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.
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.
That 3b1b video encouraging others to make their own similar videos injected hundreds of high-quality math content onto UA-cam 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.
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.
@@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
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 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 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.
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.
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 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 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
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!
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. :)
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!
@@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.
@@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.
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 !!
@@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!
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!
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.
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.
Same in Portugal! Calc 2 ends with the divergence and Stokes Theorem, Calc 3 is mostly about differential equations, Laplace transform and complex analysis.
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.
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
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.
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.
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.
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
Thank you. It really helps knowing the big picture. I got an A in Calc 3. Big deal. Without the actual big picture the little A's don't have meaning. In other words, you have given meaning to my paltry existence. Seriously, thank you.
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!
🎯 Key Takeaways for quick navigation: 00:14 🧭 *Functions in 3D space have two inputs (X and Y axes) and produce an output on the Z-axis; vectors in 3D have direction and magnitude.* 01:01 🧲 *Dot product of vectors involves multiplying corresponding components and has geometric significance; cross product results in a vector orthogonal to the multiplied vectors.* 02:28 📐 *Limits and derivatives of multivariable functions are defined similarly to 2D; directional derivatives represent rates of change in specific directions, and gradients generalize derivatives.* 03:13 📊 *Double integrals find volume under a 3D function; polar coordinates can be used in double integrals, changing from rectangular to polar coordinates in integration.* 03:55 📐 *Triple integrals extend to 3D regions; cylindrical and spherical coordinates are alternatives in triple integrals, each with radius and angles.* 05:12 🔄 *Coordinate transformations involve the Jacobian when switching coordinate systems, adding a function to account for distortion.* 06:32 🔄 *Vector fields assign vectors to points; scalar line integrals are done over scalar fields, and vector line integrals involve work done on particles in a vector field.* 07:13 📡 *Vector fields have divergence (outflow from a point) and curl (rotation around a point); conservative vector fields have path-independent line integrals.* Made with HARPA AI
My good Sir, I would be blessed if you could make similar explanatory videos of the above topics of calculus in detail, like you would cover in a college curriculum. I'm an undergrad computer engineering student and I would like to understand and *visualise* calculus like the way you did in this video. My professors have not done justice teaching such an incredible topic in the most bland way possible. Thank you in advance.
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 🇧🇷!
Im studying for my finals on calc 3 and its actually quite possible to fit the entire syllabus into a 1 hour ish video. Even this 8 minute one loosely covers most of it excluding formulas and proofs
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
As a HS senior having difficulty in my Calc 3 class, this turned everything into a more “human” way of understanding things. Amazing visuals as well :)
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.
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
The curl is very interesting! Imaging trying to find the effect of 2 liquid curl systems interacting at specific points while each system have different flow rates in 3 different coordinates.
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!
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.
Welp, You got me as a sub :D Fascinating stuff. Never thought I was keen enough to follow Calculus but now, many years after HS I'm fascinated by it all. Going back to school this year :D
Do a lot of algebra refresher work first. If you struggle with polynomials (factoring, finding roots, imaginary numbers) you will have a very rough time
I'm in precalculus trigonometry right now. I'm liking it and trying to decide if I want to pursue a degree that involves more advanced maths. This video shows me what the road ahead looks like, and it doesn't seem too scary! Thanks for making this!
If you’re in precalc trig right now, I assume you’re a junior in high school, which means you have a couple years to decide yet. Finish high school, take more advanced maths, and take stem related classes as an undergraduate in college. Then, it will be you who knows best what’s right for you.
@@MrTit-ey8cx nah, I'm 25 and got sick of working in fast food, so I'm in community college trying to finish up my AA and deciding where I want to go next. I declared a neuroscience major but I'm not sure yet what I would want to do with it. I'm thinking maybe I should switch my major to something more broad like engineering or computer science to avoid pigeon-holing myself into one industry. Any ideas?
@@maiamaiapapaya The first year or two of engineering and even comp sci are all very similar. If you change your mind, yes you'll have to retake some different courses, but you'll also have a lot of courses that are all the same, like calc, phys, intro to coding, etc. I'm personally in mechanical engineering because it is very broad (its basically engineering engineering) and you can do almost anything with it
![Lp. Сердце Вселенной #60 РОЖДЕНИЕ ЛОЛОЛОШКИ [Финал] • Майнкрафт](http://i.ytimg.com/vi/YoR0pAV9FVQ/mqdefault.jpg)
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.
This is correct. Thank you for catching the error
@@calendarG Will you upload another video
I was about to say the same thing. Great catch!
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.
That 3b1b video encouraging others to make their own similar videos injected hundreds of high-quality math content onto UA-cam 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.
I agree you5ube had a.few bad months recommending me shit I didn't want to see aswell
cant wait to use this to
I love it when UA-camrs can explain most of a semester of school in a single video. It shows how much you really get it
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.
Prof. could drag this out to take one semester. This flows together very well, instead of being fed bits and pieces.
@Max True but it is a really nice and concise refresher over some of the topics
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.
I'm finishing up this math course now, and it's a fun review to see what I've learned presented in a neat way.
I've taken Calc 3, and this was a GREAT concise summary and actually kind of clarified some things for me. Excellent job.
Can I ask where are all you guys from?
Except point 7 I am pretty sure all the rest is Calc 2 material
@@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
@@thelogicalvoice-shorts1674 at least I am not the only one questioning the differences in the prograns
@@feniceazzurra7168 you do triple integrals in cal 2? what uni do you go to?
@@Loots1 University of Torino, Physics faculty
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)
Can you name any other examples?
@@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.)
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
@@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.
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.
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?
And what help did you exactly got from this
@@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
@@yigiteldekwell you still gotta learn optimization + surface integration and like stokes thm, divergence thm etc. good luck man you got this
@@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
woah 50 subs to 2k subs in just 10 days?
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!
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. :)
As an engineering student, this is by far more comprehensive than my illiterate thousand-page notebook. Congrats on your first video!
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!
Still waiting for Calculus 8 in 3 minutes
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
haha thats because calc 3 is out of reach for 99% of youtube users' brain capacity
@@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.
@@ederamin9697 or 99% just don't need to know it.
This is prob because calc 1 and 2 can be taken in high school with ap calculus bc
@@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.
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 !!
Algebra: When in doubt, set it equal to zero
Trignometry: When in doubt, soh cah toa
Calculus: When in doubt, take the derivative
lol so true
linear algebra: when in doubt, cry
@@siwonchang3818 Nah, more like when in doubt, create a determinant
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!
now we need all of calculus 8 in 3 minutes, calculus 8 would be fractional calculus on operator algebras lol
y e s
Lambda Calculus in PI minutes.
@@skilz8098 LOL
I love how you managed to explain the purpose of dot products better in a few seconds than my professor could
FLY HIGH 🕊This video inspired many to pursue higher level calculus, so sad you died so young.
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
oh that's actually interesting. I did use LaTeX to display the integrals but not that. Thanks for the suggestion!
@@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
@@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!
LaTeX gang rise up
You can use word if you want which makes it a bit easier imo
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!
Thank you , I watched this video and mastered calculus now i have made 8 discoveries and have won nobel prize
Please do one on Calc 4. This was a beautiful video.
Dude, calc 4 is where they teach you the secrets of levitation and mind-reading. He can't just make that information public knowledge.
@@matthewstuckenbruck5834 😂
@@matthewstuckenbruck5834 lol...
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.
Just wait man just wait
Thank God I only had to take up to Calc 2. This genuinely blew my mind. Clear explanations, great editing, and fantastic illustrations. Kudos
Believe it or not, calc 3 is way easier than calc 2 just saying...
They're different fields with different problems, I personally liked Calc 3 than Calc 2 at university.
I think difficulty-wise, they're comparable
@@0mniVerse777 very true
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.
Same in Portugal! Calc 2 ends with the divergence and Stokes Theorem, Calc 3 is mostly about differential equations, Laplace transform and complex analysis.
Pretty much the same here in Munich, Germany
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
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.
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
Forwarding this to my students this semester for sure!
alright I finished the video, now where's my diploma
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!
How is this easy?
@@IsshinTheGlockSaintSome people can just understand higher level math. :)
This video makes me realize I how much cooler math is versus when my teachers taught it to me. More mathematics content please
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.
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...
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.
How did it go for you?
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.
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
bro had one video and made it an absolute banger
This video, like all calculus videos, is an excellent source for ASMR ambience. Thank you!
A wonderful video! I found it incredibly helpful and useful. So well deduced, explained, and explored. Job well done!
Thank you. It really helps knowing the big picture. I got an A in Calc 3. Big deal. Without the actual big picture the little A's don't have meaning. In other words, you have given meaning to my paltry existence. Seriously, thank you.
one of the best recaps ive ever seen
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!
I haven’t even taken pre calc but I just sat down and watched this for no reason 10/10
how old are u vtw
@@gamingzeraora443im 1 year old 😃
This is so helpful for a quick recap when taking diff eq and higher level math/engineering classes!!! Thank you for this!
It’s been 30 years since learned this stuff. If feels so good to fire up those neurons again. Thank you!!!!
This is phenomenal.
There's no way this is your first video! 10/10
Dude drops this and ghosts, must have watched “theory of everything in 8 minutes” and slipped out of the continuum
Got a sub and a like for this high quality video, very excited to see future videos.
🎯 Key Takeaways for quick navigation:
00:14 🧭 *Functions in 3D space have two inputs (X and Y axes) and produce an output on the Z-axis; vectors in 3D have direction and magnitude.*
01:01 🧲 *Dot product of vectors involves multiplying corresponding components and has geometric significance; cross product results in a vector orthogonal to the multiplied vectors.*
02:28 📐 *Limits and derivatives of multivariable functions are defined similarly to 2D; directional derivatives represent rates of change in specific directions, and gradients generalize derivatives.*
03:13 📊 *Double integrals find volume under a 3D function; polar coordinates can be used in double integrals, changing from rectangular to polar coordinates in integration.*
03:55 📐 *Triple integrals extend to 3D regions; cylindrical and spherical coordinates are alternatives in triple integrals, each with radius and angles.*
05:12 🔄 *Coordinate transformations involve the Jacobian when switching coordinate systems, adding a function to account for distortion.*
06:32 🔄 *Vector fields assign vectors to points; scalar line integrals are done over scalar fields, and vector line integrals involve work done on particles in a vector field.*
07:13 📡 *Vector fields have divergence (outflow from a point) and curl (rotation around a point); conservative vector fields have path-independent line integrals.*
Made with HARPA AI
Great video! You covered the major concepts very well.
I was chewing my chips so hard that I was unable to hear anything this guy said.
My good Sir, I would be blessed if you could make similar explanatory videos of the above topics of calculus in detail, like you would cover in a college curriculum. I'm an undergrad computer engineering student and I would like to understand and *visualise* calculus like the way you did in this video. My professors have not done justice teaching such an incredible topic in the most bland way possible. Thank you in advance.
3blue1Brown does this also, in a similar way
@@yaboi269 Yes but his videos are mostly focused on the more obscure/interesting topics in mathematics, not comprehensive enough for college.
It's so clean that this was his first video, but it somehow still popped up in my recommended.
1 min 32 sec you just taught me something my proffessor with a heavy accent could not. WOW.
this is helping me prepare for calc 3 pretty soon thanks
Well done! Really. Everything of value that I took from Calc 3 as an engineer you summarized here. Well earned Subscriber and like!
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 🇧🇷!
You have truly made me interested in calc 3 while destroying my mind that's still comprehending calc 2
PLEASE WE NEED MORE VIDEOS!!! I love this!
I do not know much about Mathematics…
But this video is ABSOLUTELY EXCELLENT!!!!!
Thank You. 👍🏾 :::
perfect video to watch right after my calc 1 exam
maths is truly beautiful, this video proved it to me even more - thank you for that!
This was actually calming to watch as I study since I can see I grasp all the basic concepts, thanks
I still can’t get over dot product. It’s so sick. Just beautiful math.
Hey nice one man, gives a clear image of the solution.
Very great explanation as well as video quality! Continue in the same spirit!
Im studying for my finals on calc 3 and its actually quite possible to fit the entire syllabus into a 1 hour ish video. Even this 8 minute one loosely covers most of it excluding formulas and proofs
This is one of the more useful videos I've watched.
THIS VIDEO CAME OUT AT THE PERFECT TIME DUDE, HOW THE HELL DID YOU EXPLAIN IT SO WELL
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
Damn bro this is great, huge huge future, keep it up
Great video. Just last semester, I got an A on Calc 3 at Syracuse University! It's excellent and beautiful math
As a HS senior having difficulty in my Calc 3 class, this turned everything into a more “human” way of understanding things. Amazing visuals as well :)
im sorry... hs... CALC 3?!?!?!?!?
@@chancellorpalpatine ikr...
I'm also taking calc 3 in high school with diff eq simultaneously. Both are very fun classes!
Are you guys in the US taking that?
@@ianzhou3998damn thats a lot. I took diffy junior year and am taking multi as a senior. Both at the same time is crazy
A great video as an introduction to calculus 3 course. Nice
god why did yt recommend me when i'm literally getting panic attacks on my every calc3 lecture this semester
great video tho
good refresher before the semester starts up
Keep doing videos m8, this is your thing.
thanks! I've only done calc 1 and 2 so getting an overview of 3 is super cool
Saving this. I'm a undergraduate student majoring in Comp Sci and I just know Calc 1 and 2 are going to beat my ask.
lol, I'm studying on Unicamp here in Brazil and this content is acctually taught to us in calculus 2
im literally watching this even tho i only took pre calc and u did a really good job im actually understanding some of this!
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.
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
The curl is very interesting!
Imaging trying to find the effect of 2 liquid curl systems interacting at specific points while each system have different flow rates in 3 different coordinates.
I did similar exercises in my fluid mechanics class, and they are a bit of a doozy. A lot of math
One of the best videos I have seen on UA-cam. Congrats man, You inspire me to make ,,my one videos.
This was really cool. Subscribed. Keep it up!
so grateful for your wisdom, keep the advice coming!
I will come back to this, when I made my journey to this point in math.
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!
Fantastic, the video skipped over some power series stuff but got nearly everything else.
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.
thanks for reminding me, I actually learned a lot
I feel like I'm almost an expert now in calculus. Thank you.
Awesome video dude! It's very clear explained
this really was helpful for my Pre-Cal class
tysm this helped me so much with calculus 3 ❤
As a HS student in calc 2, this makes me very excited for calc 3 :D
I just learned that a curly is the most curly in the middle 🫡👍🏼 thank yu sir!
Welp, You got me as a sub :D Fascinating stuff. Never thought I was keen enough to follow Calculus but now, many years after HS I'm fascinated by it all. Going back to school this year :D
Do a lot of algebra refresher work first. If you struggle with polynomials (factoring, finding roots, imaginary numbers) you will have a very rough time
@@PelosiStockPortfolio Thanks for the supportive advice.
Perhaps I went very deep into one math analysis, I need a new one!
I'm in precalculus trigonometry right now. I'm liking it and trying to decide if I want to pursue a degree that involves more advanced maths. This video shows me what the road ahead looks like, and it doesn't seem too scary! Thanks for making this!
If you’re in precalc trig right now, I assume you’re a junior in high school, which means you have a couple years to decide yet. Finish high school, take more advanced maths, and take stem related classes as an undergraduate in college. Then, it will be you who knows best what’s right for you.
@@MrTit-ey8cx nah, I'm 25 and got sick of working in fast food, so I'm in community college trying to finish up my AA and deciding where I want to go next. I declared a neuroscience major but I'm not sure yet what I would want to do with it. I'm thinking maybe I should switch my major to something more broad like engineering or computer science to avoid pigeon-holing myself into one industry. Any ideas?
@@maiamaiapapaya The first year or two of engineering and even comp sci are all very similar. If you change your mind, yes you'll have to retake some different courses, but you'll also have a lot of courses that are all the same, like calc, phys, intro to coding, etc. I'm personally in mechanical engineering because it is very broad (its basically engineering engineering) and you can do almost anything with it
Mlk, eu nunca assisti nada de matemática no UA-cam, e me vem um vídeo de cálculo 3, obrigado UA-cam
Eh bem interessante pra falar real
Fun video about what is in store and how my current studies will be used in the future, signed, a burnt out Calc 2 student.