The Divergence Theorem

[@stephend.4342]

I finished watching all 165 of your math videos and would like to thank you for preparing them.

[@ProfessorDaveExplains]

Thanks for your support!

[@user-ql5cc5eq4e]

How much time it takes you to complete this playlist

[@stephend.4342]

@@user-ql5cc5eq4e It took me several months, taking notes from each video.

[@johndodge4210]

Bro became learned

[@lurdeshorta2744]

@@user-ql5cc5eq4e this playlist for me took me a day. But i already learned this stuff in class, just trying to understand it better

[@NobleDorito8698]

This whole course fixed up my broken basic mathematics which i ridiculously forgot and sucked at which also haunted me now. But this whole course has changed my life. Thanks Proffesor Dave

[@Stormroot125]

exam is today what a blessing you are sir

[@navyakukreja2886]

@Professor Dave I say this with complete honesty, that your channel is beautiful. The amount of work you've put into it in unparalleled to any amount of work or passion I've seen in any person, not to mention how it pains me to see that your channel is severely underrated and deserves a lot more respect. (You literally have a playlist with all of mathematics in it and it blew my mind!) I can't describe how happy your videos make me feel when I finally understand something, which I couldn't before despite attending all lectures so thank you, for all you've done for your viewers and most importantly, for Math and Science, hats off to you, sir.

[@franke881]

Am I the only one who feels like these concepts are completely arbitrary? Sure divergence is stuff spreading out, but how does it even work? I guess I just need to have faith in the due diligence of the mathematicians and physicists who came up with these formulas.

[@CharlieCGofficial]

I like how this series went from something that would look like a kids channel to the most complicated math in the existence of anything edit: omg mom I’m famous

[@paridhaxholli]

he probably solved the reimann hypothesis somewhere in the middle of it

[@lawsonashurst7314]

This is something you would learn in Calculus 3/4 (depending on what your institution calls Multivariable Calculus). It is complex- but it is FAR from the most complicated math in existence. This is something the average student the sophomore year of a Math/Physics/Engineering Major at an average institution. Continue to learn Math, it is awesome!

[@shaheenbean]

Hello professor! These videos have been an absolute blessing for students trying to self-teach math like myself: words cannot describe how much these have helped me over the years. On that note, I was just curious if you were planning on returning to this series anytime soon? I would love to see more math content like this and I'm sure I'm not alone. In any case, thanks again for your hard work!

[@jonathanhuwe4791]

Thanks!

[@kchrome5796]

Finally, I finished the complete mathematics playlist over the course of around 3 weeks. Thank you Professor Dave! you are an absolute inspiration!

[@AZUMAI]

Hello Im hoping to complete this playlist as well what video do you think covers up until grade level 10.

[@Stoirelius]

3 weeks? Damn, man.

[@propoop6991]

i dont think this is supposed to be an entire course

[@paulwilliams4371]

@@AZUMAI this playlist covers up to calc i believe so about grade 12 it doesn't cover everything in depth though so its worth your time going back over a lot of this stuff separately if you are trying to finish 2 years of high school math. I should also mention that it depends on what math you take in 10th, the standard is algebra 2 however it is not uncommon to take trig or even pre calc if your advanced.

[@miliman5282]

@@paulwilliams4371 To be fair this playlist covers the vast majority of University mathematics at an undergraduate level not just high school.

[@nanovatixstudio]

Amazing! Every math lesson I took between age 5 and age 19 is now in a single video list! You must have a great talent in teaching.

[@SEGAClownboss]

It's been forever since I've practiced any math and the last time we ever had it was in high school. We didn't learn calculus. In university I had an attempted introduction at linear algebra and I didn't understand a word from my professor. I bailed math and decided not to return until I felt ready. Now it's 13 years later and I found this series. In over about 2 months, I have watched all 165 videos, done every single end-of-video test, and if one solution was incorrect, I would redo it again while carefully watching instructions or reading about the required methods in the comments. I finished this last one and now I can finally say I've gotten such a greater grasp and appreciation of math than I ever could have imagined. If this series should continue and encompass more of university-level math, I would be very thrilled for it. Thank you David, your knowledge changed my life.

[@SAMSULEKMOTIVATION12]

How did you find the journey of relearning maths after some time?

[@SEGAClownboss]

@@SAMSULEKMOTIVATION12 I'm a believer in math now, put simply. It's an endlessly fascinating science I will probably get back around for the rest of my life. I also know that for the most part I now have the main practical math I would ever need in any job. But especially I wanna spread the word about this channel cos it's doing essentially what I always wanted to see: A free-to-access internet university.

[@georgiareback5905]

I have a multivariable calculus exam on Tuesday, these videoes have been lifesavers! thank you so much :)

[@victornnaji7271]

Haha clutch timing we literally just covered this in class today

[@nileshkulkarni6196]

We want videos on topics such as probability , combinatorics, topology, abstract algebra, logic, tensors , tensor calculus , group theory , algebraic topology , complex analysis , linear algebra ,differential geometry, optimization , etc. Please expand this series . We love your videos very much .

[@gokudegrees]

dude asking for a whole degree

[@JOHN-rt1gd]

this 165 lesson is last one

[@vintagegamer7027]

He's not a math man he a science boy

[@lisejl]

@@gokudegrees Fr pick one or two like damn

[@NASAFanboy]

Why don’t we just add circuit analysis, embedded systems, data structures, algorithms, numerical analysis, pde’s, quantum physics, organic chemistry, physical chemistry, etc? Lol

[@TheDreRock]

Always wanted to start over and try to learn “all” math from the beginning. Going to come back here once I finish learning all math and see how much more I understand. I have adhd and no incentive other than on-and-off curiosity, so let’s see how many years/decades this takes

[@ЭддардСтарк-к7е]

There's not a lot of material, where are you staying?

[@RC32Smiths01]

I'm only 18, but ideas of math and science like this are always up my alley. Your ways of teaching have really helped me. Cheers

[@i.am.sir_014]

You're now 22 I guess and I'm 18😅

[@kernelkorp4348]

I can't believe my professor wasted 1 week on this 6 min topic. Thanks

[@mouizeddinekisma4226]

Thanks prof, very simple and straight to the point

[@user-lb8qx8yl8k]

You are so well rounded. It wasn't long ago since I watched your entire playlist on evolution!!

[@subscribetopewdiepie8746]

Please do a video on statics. Keep up the good work.

[@alexdorosin8280]

you know he talks business when the automatically generated subtitle is so accurate. good job, sir

[@ProfessorDaveExplains]

that's not auto, i input my scripts!

[@alexdorosin8280]

@@ProfessorDaveExplains give that man 1 mil $ pls

[@brucedienst7553]

Professor Dave Explains is this the last video in the advanced math series? Thank you so much professor dave!!!

[@emanomairey8322]

Hi, very clear and nice explaination. Can you please show how would the comprehensive example look like if plotted?

[@gp873]

Such a good and easy to understand explanation

[@jaxx6712]

amazing content, your from-the-basics approach as well as your presentation style and passion make for an incredible experience for your audience and I would not be surprised if your videos alone have been the difference between 1000s of people graduating into their dream job rather than dropping out when they got a dodgy professor on there second year.

[@matthijsgeerlings]

Great explanation 👌

[@MrCEO-jw1vm]

Hats off, sir! I can now finish my term strong with the knowledge in this vector calc playlist. I'm very grateful 🙏

[@d1psh1tc1ty]

That example problem was perfect for illustrating the utility of the theorem.

[@bimini8425]

1 year ago i was crying hard for failing my first precalculus exam. i told myself i will go back to the basics and this series helped me along the way. four calculus courses later, i received my final grade in my last calculus course. i passed! professor dave, i wouldn’t have understood and found the beauty in mathematics if i hadn’t stumbled upon this channel. i was once a student who was very scared of numbers and now i genuinely enjoy math, it all started with you! so, thank you and you are the GOAT

[@fromaggio7654]

I'm studying chemistry but I just like hearing your explanations

[@emlmm88]

Fromaggio Any chemist worth his salt should know how to use the divergence theorem.

[@fromaggio7654]

emlmm88 What I meant was I am reading Organic Chemistry, this stuff will be relevant a bit forward into my course

[@emlmm88]

@@fromaggio7654 Actually in ochem likely not - the second half of the o-chem sequence is all about memorizing reaction pathways (and you don't even do any more spectroscopy stuff). In pchem, and particularly, in fluid mechanics, the divergence theorem will come back up. Similarly if you decide to take quantum electrodynamics or quantum field theory, this theorem becomes really indispensable.

[@jayw8726]

I just am still going through your basics of Maths. But was curious to look at the end. I guess one day I understand these. But seriously is this the last video of your Math series? 😊

[@ProfessorDaveExplains]

there will be more at some point!

[@thearyan0000]

@@ProfessorDaveExplains sir plz add more latest videos

[@kowshikkandukuri7527]

Bro did you completed the series, if yes how was your experience I'm also in the basics right now but i wanted to the end.

[@toothpaste_tm7323]

Started this series by counting apples and now we are here, i never thought id bingewatch a series on math haha

[@bilalkerem145]

how can we apply the divergence theorem of Gauss for an open surface?

[@theuser810]

These videos manage to put a topic which my lecturers take 1h into 5-10 minutes!

[@Kiky_MedPhysicist]

Thank you sir for your dedication and for making this free! 🙏

[@03J45]

The day you need us. We'll be there to follow your career 🤞🏻💯. You're up there with the greats. You proved(1) the possibility that knowledge is free, just like kindness, just like good. May the exams challenge if we truly paid attention and be rewarded for the hard proven work. But you gave us a chance (0.01). Thank you.

[@rajashruthim5451]

Our life line for mathematics examination 🤩💯👍

[@sciencewithali4916]

What software do you use in order to have this math stuff excellent video as always

[@ProfessorDaveExplains]

adobe after effects!

[@berserk.958]

Finally completed all maths videos 😁

[@ShandyTheMan]

Pretty fitting that Maths ends with a thorem that gives us wave packets in quantum mechanics, pretty much the point where our knowledge of the nature of Physics stops. Please make an episode 166 so humanity can finally move forward again in our understanding.

[@ShandyTheMan]

Or do you merely make KZbin videos rather than the laws of nature themselves? 🤔

[@joanneal-adham2068]

Does anyone know of a book which has the integral and differential form equivalency proof for Gauss' electrostatics law? much appreciated :)

[@senarmstrongfanaccount]

will you continue this series or is it done? excellent work btw on all this

[@crastycy7207]

Thank you sir, well explained and straight to the point! Btw the intro is hilarious

[@nyangmaluil1087]

Good explanation. May you show all steps of solving this comprehension

[@BANNEDmoney]

I finished watching all: I NOW MATH!!!!! ty Dave

[@billk8579]

In the step when integrating wrt dy you have a factor of (1-x) should this be (y-xy)(y^2+xy/2+y/2)

[@londisibanda1421]

no

[@antihero69420]

One day I am going to understand this video, I'm starting from Day-1 today as an absolute noob in maths🙌💕

[@Thatguy1309]

I swear god sent this man right here

[@krishshah3721]

Hi, Could someone explain when to use stokes' theorem and when to use the divergence theorem?

[@aryyancarman705]

line intwgral vs surface integral

[@thekwjiboo]

Since this is the last one on your advanced mathematics Playlist I figured it was the appropriate place to ask have you considered doing a video on the Riemann hypothesis? Or is that a little too far off the chart for what you're looking to teach?

[@ProfessorDaveExplains]

There will be more! I just have to find the right writer. Could include that topic.

[@aashsyed1277]

@@ProfessorDaveExplains i want differential equations , integration by partial fractions and max and mins of a multivariable function and more!

[@TheKids422]

@@aashsyed1277 same i want differential equations

[@spearmintlatios9047]

You realize you’re grown up when your classes are covering the last topic in a playlist called “math: all of it”…. And you still have 8 more math classes to take

[@tactissue32]

GPA-saving content right here

[@ahmedkamal3977]

Bro what has this man not studied.

[@nowdays996]

Not Professor Dave Its professor Awesome

[@svijayiitk]

Best teacher on YT! P.S. First comment

[@MohabTrading]

can you please complete i reached to this video and i am waiting for more i finished the series and i need to complete before i lose my pace all love and thanking to your efforts all the videos are amazing

[@kimdivinaa]

very interesting thank you for this video

[@Aaron_1112]

Soo this is the boss fight huh... Seems ez

[@Alex-pt6pu]

this is the 1%.

[@user-lb8qx8yl8k]

Is the author of your main source James Stewart?? I'm only asking because I know that he uses the angle bracket notion for vectors, .

[@om3rbenbrahim488]

Is the playlist finished ?

[@ProfessorDaveExplains]

No I will do more, I just have to find the right person to write the scripts, I can't go any further myself.

[@om3rbenbrahim488]

@@ProfessorDaveExplains Thank you for all your work !

[@samjum]

Solution: \int_0^2 \int_-2^2 \int_0^x2 (3x) dzdydx = \int_0^2 \int_-2^2 (3x3) dydx = \int_0^2 (12x3) dx = 48

[@tylerkutschbach]

What day this month will you do William Howard Taft

[@davonbenson179]

Do you have a video on Boolean Algebra?

[@yagmurterzioglu1916]

thank you!

[@arbazkhanpathan9259]

Thank you sir!!

[@drioko]

wow i can’t believe i actually got that correct. it seemed so complicated in class

[@jaymodi5378]

what exactly is a surface integral (i watched the earlier video already and i dont understand). Is it used to calculate the surface area of the surface or volume inside the given surface?

[@GOURABCHAKRABORTY10287]

it calculates the 'volume'.....check out khan academy line integral video

[@carultch]

Imagine you are painting a surface, and you are using a different density of paint at each point along the surface. Some places you paint with a lot of paint in one spot, other places you paint very sparsely. A surface integral of the density of the paint, would calculate the total mass of paint you use for covering a given portion of the surface. It could also be a vector function, in which case you are calculating the vector dot-product the perpendicular area vector differential of the surface. Common in Gauss's law.

[@trulysal2476]

Thank you professor.

[@ericmojica6135]

As someone who wants to start watching this series, does anyone who watched the whole thing and practiced it found it to be an effective teacher?

[@Clipsandedits1224]

Yup, it's really good, but after a video, I did some practice questions on other things just to make sure I understood.

[@SEGAClownboss]

Absolutely, I had discovered many first-time concepts here, and yet I was able to understand them perfectly at a slightly older age(I'm in my early 30s). Make sure you do have a paper notebook and pencil around since you absolutely will want to write down and solve the quiz questions - and to write down formulas since you're gonna rely on them a lot. Once you reach trigonometry, you might wanna have a calculator beside you.

[@kowshikkandukuri7527]

​@@SEGAClownbossbro did you completed the whole thing I really want to know how did felt after completing the series

[@SEGAClownboss]

@@kowshikkandukuri7527 Yes I did. In short, it felt like really going to college. The gain of knowledge feels great but your brain really will wrestle with all this new math trying to make sense out of it all and even paper and pencil barely help. But credit where it's due Dave is a REAL pro at this. He truly does explain everything so well, but you just have to be alert and not wander your attention off in a moment. Definitely get a notebook and write down formulas you see. The current playlist as it stands only takes you as far as 2nd year of applied math university. Dave said he wants to return to the series someday. Imagine the pain then.

[@culture21133]

great explanation

[@UCh-cv7ls]

is there a worked out solution of the comprehension?

[@fazleyrabbypatwary7136]

Thanks,professor Dave.

[@BrunoPeitl84]

What you have already done is invaluable and, I believe, has taken a huge amount of effort. Whether you are an atheist or not, I'm sure you already have your place in heaven guaranteed. Still, I have to ask: will this series of tutorials continue?

[@ProfessorDaveExplains]

I hope soon! Gotta find a writer.

[@mohamedrohtur2627]

@@ProfessorDaveExplains After this playlist, do I have enough mathematical knowledge to start Walter Lewin's classical physics?

[@Stuytz]

@@mohamedrohtur2627 he’s a maths guy

[@Stuytz]

Wait sorry HE KNOWS A LOT OF STUFF! (Really he does)

[@levidazai8738]

Which grade math is this video about?

[@aker8133]

2nd or 3rd year undergrad of engineering like electrical and mechanical on calc III or applied maths III

[@galqpinky]

I tried to solve the comprehension problem in the end and I got 3 as a result instead of 48, I think the difference is that in the end I got 12(x^4)/4, x=[0;1] . How is it 48?

[@blackkiller753]

x supposed to be from 0 to 2

[@Oscar-jg9gg]

@@blackkiller753 thanks!!! i got 12x^4 and was like "tf?"

[@Oscar-jg9gg]

replace x^2 with 2 and you get 48

[@eggxecution]

so it's different from green and stokes then because they have arrows and this one doesn't

[@eggxecution]

@@Oscar-jg9gg replace it with 4 you mean. Lower limit is 0 and upper is 4 to get 48

[@KishoreG2396]

I have a test on this today! Thanks!

[@Engineer-t9z]

Dave you can do Engineering if you wanted to

[@omarberraqui8193]

Really good simpel example just perfect.thnk u

[@jaydoubleli]

what happened to the "more advanced topics"?

[@aisyahazalia1282]

Is the answer 48?

[@govamurali2309]

Please do z transform, analytic functions.

[@eggxecution]

so compared to stokes and greens this one doesn't have direction so no need to place functions at lower and upper limit I guess just rely on points

[@khanmaluitjiek669]

Hello dear professor, can you do the example that you write only the answer

[@MiltonRosso]

I need more math!

[@ani_mee07]

We did this time . ( 2x+x) is the equation and simply integrate it w.r.t. dx dy dz and put the limits

[@akhileshtiwari7099]

Thanks lot sir

[@JOHN-rt1gd]

I don't know math is this course help me I'm absolutly begginer in math

[@NoOne-il4hw]

Someone pls explain. If I calculate the surface are of the 5 surfaces it is more than 5/3

[@natnaelberhanu-i8w]

When converting to triple integrals, why does our lower bound start at 0?

[@tennmatthews1160]

starts @ 0 because there region is bounded in the first quadrant

[@ronch550]

You lost me at 0:14

[@ProfessorDaveExplains]

you'd better go back to earlier in the math playlist! all the background information is there for you, no matter how far back you need to go.

[@ronch550]

@@ProfessorDaveExplains well sorry Prof, it's been decades since I opened my math books. 😔 But yeah, thanks for the encouragement!! 😊

[@ImJustKnownAsAnonymous]

hi professor, any good websites you recommend to practice math?

[@NASAFanboy]

Paul’s online math notes and khan academy

[@LateNightRituals]

that was greatness

[@amazinggracechannel7749]

It will be good if you have did that example Please I need to do that example

[@arik9842]

dave, you fucking gem

[@darkswamp6830]

Can you please teach us Fourier Series, Fourier Transformation and Laplace Transform please. Thanks. Oh and also please teach us Lagrangian Mechanics. Thank you very much Professor Dave 🙂

[@hellohumans9181]

Professor Dave can u please explain time dilation and general relativity

[@ProfessorDaveExplains]

check my modern physics playlist for all that stuff!

[@نورالاسلام-س2ن]

Very good.

[@anithamohan8749]

Nice

[@laioszafeiriou4388]

So... Where're the algebraic topology lectures?

[@newjade6075]

Prof u d best!!👍

[@pretty.946]

I don’t understand why integrals of dz first then dy then dx!

[@tanyapunyo2074]

so now first I have to learn Green's theorem first, and for that I have to learn integration first, for which I have to learn linear algebra and so on...