Calculus 3 Lecture 13.5: The Chain Rule for Multivariable Functions
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- čas přidán 15. 03. 2016
- Calculus 3 Lecture 13.5: The Chain Rule for Multivariable Functions: How to find derivatives of Multivariable Functions involving Parametrics and/or Compositions. Focus will be on deriving the Chain Rule and practice of examples.
![The Chain Rule for Derivatives in Calculus - [1-5]](/img/n.gif)
can u give some lectures on body building
Having a good body depends on your genetics, diet, sleep, mental state of mind and training.
I don't think he ever will.
JustAdreamer Forgood genetics aren’t a very big factor in obtaining a “good body” it’s mostly consistent training, proper nutrition, and sleep.
hahahahaha
@@justadreamerforgood69 Nah a body builder level body required good genetic, a good body as in athletic just requires constant effort and progressive overload as well as everything else you mentioned.
Universities forget how important mathematics really are. They cut down the hours of lessons and professors just give you the main ideas and formulas, no proofs no nothing. However proofs and deep understanding are what get you beyond just passing the semester's exams. They develop your cause-result imagination and allow you to really cultivate original thinking. Thank you Professor Leonard for giving us a chance to choose to differ and study deeply and pointfully.
EXACTLY ! MY SCHOOL EXPLAINS THE BASIC RULES IN LECTURES, SOLVE 1 PROBLEM AND ONTO THE NEXT TOPIC LOL. THEN I HAVE TO TEACH MYSELF EVERYTHING. i am only paying for the degree smh
@@fenerbahceqwe3756 what degree are you studying?
@@CHROMIUMHEROmusic CS
Depends on how the proofs are presented, though.
Some math books present proofs in as confusing ways as possible and use a lot of overly complicated terminology and symbols even when the students for that course aren't expected to be familiar with that stuff.
It's almost as if the authors had written those texts as summaries for _other math professors_ or something, even when they were intended for students, and I really hate that.
Proofs should only be as formal as actually necessary, and keep things in Layman's terms if this is possible without hurting the overall quality of the proofs.
The author David Morin already managed to do that in his physics book "Introduction To Classical Mechanics", which seriously feels _almost_ like a children's book despite bringing up topics like "Principle Of Stationary Action" and space mechanics - it has the same type of charming enthusiasm as a children's science book, and it is good enough to actually be used as course material in one of my physics classes - and yet does an excellent job at explaining all the concepts.
Laurelindo well said
00:00 - Intro to Chain Rule with respect to t
44:00 Examples of Chain Rule w/ t
(Organization Tree Method at 47:00 w/ Ex)
56:20 More Intermediate Variables
1:06:00 More Independent Variables
1:10:00 Examples of "More Independent Variables"
1:51:00 Implicit Differentiation of f(x,y) where y=g(x)
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how'd it go ?
Really well actually! Thanks!!
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Hannah X how’d it go
Erich Fernandez actually it went well :D thanks for checking 💙
In case you didn't know, professor, English is not even my native language, yet I'm watching your videos instead of my professor's, because you are so smooth and clear with math. It always make me feel like I can follow without sacrificing any comprehension. If I don't, you make it clear what section of your previous videos I should revise.
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He is cool, in fact he actually has a speech uploaded here on CZcams where he talks about laser light and waves.
@@Peter_1986
Where is the video ?
@@justadreamerforgood69
The video is called "Laserljus och vågegenskaper; en orienterares perspektiv - Erik Olsson, Luleå tekniska universitet".
@@justadreamerforgood69
Here is the link:
czcams.com/video/BDwddSrdqaQ/video.html
Hearing the laughter at the end of the video made me truly appreciate how valuable of a teacher you are. The manner in which you combine humor and education keeps me engaged and makes my learning experience phenomenal. Because of you, I understand what a good teacher is and how special it is to have one. Thank you so much for uploading your videos. They are incredibly helpful.
Could you PLEASE do Differential Equations for us? (Please)
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Professor, I am currently taking Calculus 3. I am an engineering student at the University of Alaska. I sat through the lecture on this topic today. I have never been so confused. Usually my professor does a pretty good job but today it just didn't click. I was pretty worried about my understanding. I watched this video and now I understand. Thank you for this Professor. :-)
"I watched Leonard on one half speed..." Cracked me up. Understanding this chain rule material is incredibly useful for pretty much any kind of higher physics and diff eqs. Fantastic work.
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Professor Leonard ,thank you for a powerful analysis of the Chain Rule and Implicit Differentiation for Multivariable Functions in Multivariable Calculus. Although I encountered this material in Calculus one, I fully understand the Chain Rule and implicit Differentiation that is presented in Calculus Three.
Greatest math' teacher , bar none. These students should relish this education, for they will find none better, anywhere.
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22:05 dt -> dx & dy -> dw
~42:00 dw as partials of x y
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I agree with the others -- I hope you can do a Differential Equations course at some point. I am learning it from my textbook and teacher, but I feel like I'm lacking on theory because of how formulaic it can get. I would love to get intuition and really understand DE, and I feel like your teaching would make it much better.
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Professor Leonard 1:05:15
Spoken like a hollywood movie star
Prof. Leonard, are you going to make Differential Equations videos? Please consider doing so :( You're the best !!!!
+Karam Alnadi
If you need material for differential equations, then check out the site Paul's Online Math Notes.
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Great Stuff.
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The God of Mathematics, ladies and gentlemen!
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@1:28:20 It should be dx/du, since there's only one independent variable that relates to x. Similarly, dy/dv. These shouldn't be partials.
you sure? I was wondering about it too.
1:52:02
Noticed a lot of people pointing this out. Does anyone know why he took a partial derivative there? I'm still confused.
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Life saviour!
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Thanks
Just took my final exam for Calculus II (which has many Calc III concepts like directional derivatives and triple integrals) and I felt so good and confident walking out of there thanks to your videos. I went from a 47% on the first exam, to 89% on the second, ending with a 92% on the last exam before the final. I used to try and read the textbook and pay attention in class but was not really absorbing any of the content. I stumbled through the homework and was lost on the smaller quizzes in the beginning. Your videos and explanations helped me actually understand what was going on rather than copy a formula down with no idea where it came from. Thank you so much! Legit the only reason I passed Calc *all the way from a D to a B+ going into the final
thank you sir
Hi professor, your videos are very much appreciated and inspirational. Even when you don't the right feedback from your pupils you don't despair and are willing to go over the topic again until it becomes clear to them, patience personified. May I just ask you a question?. At approx. 1:14:57 on this video the partial w with respect to u or v on the left hand side of the equation is set equal to the expressions on the right hand side, however shouldn't the partial Dx/Dx and Dy/Dy [ I use " D " here to mean partial ] cancel out giving the right hand side of the equations twice the value of the left hand sides of the expression. This I don't understand......any clarification would be gratefully appreciated. Thanks , and kindest regards .Barry.
thanks
The number of components of the derivative of a specific independent value is equal to the number of intermediate variables that are composed of that independent variable! I think that sums it up!
Too bad you don't even get to see these concepts shine when you first learn them.
This is so useful for linear approximations of nonlinear systems of differential eqns.
51:47 the "dependent variable" header is supposed to be the "independent".
I have noticed this as well haha but its ok professor havent seen it
@Professor Leonard, just a suggestion. At 1:50:19 you start talking about implicit differentiation for multivariable calculus. I think you should mention that on the the title of the video.
49:38 "tryna be cool, shouldn't have been a math teacher" gave me a sensible chuckle.
this one was fun. :-)
It’s not a rigorous proof, but it makes good intuitive sense!
1:37:40 We watch you professor! 💚
PLEASE do linear algebra!