
@@trevor6711 th-cam.com/video/UqMUokFP438/w-d-xo.html, on this channel there is a 44 episode series on diff equations that are very good
@@Peter_1986 The originial comment was 5 year ago, i think this person has graduated by now XD
You don’t know how great you are. Thank you so much
'There's this class called calc 1' I lost it lol
You sir are my hero.
Thank you Mr Professor....:) God bless you....:)
one of the best you make calculus a hobby keep up the good work sir I truly appreciate what you are doing
So TH-cam was Autoplaying videos throughout the night while I was sleeping and I wake up 2 1/2 hours into a calculus III lesson. I think this is the moment I really realized what a nerd I am. I’m about to go into junior year of highschool and taking Calc I
Jesus, I wish I had any professors in any class who taught this simply. My professors' lectures are almost entirely comprised of proofs. Yay, universityyy.
Thank you , for these videos you are so brilliant
My teacher couldn't teach this lesson worth a damn. I was utterly lost. I completely understand the section thanks now, thank you for posting your lectures Prof.
You're absolutely welcome!! I'm very glad that they helped you to understand
+Professor Leonard
Your lectures flow so well that they don't even feel like lectures, they feel more like exciting adventures.
Teaching should be done with the utmost continuity and you are a bonafide professor in an age where teaching is a lost art.
My prof's teaching is so hard to understand, but with you Leonard, I am going to do really well in math2011.
My prof and tutor are not able to write 5 and sqrt 2 clearly which made me difficult in understanding their notes.
Theres some maaad sniffin goin on in that class, gotta love allergy season.
Razzer racer it’s just Covid-19
Sir i appreciate your hard work and hope you keep on teaching like this👍
We know that a saddle point appears when D(x,y) is negative and each of the second derivatives has opposite signs. However, for the third critical point, when we get zero for f(xx) and a negative value for the f(yy) the professor ignores the situation to explain more. I am having a hard time visualizing the result output of such a condition, as the second derivative of zero implies no concavity; thus no saddle point.
Further explanation would be highly appreciated :)
Chears
Don't get too stuck on the image of a horse saddle. The mathematical definition of a saddle point goes something like; it is a critical point where there is no local max/min.
Thanks sir! Ive been confused about this for a long time and you literally cleared up all my confusions :)
i seriously appreciate how you're recording your actual lecture. Your attempts to bring your students' attention bring my focus back. It works out perfectly
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bro looks like superman fr. A GREAT TEACHER as well
Nodded my head the whole time. Thanks!
@3:08:00 Wolfram Alpha can do it in a blink of the eye: type this into Wα query box..
_Extrema {xy-x^2} given y=x^2, y=4_
but don't tell Prof Leonard, it might upset him!
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my current calc 3 professor is great, but unfortunately he has to skip a lot of the intuition because it's only a 6 week course. these videos are the perfect supplement to all the materials we're covering :-)
This is true meaning of maths thank you prof.
Watched through the whole video, great work. Hope you will continue stay passionate and motivated with your teaching. :)
Oh man, I am so excited to see you go through some 'tricky cases' for solving for critical points. This is exactly what I need. You are a sweet angle refreshing algebra in your calc video. Do you still teach math? Where do you teach?