ALL of calculus 3 in 8 minutes.

FuzzyPenguinAMS's video on Calc 2 (inspiration for this video):
• ALL OF Calculus 2 in 5...
Some other great videos:
• Divergence and curl: ...
• The 3D Cartesian Coord...
Non video sources:
openstax.org/books/calculus-v...
0:00 Introduction
0:17 3D Space, Vectors, and Surfaces
0:44 Vector Multiplication
2:13 Limits and Derivatives of multivariable functions
3:02 Double Integrals
3:44 Triple Integrals and 3D coordinate systems
4:57 Coordinate Transformations and the Jacobian
6:02 Vector Fields, Scalar Fields, and Line Integrals

[@davidlu631]

3:52 unfortunately the depicted 3d region describes y going from 0 to 2 - x as opposed to the listed 0 to x, meaning that the actual region you're solving for in the triple integral would differ from what the depicted region would lead one to believe. Although you end up getting the same answer due to the correct shape simply being a reflection of the depicted shape about the x = 1 plane, the setup is still not technically correct.

[@calendarG]

This is correct. Thank you for catching the error

[@lokeshanhjeriti]

​@@calendarG Will you upload another video

[@machineman8920]

Finally feel like youtube gave in and stopped recommending me random trash i don't watch or care about. Truly we are in a golden age of online education. Take it from a 10 year and counting numberphile viewer.

[@TheInevitableHulk]

That 3b1b video encouraging others to make their own similar videos injected hundreds of high-quality math content onto KZbin in an incredibly short period of time. I only have my own experience to confirm but my own recommended videos would rarely show content like this. Since the day that video came out, about 1/8th to 1/4th of all my recommendeds are very new, very well explained math concepts.

[@jameslucarelli7172]

I agree you5ube had a.few bad months recommending me shit I didn't want to see aswell

[@brycesmith5784]

I love it when KZbinrs can explain most of a semester of school in a single video. It shows how much you really get it

[@charliemaybe]

really only a bare bones demo of the concepts were shown while actually learning this will take months. I would agree with you that there are other math courses that actually can be explained and basically tought in a matter of hours or min, but not this.

[@jarnailbrar6732]

Prof. could drag this out to take one semester. This flows together very well, instead of being fed bits and pieces.

[@Jacob-bn1nj]

@@Max-bm5rs True but it is a really nice and concise refresher over some of the topics

[@aurelia8028]

Yeah... no it doesn't. It's one thing to just list a couple of subjects it's a whole other thing to have actually understood it.

[@hunter_69_69]

Algebra: When in doubt, set it equal to zero Trignometry: When in doubt, soh cah toa Calculus: When in doubt, take the derivative

[@ugestacoolie5998]

lol so true

[@siwonchang3818]

linear algebra: when in doubt, cry

[@tl5429]

​@@siwonchang3818 Nah, more like when in doubt, create a determinant

[@natureshorts6657]

I've taken Calc 3, and this was a GREAT concise summary and actually kind of clarified some things for me. Excellent job.

[@feniceazzurra7168]

Can I ask where are all you guys from? Except point 7 I am pretty sure all the rest is Calc 2 material

[@thelogicalvoice-shorts1674]

@@feniceazzurra7168literally. i’m from the UK and literally all of this is juvenile compared to what we do in literally the first few months- i know it’s summarised but still

[@feniceazzurra7168]

@@thelogicalvoice-shorts1674 at least I am not the only one questioning the differences in the prograns

[@Loots1]

@@feniceazzurra7168 you do triple integrals in cal 2? what uni do you go to?

[@feniceazzurra7168]

@@Loots1 University of Torino, Physics faculty

[@yigiteldek]

i didn't expect for a channel that randomly dropped on my feed with 50 subs can save my life. that video was amazing thanks for the video. Edit: channel has 7.6k subs now wow! When is the new video coming?

[@shagunshukla8490]

And what help did you exactly got from this

[@yigiteldek]

@@shagunshukla8490 bruh I was literally getting ready for a calc 3 exam on udemy to get my license and I was almost trash on line integrals, this video did resembled some really critic things to me

[@stephenzhang3825]

@@yigiteldekwell you still gotta learn optimization + surface integration and like stokes thm, divergence thm etc. good luck man you got this

[@yigiteldek]

@@stephenzhang3825 thanks man, I was talking about the fundemantals actually, I was having a hard time on the idea of such an integration and re watching the course after this video got me a lot better on the theory. And I did pass the exam and got my license yesterday, but still thanks a lot for the talk man. I really appreciate it

[@ldman538]

woah 50 subs to 2k subs in just 10 days?

[@WolfrostWasTaken]

Finally a youtube video about calc 3! I feel like most math youtubers intentionally leave it out, but it's super interesting because with it you can finally tackle real life problems! (e.g. average temperature in a room)

[@NealIRC]

Can you name any other examples?

[@Benthehuman]

@@NealIRC It also has a BUNCH of applications for electricity and magnetism. Like for finding the magnetic force of a flat plate on a magnet a certain distance away you need calc 3 to do it (or just do the math with pre-memorized equations with basic calc 2 knowledge.)

[@kubs1162]

If you’re only finding real life applications for calculus in calc 3 something is wrong, and I dont know how you get this far lmao

[@EatonArrsenik]

​@@kubs1162 Ignoring the abnormality of your statement... You said "average temperature in a room" out of all the applications shown in an common calc 3 textbook. This reads as someone who hasn't taken the course in their life and just wanted to comment.

[@puppergump4117]

I've only cared to learn calculus for one thing in programming, and that's gradient descent for neural networks. I'm pretty sure there will be more applications for stuff like integrals when I start working with 3d applications or graphics.

[@taylermontgomery2004]

As an engineering student, this is by far more comprehensive than my illiterate thousand-page notebook. Congrats on your first video!

[@TheGreatIronWalnut]

I remember going through calc III during summer session and being a little sad I couldn’t fully grasp the topics enough to appreciate it more. This was super pleasant, lots of nostalgia. Thanks!

[@anandkalra]

Wish I'd had this as a resource in 2005!! I spent most of calc 3 spinning in my own head and grasping as straws. These visuals and explanations are so generous, kind, and clear. Bravo!

[@prome666]

ya, at the time tutorial youtube videos weren't really a thing. Or maybe i was too occupied playing WoW. I urge all the young people to take advantage of these great videos. This gives a great big picture to many things, and in my case, would have helped with electromagnetic theory. :)

[@TheGeckoIsKing]

I can’t stress enough how amazing the quality of this video is! Keep up with the awesome content and it’ll pay off well!

[@fantiscious]

This is cool. I feel like calc 3 doesn't get enough recognition on youtube as calc 2 or calc 1 does. You get my subscribe

[@ederamin9697]

haha thats because calc 3 is out of reach for 99% of youtube users' brain capacity

[@heyman620]

​@@ederamin9697 it's not that 3>2>1, in fact, 1 is probably the hardest to learn for most people. If you can learn 1 (math department level, not engineers and so), you can learn 2 and 3.

[@breakdancerQ]

​@@ederamin9697 or 99% just don't need to know it.

[@ale4462]

This is prob because calc 1 and 2 can be taken in high school with ap calculus bc

[@shipwreck9146]

@@heyman620 Yeah, I was about to say that. Calc 3 was much easier than calc 1. But then things got difficult again when I took differential geometry, which would I guess if you continued with the number scheme, that'd be like, calc 5.

[@passionisinspiration1912]

holy!! I'm studying calc 3 currently and this video made the visualization so simpler and made the physical significance of divergence, curl so cool !! Thankyou !!

[@CreativeMathProblems]

Nice vid, you can use '$\sqrt{x^2+y^2}$' to have it render more nicely. Adding a '\' before the 'sqrt' makes it render as a square root in LaTeX

[@calendarG]

oh that's actually interesting. I did use LaTeX to display the integrals but not that. Thanks for the suggestion!

[@skylardeslypere9909]

@@calendarG To add onto the comment, if you use \sin and \cos instead of just sin and cos, it gets displayed in normal text instead of cursive text

[@fares8005]

@@calendarG Also notice how digits aren't well aligned in, say, "3D". Better would be "$3$D". More generally, any and all math should be in latex. It's worth your time to learn it a bit more in depth, perhaps by going through a textbook. Otherwise, great vid!

[@notsojharedtroll23]

LaTeX gang rise up

[@saturapt3229]

You can use word if you want which makes it a bit easier imo

[@jimmyt_1988]

Bloody hell. Perfect amount of detail for 8 mins. Well played!

[@henrik897]

This was actually calming to watch as I study since I can see I grasp all the basic concepts, thanks

[@olivergonzalezgarcia4663]

A wonderful video! I found it incredibly helpful and useful. So well deduced, explained, and explored. Job well done!

[@mastershooter64]

now we need all of calculus 8 in 3 minutes, calculus 8 would be fractional calculus on operator algebras lol

[@calendarG]

y e s

[@skilz8098]

Lambda Calculus in PI minutes.

[@vintage_osu]

alright I finished the video, now where's my diploma

[@Name-ps9fx]

This video, like all calculus videos, is an excellent source for ASMR ambience. Thank you!

[@aAtom596]

I’m currently in the Triple Integrals unit of Calc 3, so thanks for the heads up about line integrals and fields. Can’t wait to learn about those! Also, I my math teacher never told my class why there is a ‘conversion factor’ for polar, so it’s cool to realize it’s due to distortion.

[@JedediahTombstone]

Thanks for your video. I took calc 3 in college and never really understood what was going on, because we got bogged down in the algebra. Seeing the concept of it all laid out is empowering. Thank you again!

[@luispadilla2394]

Great video! You covered the major concepts very well.

[@AFSmashMan]

I love your video! But instead of me being fascinated, I'm incredibly stressed out more because I'm in the middle of Calc 3! Now I need to know so much more. Thanks for shedding a light though on many of the important points.

[@lowlightevangelist9431]

Thanks for sharing your gifting in mathematics and computer science. You helped me understand better where the matrices go. Never could understand their importance until this video. Thanks!

[@eddyhighwind6852]

Forwarding this to my students this semester for sure!

[@fuzzypenguinams3207]

Very nicely put together!! I am glad that I inspired someone out there to create something amazing! I am actually still learning how to use 3d spaces in Manim, and I am curious as to how I can use that to create visuals! Regards, FuzzyPenguin

[@jadeharley413]

PLEASE WE NEED MORE VIDEOS!!! I love this!

[@SecondFool]

This is phenomenal.

[@Fasteroid]

I've never officially taken a Calc 3 course, but according to this video I'm apparently familiar with most of it. It'll be nice being able to tell myself this confidently for a change.

[@ethanlandis8426]

Just wait man just wait

[@mochamp4353]

This is so helpful for a quick recap when taking diff eq and higher level math/engineering classes!!! Thank you for this!

[@ferus5583]

KZbin keeps recommending me great channels! Great video man!

[@K4IJU]

I haven’t even taken calc 3 yet, and this made it seem far simpler / easier to understand than I thought it was gonna be! Thanks dude!

[@IsshinTheGlockSaint]

How is this easy?

[@maxcrss2845]

@@IsshinTheGlockSaintSome people can just understand higher level math. :)

[@flantc]

It’s been 30 years since learned this stuff. If feels so good to fire up those neurons again. Thank you!!!!

[@bobphilishen]

Thank God I only had to take up to Calc 2. This genuinely blew my mind. Clear explanations, great editing, and fantastic illustrations. Kudos

[@0mniVerse777]

Believe it or not, calc 3 is way easier than calc 2 just saying...

[@nucle4rpenguins534]

They're different fields with different problems, I personally liked Calc 3 than Calc 2 at university. I think difficulty-wise, they're comparable

[@hadyhamed5139]

@@0mniVerse777 very true

[@cristianr.s.5537]

I remember reaching the Stokes and Divergence theorems at the very end of the course. We were pretty much doing everything we had learned up to that point while solving those problems, from matrices to triple integrals

[@timmydirtyrat6015]

Got a sub and a like for this high quality video, very excited to see future videos.

[@stevenohanesian3188]

Well done! Really. Everything of value that I took from Calc 3 as an engineer you summarized here. Well earned Subscriber and like!

[@nicholascunningham6936]

Sure, I didn't expect to learn all of Calc 3 from this video, but it's never a bad idea to get a general overview of the course you're taking. Now I can stop going through this course blind and actually have a rough idea of what topics to look forward to. Currently learning about double integrals right now

[@ainbrisk545]

thanks! I've only done calc 1 and 2 so getting an overview of 3 is super cool

[@Alfurwan]

so grateful for your wisdom, keep the advice coming!

[@sweartoyeezy3439]

The spherical vs cylindrical coordinate breakdown was so good thank you. Just finished this class and there's still so much I don't know...

[@wasted3secondsreadingmyuse30]

This is 3blue1brown quality. It’s very clear to understand and the visual intuition makes it icy easier to understand . I only have calc 1 knowledge but i still got the main idea behind it. Well done

[@rodomoyo9122]

bro had one video and made it an absolute banger

[@matthewjackson9615]

Wish this could have been explained to me when I first took calculus in college. Got thru the math classes anyway but it's nice to have someone explain these things to you in layman's language.

[@moomoo6045]

maths is truly beautiful, this video proved it to me even more - thank you for that!

[@RafaelRabinovich]

Thank you for sharing. Good conceptual intro to Calculus 3.

[@CoNfUzLeDaNdLoSt]

Interesting! I’m in Calc II right now and I’m actually not too worried if I have to do Calc III thanks to this video. A lot of the Vector and matrix math looks strikingly similar to linear algebra, which I’ve already taken.

[@angrycyclone4353]

How did it go for you?

[@lamashtu3449]

Holy shit , this just changed my life. Please make more!

[@burgersteig6536]

I haven’t even taken pre calc but I just sat down and watched this for no reason 10/10

[@146fallon9]

A great video as an introduction to calculus 3 course. Nice

[@HyrumCooper]

This was perfect, a great refresher for me as I head into more abstract concepts in Differential Geometry. My only suggestion: it would be nice if the video was rendered at a higher framerate and resolution. In my opinion, this is the last element of polish that the video needed. The actual content was spectacular though!

[@chuckmiggs6703]

This video makes me realize I how much cooler math is versus when my teachers taught it to me. More mathematics content please

[@jarnailbrar6732]

We need more people like this to be teaching. Feels like some teachings are purposely made over complicated to keep some people out of that field and keep old school profs in their jobs.

[@MrFTW733]

Bravo! Very well summarized.

[@VocalBeast]

I study math and econ in the university of London program and I was curious as to how my further calculus course in my second year matches up in terms of the calculus courses in the US. We have covered all of the content on calc 3 with the exception of the last topic you covered. Interesting stuff!

[@samfortunato7679]

Great video. Just last semester, I got an A on Calc 3 at Syracuse University! It's excellent and beautiful math

[@DisneyPlayhousetv]

Please do one on Calc 4. This was a beautiful video.

[@matthewstuckenbruck5834]

Dude, calc 4 is where they teach you the secrets of levitation and mind-reading. He can't just make that information public knowledge.

[@ictechpro9192]

@@matthewstuckenbruck5834 😂

[@haleyanderson2258]

@@matthewstuckenbruck5834 lol...

[@ad.i]

THIS VIDEO CAME OUT AT THE PERFECT TIME DUDE, HOW THE HELL DID YOU EXPLAIN IT SO WELL

[@LuisTheGreatMan]

Keep doing videos m8, this is your thing.

[@shreddaification]

This was really cool. Subscribed. Keep it up!

[@guilhermemotapereira5917]

LOVED IT! I'm so glad that YT recommended your video to me! Subbed and looking foward to eventually other videos of yours. Best regards from a CS Bachelor sudent here in Brazil 🇧🇷!

[@patooliverazapiola5022]

Awesome video dude! It's very clear explained

[@jamiegreenberg8476]

im literally watching this even tho i only took pre calc and u did a really good job im actually understanding some of this!

[@depress_the_clutch2118]

I was chewing my chips so hard that I was unable to hear anything this guy said.

[@Georgehanes-GJH105775]

This is one of the more useful videos I've watched.

[@SailboatAqua]

Loved the refresher, Thank you! Would love an 8 minute video on the integral of the curl theorem in calc 3 (stokes theorem?)

[@jomamma4729]

It's so clean that this was his first video, but it somehow still popped up in my recommended.

[@nomic655]

I'm in precalc/calc1 and all of this kinda makes sense. I can't even imagine the functions and methods used in calc3, but working on the 3D space with multivariable functions, integrals of volumes of any kind, other coordinate systems and vectors.

[@6lack5ushi]

great refresher!!!

[@dog-with-knife]

This video is so well done! The graphics are very professional looking and your voice is perfect for narrating. You deserve so many more subscribers!

[@shrimpjar2]

tysm this helped me so much with calculus 3 ❤

[@mike2884]

Great vid ! Hope to see more !

[@duyvo5315]

I'm from Vietnam and here the courses are different than those I see in the West. Here we study all these in Calc 2 and in Calc 3 we study Laplace and Fourier Transform with a little bit about complex numbers and z-transform. I still don't know why we have such courses. Anyway, your video is very well-explained, a very good brief overview.

[@Pedro-dt8ld]

Same in Portugal! Calc 2 ends with the divergence and Stokes Theorem, Calc 3 is mostly about differential equations, Laplace transform and complex analysis.

[@manuelmoertl2077]

Pretty much the same here in Munich, Germany

[@holeesheeetgonzalez]

In Chile we have calc 3 and then after u finished calc 3 u have Differential equations (calc 4) where we study fourier and laplace transform

[@fruchtmann4378]

We did differential forms on Riemannian manifolds, Fourier series theory and complex analysis. It's all random, I think we just cover more in school. Granted it's also a class for math and physics majors.

[@niccolobruno4272]

Because in the US they have smaller courses, so the program is divided into more classes. Each of my calculus (named analysis) in Italy is 10 ECTS, in US is more likely 6 or sometimes 8 ECTS

[@morvin.]

Thank you , I watched this video and mastered calculus now i have made 8 discoveries and have won nobel prize

[@austeyen5628]

so high quality!

[@sudokode]

Still waiting for Calculus 8 in 3 minutes

[@anastasiaskyba]

Very great explanation as well as video quality! Continue in the same spirit!

[@jackkennedy98]

Good video. I think showing the coordinates you've changed to, what they look like on a plane/space, would've been a great thing to include!

[@technoultimategaming2999]

There's no way this is your first video! 10/10

[@ranchsalad2580]

What a KZbin idea! Thank you!

[@worldshaper1723]

One of the best videos I have seen on KZbin. Congrats man, You inspire me to make ,,my one videos.

[@aemiliadelroba4022]

I love my calculus ❤ Easy to understand, just imagine !

[@tombucannon]

thanks for reminding me, I actually learned a lot

[@deidra-v6575]

Hey nice one man, gives a clear image of the solution.

[@MattBriggsTV]

amazing video. great job!

[@mrdoognoog]

Really helpful, wish i has this last semester!

[@darcash1738]

Thanks so much! I think I was able to connect the dots from calc ab, and now I’d say I’m just about ready to move on to calc 4 😏

[@birb9804]

haven’t finished algebra 1 so this is all very advanced, but I look forward to understanding anything in this video

[@bowlosoggycereal8135]

perfect video to watch right after my calc 1 exam

[@Rishith198]

This video was really cool! Thanks!

[@torridice]

This was cool. Thanks for the vid

[@lazrab1]

good refresher before the semester starts up

[@sitrakaforler8696]

Great vidéo man, bravo !

[@m1kumeeks]

you are so real for this thank you king

[@gustavsjokvist2668]

Really great stuff man

[@TheGeckoIsKing]

Calc 3 was a lot of fun to take and I’d like to take it again! I would love to see you make a video about diff eq and linear algebra because those are my favorites!

[@eccentricbass3730]

I still can’t get over dot product. It’s so sick. Just beautiful math.

[@roylim1169]

You have truly made me interested in calc 3 while destroying my mind that's still comprehending calc 2

[@maxmeza4471]

Damn bro this is great, huge huge future, keep it up

[@charlescady1669]

Fantastic, the video skipped over some power series stuff but got nearly everything else.