Calculus 3 Lecture 13.4: Finding Differentials of Multivariable Functions
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- เผยแพร่เมื่อ 26 ส.ค. 2024
- Calculus 3 Lecture 13.4: Finding Differentials of Multivariable Functions: A review of Differentials from Calculus 1 and an extrapolation towards Differentials with more than 1 Independent Variable. Focus will be on the derivation of the idea of Differentials and the application of Differentials in Word Problems.
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I dont think this guy understand how much he is changing lives especially for science students
Economics as well.
Emre Goksu i was just gonna write the same comment
I think he does know...he just needs to add up all the differentials for the total change XD
Engineering as well!!
Computer science as well
My professor covered this section and chain rule in a hour and a half. You have 4 hours of content for both these sections. Outstanding!
Same man, I suspect Prof Leonard holds class everyday for 2hrs. No way it's anything less then that
Mine went over partial derivatives, this and chain rule in a 1 hour 20 min class lmao
@Bruno Cordova Apolony Mine did it in like 1 min. he just gave us a handout and said to ask him if we have any questions
@@the_lord7961 ccvccc uhhhh.
bro my professor did it in an hour i died
Only teacher in TH-cam that can be watched for more than 2 hours straight. This guy is a magician.
I am binge-watching this playlist right now as an in-depth review, since all my current Engineering Physics courses seem to bring up concepts from Calculus 3 all the time, and I have seriously been watching up to this video in just one week. It's like binge-watching a really great television series - I can't stop, lol.
can’t believe I am not paying for this Professor Leonard has more passion than any other professor in teaching to offer this for free
He said he overtalked the one point... that is exactly what has helped so many people, is your repetition of a point so that it drives home. Thank you for the effort you put into you lessons. Coming from a former teacher and engineer.
Best way to cram half a semester in three days! thanks!
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yea he is just awesome...
literally, a superhero, patient, understanding, a love of learning and teaching, a perfect amount of sarcasm, fit like a superhero, AND he loves his wife... how much better could he possibly get??
-What are differentials in 2D - 24:24
-What are differentials in 3D - 58:42
-Ex:1 - 1:03:29
-Ex:2 - 1:08:29
-Ex:3 - 1:16:16
-Ex:4(pressure problem) - 1:24:28
-Ex:5(specific gravity problem) - 1:35:16
-Ex:6(tension in cable) - 1:51:03
This channel should be called King Leonard instead.
+Kev Twine
Professor is much better than a king. Anyone can a king if he/she was born in a royal family, but not everyone can be a Professor.
+Kev Twine Grand Master Leonard
My vote is for Grand Master Leonard because he literally is, without exaggeration, saving my calculus grade.
@@user-iz4gk7fm9p Thats right. Most kings are douchebags.
@@romanemul1 most professors are too lol.
I come back from Analysis 1+2 with relatively good marks in the exam just to review it. Professor Leonard, I want to thank you for this because before I watched this video I just juggled around with those signs in the equation without really having understood them. Your style of teaching is really acknowledgable.
I wish my Uni would offer Math class online, I would be able to pass it so much better. You are a good man Prof. Leonard for helping out everyone understand Math.
Wow, wish I found this guy earlier. Clear explanations and makes math understandable and fun.
Thank you for uploading all these videos and thank you for actually caring about proving all of this! I now truly understand what the differential is. I'm not just using the equations that supposedly popped out of no where to answer exam questions. This is exactly what I needed and I couldn't find it even in some highly acclaimed maths textbooks. A couple of years ago your videos helped me get not only a great grade on my IB Math HL Paper 3 (calculus) exam, but truly understand its content. Here I am 2 years later studying engineering at uni and still going to your videos for the best explanations.
I love watching your instructional videos on calculus, they are very informative and detailed information, You truly do an exceptional job at presenting the material.
شرح كافي, اسلوب رهيب, كفيت ووفيت يبوليو. جعلك تسلم بس ووقتها بعزمك بعزيمة خاصة جدا.
After all....he is indeed a Professor of Mathematics. That's all there is to it. Mathematics never seemed an easier task on listening to his lecture. Great job Prof.
keep it up. God bless!!! All the way from Nagaland
From the question related to the ideal gas (1:21:55), all of the units need to convert to SI units, which is the general units in physics so the data won't be confused. The SI unit for volume is cubic meters and that for temperature is Kelvin, so the actual approximate change in pressure is -3.3256e3 Pascals.
Underrated comment!
also the value of gas constant is 8.314 which is Ru, so the right equation should be PV=nRuT
and n which is the number of moles is missing here, so the question is not valid.
But anyhow, the concept of the topic itself was illustrated, the rest is physics which doesn't matter here to be honest :P
I thought this topic was daunting until I stumbled upon your videos. You are an amazing teacher and your explanations are brilliant! Keep up the good work!
Thumbs up! Yes, showing the proofs and the reviews of Calc I (and even Algebra) in your lectures are the most helpful parts in my opinion. Thank you!
You should put up sub titles so i can watch this during class without bothering anybody or my actual professor.
just put a small earbud in your ear and connect bluetooth
buy airpods
From Turkey, with loves Mr Muscle!
What a explanation sir....Thanks a lot🙇♀️.🙂
Thank you Professor Leonard for your care for the students and for the lectures here.
Professor Leonard ,thank you for another solid video/lecture on Finding Differentials of Multivariable Functions in Calculus Three. These concepts are also familiar from Calculus one in a single variable. All topics in mathematics follow some pattern that all students should recognize.
Dear Professor Leonard, as one of your foreign students, I kindly request permission to add subtitles. Your speech is very clear and understandable, but it's still not as easy as listening to a lesson in our own language. Thank you for your understanding.
when he asked if there are any engineering majors here I raised my hand like I was actually there smh. That's how engaged I was in his lecture lol
It breaks my heart to see probably be best math professor on the planet go WAY out of his way to explain important concepts that will help his students understand the material, and most of his in-class students just don't appreciate it at all. We care Papa Leonard. We love you.
His ratings on Rate My Professors are insane;
pretty much everyone has given him a perfect Quality rating.
THANK YOU FOR MAKING THIS. After Calc 1 content to help you understand what's going on is slim to none. AND you're a good teacher??? It's like a dream come true I almost don't believe it lol
Some of these students may never know how lucky they are. I have been looking for intuition all this while
Where does this guy teach? I'm gonna transfer
at Merced College
Just recently found these videos and these are amazing! I waited far too long to actually study, so going through in 1.5x I can still grasp what is being taught (my prof goes in 1.5x during lecture or so it feels). You are amazing sir! The way you teach and the way you actually care if your students understand is awesome!
I just had a massive light bulb moment!!!!! Thank you Sir for taking the time to work through the reasoning as carefully as you do!
I feel your frustration Leonard , you put so much energy into explaining all the concepts and most of the class still gets it wrong at the end lol , they are lucky thay have you , if they had my teacher they would have to do like 10x more work at home to understand 1/2 of what you are explaining.
i did this class several years ago but I honestly really like watching these
Geez you should be on the Ellen show. You show kindness by sharing your passion for Math with us Science and engineering students. I’m not taking this for granted. Trust and believe these lectures are put to good use. Oh and I’m acing my Calc 3 class because of u. Thank you.
Man, you made Calc 1 and 2 so much better for me and I cannot thank you enough for posting your vids. Unfortunately, I took Calc 3 when these weren't up yet, but I am glad to see you are posting Calc 3 stuff now and it will definitely be helpful for a brush up. It takes a certain ability from a teacher to maintain the perspective of a student that doesn't understand what he/she does and I think you got it. It literally only takes a good one liner from you to make fuzzy concepts click. Keep up the good work! Oh, would you ever consider doing differential equations? That would be the fleas eyebrows. Take it easy
Greatest math teacher to ever have walked the surface of earth!
What textbook does he follow? I follow the james stewart one and its just the same topics but one chapter ahead
GOAT coming in strong on this lecture! I actually think im getting it. Its glorious.
Great video!! Not too many people spend the time explaining the concept in detail.
from @purpleapple-el7kb
What are differentials in 2D - 24:24
-What are differentials in 3D - 58:42
-Ex:1 - 1:03:29
-Ex:2 - 1:08:29
-Ex:3 - 1:16:16
-Ex:4(pressure problem) - 1:24:28
-Ex:5(specific gravity problem) - 1:35:16
-Ex:6(tension in cable) - 1:51:03
Doesn't really matter, but for future reference, Kelvin/liter is not Pascal of course. What happens is that the coefficient is not dimensionless. In the ideal gas law it has units of J/(mol*K). Since there's no "amount of material" in this example the coefficient would just be 8.31 J/K. Remembering that 1 liter is 0.001 m^3 this gives a unit of J/m^3 on the right hand side, which simplifies to N/m^2 (force per unit area) or Pascal.
You are the best you don’t know how much i love math because of you thank king
This video needs 300 million views.
I wish i was known u , i regret that , now i'm in calculs 3 and ur video are very helpfull , thanks u so much ❤
All the best
Thank u so much my professor 29 june will be memorable as i find u lots of love from INDIA love uuuuuuuuuuuuu
Than you Sir for your dedication. You help people allot by posting these videos and great explanation...
Just wanna say this guy is way better than man of those pretentious "math" professors out there teaching nothing, but writing down random equations they probably they don't understand about.
i wish you were my professor at my school :( but I'm soon glad i saw your videos you have saved me :)
I want to understand first then apply it to the problems so thanks for the thorough breakdown😀
I am an old guy who did math some 30 years ago (university math). I am heterosexual as well, but I love you very much! Thanks for your work and your sincere passion, young man.
Long life to you! Kisses! :)
yop, from switzerland
So happy to see the example @ 1:08:23. Chemistry Majors take this class, too.
wow cool realizing that prof Leonard is a machinist. probably wont see this comment cus this video is so old but I'm really curious as to what types of machines you're familiar with/ what type of parts you make prof Leonard. p.s. thanks for all these videos you're the goat man
Nice lecture as usual, I like to understand the concepts or the ideas rather than just simply learning the mechanics of solving the problems; and you do just nicely: present the concepts very clearly. Thanks.
I noticed how he makes those small mistakes while explaining something on the board and then goes back to fix them. It feels like he makes the mistakes on purpose just to vibe check the students and see if they are following him attentively. If that is the case, Mr. Leonard is on another level. Nevertheless, his teaching skills and attention control are amazing.
I got my cal3 test next week. You saved my life.
thank you so much for the class teacher, i really learned it this time
Amazing lecture with clear explanations, thank you so much. Just a note, I think the answer to max error example is 1.4625 lb, not 0.775 lb
What an absolutely fantastic teacher. Just perfect. I wish would also teach stochastic calculus.
you make me excited to study maths I wish there is a professor for physic s as good as you are
A triangle has two of its sides 8 in. and 10 in. respectively, and the included angle is 30 degrees. Calculate the change in area caused by increasing the length of each of the given sides by 0.01 in. and the included angle by 1 degree. Calculate also the differential of area corresponding to the same increments.
A = ( 1 / 2 )bc sin theta
dA = ( 1 / 2 )c sin theta db + ( 1 / 2 )b sin theta dc + ( 1 / 2 )bc cos theta dtheta
dA = ( 1 / 2 )*8*sin (pi / 6 ) *0.01 + (1 / 2)*10 * sin (pi / 6) * 0.01 + ( 1 / 2 )*8*10*cos (pi / 6 ) * (pi / 180 )
dA = 0.02 + 0.025 + 0.6046
dA = 0.6495
delta A = actual change in area = ( 1 / 2 ) * 8.01 * 10.01 sin 31 - ( 1 / 2 )*8 * 10 sin 30 = 0.646
After finding the error, you have to put + or - to indicate how much value you are off or away from the original value ie the height.
This man should get some kind of prize, like best teacher on the planet prize or something
Outstanding lecture sir .i finally understand the concept.
ok Leonard. the next time im out in california I am showing up and bringing you a gift basket and a gift card. I sit here and take notes on everything and you are just awesome
Thank you for elaborating on these concepts!
You completely saved the bombing of my calc three class. I am not the first to say this but BROTHER THANK YOU SOO MUCH !!
i have became your biggest fan sir .
your playlists are really helpful.
love from india.
Your students don't deserve you! Thanks Professor Leonard!! :D
During years of Chemistry and Physics, _T_ is always temperature, usually in Kelvin.
You are really good at what you do Professor. Keep on doing a good job. Mathematics made easier
Thank you prof leonard, it turns out my problem wasn't differentials in multivariable funct. It was just that I had forgot what differentials were.
I thank God for you. Thought you should know!
Sometimes it's the most intuitive concept that's the hardest to analyze and quantify.
I was searching this explaining for long time , thank you so much sir
Congrats on 500K sub sir🎉🎉🎉❤️
Dear professor Leonard, thank you for such a great lecture full of kind explanations!
I have one question!
45:00 doesnt equality Δz = Δzx + Δzy only hold when z is a plane (or flat surface)? but not when z is curved?
Hello, just wanted to take the time to thank you for uploading your lectures. More than that, to thank you for caring that students do learn the content and the logic behind formulas and procedures. I have been focusing on mastery learning, which is difficult with a math class that is taught with slides and covers two sections per meeting, but you definitely help me clearly understand what I'm doing and why I do so. Again, thank you so much.
prof. you are the best ....love from India
Thank you.your way of teaching is amazing.
8 years ago but still gold ❤
I spent like one semester, searching for what was exact diff equation!!!!.Finally found it after 5 semesters...
God Dammit you are amazing, you make me contemplate paying for tuition !
Why pay when he gives this information for free!
Sir. you are the best professor l need to thank you so much
Professor Leonard: "I get it some of you don't want to understand it. You just want to know how to do it."...pretty much the difference between me when my homework is due vs studying for a test. Why I still watch his videos after my lectures
59:00 examples on differntials
gracias professor leanard hahaha you help a lot to undertand the concept more tham just doing the math . saludos desde mexico
Genuinely very entertaining,
These videos are so good that I almost think of them as an exciting television series, rather than "those typical boring lecture videos".
At 1:22:10, Volume should be in cubic meters and not Liters to get the pressure in pascal
yeah the answer should be in kpa if we are using liters
Thank you very very very much for all these lectures
How do you know that the relative error Delta T / T is not under approximated by the differential dT / T? We concluded that the maximum relative error is 7%, but that's only using our approximation dT for delta T. E.g. how do we know that Delta T / T is not going to end up being 9%?
You are amazingg
From Argentina HUGE THANKS!
someone in the university asked asked me my teacher of multivariable calculus , i said proffessor leonard.
Excellent class. Even better than my calculus book
This guy is clearly a machinist
Amazing you're gifted
Not all heroes wear capes. Congrats from Portugal
Professor Leonard, I have a question on the "Max error" discussion (starting roughly at 1:23:00).
Since we have an imperfect measurement of the independent variables, we want to know the "maximum error" that we can make by using the imperfect measurements to tell the change in the dependent value.
Therefore, we try to use the differential to figure out how large the error can possibly be.
However, the differential is just an approximation of the total change of a function.
Does that mean the "maximum error" that we can get by using the differential is also an approximation to the actual "maximum error"?
So that, as a result, our approximated "maximum error" will be useful only if our measurement error on the independent variables are small enough?
Sorry if I said something silly.
Your lectures are awesome! Thank you so much!
I've just watched this and I have the exact same question. It would've been nice if he had answered it :/