Calculus 3 Lecture 13.3: Partial Derivatives (Derivatives of Multivariable Functions)
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- เผยแพร่เมื่อ 26 ส.ค. 2024
- Calculus 3 Lecture 13.3: Partial Derivatives (Derivatives of Multivariable Functions): How to find the slope of a tangent line to a surface in the X-Direction and Y-Direction. Focus is on the concept of a partial derivative and several examples. Also included is implicit differentiation and higher order partial derivatives.
Ive crammed so many of these videos in the past 3 days his face feels more familiar than my mom's.
Yeah feeling same 😅
he is your mom
professor Leonard, You are the best math teacher I have ever encountered. Maybe you should start a new channel where you teach other professors how to teach.
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I go to Columbia, my teachers are nit interested in teaching. Most of them give us proofs that half the class doesn’t understand. Professor Leonard made Calc accessible to me.
Well said.
@@lennybruce77 One of my teachers outright said "We'll revise C2 in C3, since many people are being taught by bad teachers".
The ones he mentioned, are the ones who gives proof the class doesn't understand...
Harsh.
Lenny Ciotti I have the exact same problem, I’m taking calc 3 at Columbia right now as well
That moment when you wish you started watching these videos from the beginning of the semester not now two days before the exam ...
literally me rn lol
Im watching it all BEFORE the semester lol
Im watching BEFORE the semester lol
Nerds detected :3
Truth lol was just thinking the exact same thing 😂 lesson for next semester I guess 😆
Professor Leonard.. Raising the bar in the classroom and the gym!
i feel like he gets slightly more buff with every video
Aedan Valle my dude just gonna be one huge arm with a marker when he starts posting vids again
What kinda fuckin name is Moogy
Ex,Partial Derivatives 40:20
Implicit Derivatives 1:16:16
Higher Derivatives 1:40:24
you're amazing
Bless
shukran
@@Fahodinho shokran* yasta
@بطل ماتين2 brilliant
-What does a derivative mean in Multivariable Calculus? (0:00-28:10)
-"Formal" definition of the Partial Derivative/Notation/Extra Notes(28:10-40:39)
-Ex:1 (40:39 - 49:09)
-Ex:2 (49:09 - 52:01)
-Ex:3 (52:01 - 58:23)
-Ex:4 (58:23 - 1:01:23)
-Ex:5 (1:01:23 - 1:05:19)
-Ex:6 ( 1:05:19 - 1:08:41)
-Ex:7 (1:08:41 - 1:15:07)
-Implicit Derivatives with "z" as the implicitly defined variable. (1:15:07 - 1:17:13)
-Ex:8 (1:17:13 - 1:31:20)
-Ex:9 ( 1:31:20 - 1:39:35)
-Higher Order Derivatives (1:39:35 -1:45:04)
-Ex:10 (1:45:04 - 1:51:23)
-Ex:11(1:51:23 - 1:58:29)
-Mix Partial Derivatives (1:58:29 - 2:00:08)
-Ex:12(2:00:08 - 2:05:45)
-Ex:13(2:05:45 - 2:16:34)
- What is a Laplace Equation/Applications (2:16:34 - 2:18:34)
-Ex:14 *human skin surface area word problem relating to partial derivatives/side notes(2:18:34 - 2:28:52)
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Goatnard
My prof said “ to do partial derivatives, you need to treat it as one variable and treat other variables as constant” that was the only theory he explained. My prof gets salary 100k+ but really teaches me professor Leonard. I believe the end of classroom lectures era is around the corner.
i mean wow you kinda predicted the future of zoom classes lol
its 2024. Still in clssrooms lol
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I shall reiterate: YOU ARE FV
Thanks!! Full understanding is truly what I strive for. I think that is what teaching should be.... NOT just "Covering material", but "Teaching material" until students UNDERSTAND. Just my philosophy of teaching.
and am now enjoying Maths ever in my life, Big Thanx to you Prof Leonard
@@ProfessorLeonard ❤❤
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Second batch of T shirts right there.
I think even Einsten wouldn't have explained it this simply. You are the best teacher in the world thank you sir.
Well probably one of the best anyway as math goes :)
Yeh probably not since Einstein became a stubborn old man not wanting to listen to new theories and calculations from the newer generation at that time.
Basically he did what he thought about the older generations he blamed when he was younger himself lmao
scientists like einstein are so far removed from learning this the first time, their level of abstraction is very high. it's why feynman's teaching was renown, he was one of the rare few to do both
Are there any podcast style interviews professor Leonard has done? Im very curious about this mans life and how he developed such an amazing ability to make understanding complex material so digestible. Like i need a JRE episode of this man lol. This guy has no doubt been the key for creating tens of thousands of engineers physicists and other stem related careers.
he explains in such a way that even a 9th grader can understand .....great lectures love you professor Leonard...watched his calculus 1 2 and now in 3 not even a single topic i didn't understand
You are the best math professor I have ever encountered. Your videos are still relevant in 2020 and will help many generations of students to come thank you for being an amazing professor. Wish everyone could be more like you.
I wish I was one of your students .
your teaching is awesome keep up 👏👍
Billion times better than my Calc 3 professor smh.
Not all heroes wear capes
But most are buff
some wear captain america’s t shirt
Mine wears glasses and has buff arms
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It's not easy to grasp and re-learn math all over, after 25 years. Yes, that was when I last took Calc 2 and I truly believed I was going to struggle with Calc 3 because I didn't want to repeat Calc 2. But thank God for "Captain America", Prof. Leonard! 👍 Your lectures are SUPER thorough and easy (step-by-step) to understand as you explain each element of the topics. Thanks to my classmate, Abraham, for spreading the word about you. You saved my world, SUPERMAN!
professor should open a TEACHERS TRAINING ACADEMY, and all professors gotta be certified from there before moving to a professional university
Thank You so much. It's hard to learn everything online in COVID season. There are so many questions I had regarding this topic, and you answered all of them.
Glad it was helpful!
Superman dresses as Captain America!
how does he have so much time to cover each material? Our professor spend about a quarter of the time that prof leonard does
on each subject
Exactly, we spent an hour on this section last week.
hundle98 this class is typically 2.5 hrs long. Your school must be doing it wrong
@@fkncompton7124 my school taught 13.3, 13.4, and 13.5 all in one lecture (1hr 45min). and we still behind schedule even tho we almost always cover 2-3 sections in one lecture, twice a week.
I speed up 1,5 times faster and still understand every single words, every single exercises very clearly dear Mr. Leonard. My cal 3 teacher also teaches very fast and until now, I don't even know what he saying is really related to Calculus...
If only I could like this a thousand times
I've been watching his Calc. III videos to better prepare me for physics. I can tell I've already learned far more from him then I would from any professors at my college.
I am a fond of mathematics and I have seen no one like you in my entire life professor..... Thumbs up!
Thank you!
Thanks to you Professor Leonard, I actually understand calculus and the ideas behind it. Words can not express how grateful I am for how you helped me and everyone else who watches these lectures. I constantly recommend you to my classmates who are taking calculus 3 with me right now, and it also helps me with my Electricity and Magnetism Theory 1 class right now as well. Thank you so much!
Diff Eq's pleaaase professor leonard :D
you are SO incredible. putting abstract, sometimes inaccessible math concepts totally within reach. this is the kind of understanding you should be able to get from every math professor!!!!
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I continue to be amazed that a person like you exists in this world!!!
Your classes should be a must to prepare any student for their next calculus class. Yours is the best online calculus course ever!!. Thank you Professor for your teachings. God bless you.
Been stuck for a minute on this stuff. Your vid gave me that "ah-ha" moment I needed.
THE BEST MATHS TUTOR EVER.....👍
Man, i watched many of your videos and you help me a lot with maths in university, your are a pedagogical genious. Greeting from Argentina.
Really wish you were my lecturer! Just a suggestion some major topic review videos of calc 1/2/3 for final exams would be incredibly helpful in the future.
Our teacher did not give us the information about partial derivative as you did you're always the best thanks
Its admirable how much effort he puts into making sure everyone understands the concepts and not leave anyone behind
TIMESTAMPS
-What does a derivative mean in Multivariable Calculus? (0:00-28:10)
-"Formal" definition of the Partial Derivative/Notation/Extra Notes(28:10-40:39)
-Ex:1 (40:39 - 49:09)
-Ex:2 (49:09 - 52:01)
-Ex:3 (52:01 - 58:23)
-Ex:4 (58:23 - 1:01:23)
-Ex:5 (1:01:23 - 1:05:19)
-Ex:6 ( 1:05:19 - 1:08:41)
-Ex:7 (1:08:41 - 1:15:07)
-Implicit Derivatives with "z" as the implicitly defined variable. (1:15:07 - 1:17:13)
-Ex:8 (1:17:13 - 1:31:20)
-Ex:9 ( 1:31:20 - 1:39:35)
-Higher Order Derivatives (1:39:35 -1:45:04)
-Ex:10 (1:45:04 - 1:51:23)
-Ex:11(1:51:23 - 1:58:29)
-Mix Partial Derivatives (1:58:29 - 2:00:08)
-Ex:12(2:00:08 - 2:05:45)
-Ex:13(2:05:45 - 2:16:34)
- What is a Laplace Equation/Applications (2:16:34 - 2:18:34)
-Ex:14 *human skin surface area word problem relating to partial derivatives/side notes(2:18:34 - 2:28:52)
Thanks man I was here only for partial derivatives , and I was surprised when I saw him explaining implicit derivatives😂 i was like see you
I just started to watch professor Leonard lectures after I failed my first quiz in very well known University and I will come and report after final.
Best of luck in the course, I know that you can bounce back!
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Every time I learn from you Professor Leonard, I smile. Because I am happy when I understand math
Professor has got an attitude of captain @defense ! Failure of merely one student to understand the concept is just failure of the him! He doesn't even move further until each and every student has got the perfect intuition on the topic. Hats off superman .
I'm an Indian from down South Telugu state , we hardly hardly hardly find a professor like u in India, without you, I'm nothing at calculus. U r the best best best .
Professor "Big Dick" Leonard back at it again with the dank math!!!
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+MudButtz95 DUDE IM STUDYING AT STARBUCKS AND THIS JUST MADE ME CRACK THE F*CK UP!
ForeverBored lmfao
hahahaha
I have to admit, with the way he is committed to explain the actual meaning of everything he is teaching, he is starting to make maths beautiful again.
thank you so much, my current teacher for calc 3 never shows complex examples nor explains the idea behind concepts and only gives us formulas. without you I'd definitely be failing, you are by far the best professor I've ever seen before.
I'm from Pakistan, I really loved your lectures and way of teach .I'm just a big fan of you
Prof Leonard: “you need to get it”. My professor : “you don’t have to get it just memorize it” 🤦♀️ this is why I am getting all my info from Prof L. Best math professor ever 🤩
sat in lecture for 50 minutes and didn't learn anything. sat here for 30 and understood it completely. the reason behind a formula is so important. thank you so much!
sir, at 1:05:22 we take derivative of cos and we do not mention negative sign after cos derivative result(-sinx)
1:52:38
"I'd be so happy if you get this. It will make my heart just flutter."
Sir tens of thousands of people got this ; not only your class. Thanks!
My professor just taught me this but you taught me how much they didn't teach me. Thank you so much! I tried my homework, got frustrated that I didn't know what I was doing, watched your video, and zoomed through two whole sections.
Suggestion for the future, although I haven't looked to see if you have it posted anyhwere: let us know what book you're using? It's easier for me to line up your lectures with where I'm at in Calc III if I can line up topics.
You are truly gifted! Thanks for giving us such a wonderful, and free, resource.
First 40 min is so rich with the conceptual idea of partial derivatives! I love it!
I loved how Professor Leonard kept the blank in the word problem to make that joke what a legend. Immaculate explanation as always
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May you long live with happy life
I have to giggle a bit when Prof Leonard gets close to the cam. It makes his arms so huge his head looks tiny.
Like he can crack his head open like a walnut with his own arms if he so chooses. WAIT I'M SUPPOSED TO BE STUDYING
i spent my entire semester so far fearing getting up to here and this dude just made this one of the easiest concepts in calc 3
My new quarantine professor! What an upgrade. Awesome teaching thanks
This video is incredible. As an econ student, that human surface area question was perfect. As well as the little mention about labor and capital.
I love Professor Leonard. The best math tutor ever.
Absolute legend is what you are
Thank you a lot. My teacher didn't teach this concept to us in class in depth at all. Glad i can find someone reliable to turn to for help.
Professor Leonard, thank you for another great video/lecture on Partial Derivatives in Calculus Three. This topic is easy to follow and understand from top to bottom. All students watching this video, should master this topic with massive problem solving.
Thank you so much for doing this. I'm going through the tail end of calc3 and I wanted to cry because I wasn't retaining or understanding things. These helped give me hope and good grades! (made a 92 on the last exam :D )
Good Job!!!
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Prof. Leonard are you going to be doing Diff Eq's anytime soon?
He is simply the best teacher ever! The first time in my life I enjoy slow speed learning
professor I like the way u proceed lecture . it is pretty easy to understand. I really enjoy them a lot......Thank you very much for calculus...........
I just tried using partial derivatives to find 2 parametric lines that touched a point on a 3D paraboloid, and I managed to use those lines to find a tangent plane to that point.
That was awesome - definitely a good problem to have on a test, in case any Calculus 3 teachers out there are currently thinking of some problems to use. 8-)
I hope and i really hope Professor Leonard this comment "you are the reason i got my confidence back in uni" This videos meant a lot to me THANK YOU so much
Professor Leonard: You are an amazing instructor. You have what it takes.
Wow Wow Wow. I have never been taught like this. Thanks for your Lectures @Prof Leonardo. You have made the beautiful math even more beautiful.
sir i am a stu dent of on of the best college of india but i hadn"t got the maths teacher like u thanku sooo much for ur effort.
thank god finally at partial derivates...whole reason i started this journey was to understand what that curly d symbol meant in my book on neural networks
I'm no longer attending my calculus classes cause I got you🤗
Just two days ago I was wondering if you had a partial derivative video.
Thank you, thank you, thank you so much for this video! I don't get why is it so hard for a lecturer to bring a balloon and a marker to a lecture. Knowing what's going on behind the scenes helps to understand partial derivatives much better.
I am so satisfy and happy because of you
Love you alooot 😘😘😘😍
And continue your work
will you ever do linear algebra?
After Linear Algebra, do complex analysis and differential geometry!
KevinCompanyTV I think you need to be a PhD to teach that high up in schools.. Besides, he's a cc professor, and cc's don't even teach that..
I personally think that Linear Algebra should come before any Calculus courses, since Linear Algebra only requires knowledge of Algebra and some basic Trigonometry (for matrix rotations etc), and Linear Algebra has several applications in Calculus (like the Wronskian, for example).
@@emmanuelpena3000 My CC offers Linear Algebra.
@@Peter_1986 That is how they do it here, in sweden . We study linear algebra before multIvariable analysis.
Thanks Doctor Leonard you have helped me from the hand of these horrific part of mathematics.
I can now do it simply and confidently.
with you professor Leonard I never get less than 90% in maths, thank you very much....
He opens with " you shouldn't be doing this stuff if you don't know what it means". Solution to our educational system right there.
One great thing about Professor Leonard is that he focuses a lot on example problems where the students are asked to participate;
the whole structure where he explains the topic, then gives example problems and finally discusses the solution steps with the students is perfect.
Really you taught that topic in such an amazing and easy manner....thank you very much!!!😊😊
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the best teacher ever , he is universal school
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crazy how much more i learn here than in class, we owe this man so much. for now though heres a like and a sub
Ohhhh that's why we hold the y or x constant. I come here for the theory explanation. You've got the best theory explanation thank you
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Your explanation makes calculus so easy to understand!!
Sir you are intellectual keep up the sevices...i ever understand the concept of p.derivative
Dear Professor Leonard, Your calculus videos are amazing. Thank you. Looking forward to your merchandise.
HE IS SO SMART TO EXPLAIN THE PARTRICAL DERIVATIVES BY A BALLON.
best mathematics teacher i ever met😍🥰🤩
Finally someone who actually teaches what partial derivatives are not like say: hold this constant this variable shit
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sir your video lectures are amazing ...i live in a small town in india and we dont have math prof. in our college...session ending exams are coming close ...and your videos helping me in preperation ..thank you so much