The Divergence Theorem

Green's Theorem gave us a way to calculate a line integral around a closed curve. Similarly, we have a way to calculate a surface integral for a closed surface. That's the Divergence Theorem. This is also known as Gauss's Theorem, and it's pretty neat, so let's learn it!
Script by Howard Whittle
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I finished watching all 165 of your math videos and would like to thank you for preparing them.

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Thanks for your support!

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How much time it takes you to complete this playlist

[@stephend.4342]

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

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Bro became learned

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

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

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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

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exam is today what a blessing you are sir

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[@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!

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

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

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3 weeks? Damn, man.

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i dont think this is supposed to be an entire course

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@@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.

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

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

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Haha clutch timing we literally just covered this in class today

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Thanks prof, very simple and straight to the point

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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.

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

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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.

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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 .

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dude asking for a whole degree

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this 165 lesson is last one

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He's not a math man he a science boy

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@@gokudegrees Fr pick one or two like damn

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[@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

[@subscribetopewdiepie8746]

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

[@cockdominator9391]

Everybody gangsta till the Triple Integral comes to play

[@i_am_ironman3380]

thank you for the smile while I'm so frustrated

[@domiankappa543]

Yeah, the double integral is all fun and games, but then I just get dz

[@domiankappa543]

@Ronan Gibson I hope you didn't already. And if, you found the reddit page to this topic. Haven't checked the details on the website from instaportal, but this seems *very* fishy, so you should handle it with a lot of care.

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@@domiankappa543 underrated comment 😭

[@cinema187]

@Forrest Raul this person and ronan are either bots or indians trying to advertise something bad

[@crastycy7207]

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

[@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

[@user-ez4iz1bf2l]

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

[@d1psh1tc1ty]

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

[@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

[@user-ry4kt2oq2t]

You're now 22 I guess and I'm 18😅

[@matthijsgeerlings]

Great explanation 👌

[@trulysal2476]

Thank you professor.

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Really good simpel example just perfect.thnk u

[@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

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

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Our life line for mathematics examination 🤩💯👍

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Thank you sir!!

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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!

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

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

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Thank you

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

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Thanks PROF

[@kernelkorp4348]

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

[@senarmstrongfanaccount]

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

[@akhileshtiwari7099]

Thanks lot sir

[@bilalkerem145]

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

[@joanneal-adham2068]

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

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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 😁

[@fazleyrabbypatwary7136]

Thanks,professor Dave.

[@user-cs9mi7vd6c]

Very good.

[@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.

[@KishoreG2396]

I have a test on this today! Thanks!

[@jonathanhuwe4791]

Thanks!

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What day this month will you do William Howard Taft

[@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!

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that was greatness

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Prof u d best!!👍

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I need more math!

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Please do z transform, analytic functions.

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Not Professor Dave Its professor Awesome

[@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.

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

[@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

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Bro what has this man not studied.

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GPA-saving content right here

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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.

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

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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 🙂

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Nice

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I swear god sent this man right here

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Do you have a video on Boolean Algebra?

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

[@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, .

[@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

[@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

[@sureshakella4263]

Great

[@arik9842]

dave, you fucking gem

[@krishshah3721]

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

[@aryyancarman705]

line intwgral vs surface integral

[@dragosstan2885]

Nice and Clear ! Actually the divergence symbol is called either Nabla or Del. Delta (letter) backwards...

[@UCh-cv7ls]

is there a worked out solution of the comprehension?

[@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

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holy moly

[@khanmaluitjiek669]

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

[@nourmhanna3217]

God bless you

[@giovannimariotte4993]

Youreamazin

[@NoOne-il4hw]

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

[@JOHN-rt1gd]

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

[@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.

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Thanks mom!!!

[@ImJustKnownAsAnonymous]

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

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Paul’s online math notes and khan academy

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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

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Best teacher on YT! P.S. First comment

[@jaydoubleli]

what happened to the "more advanced topics"?

[@user-uq8lr7ju7m]

Can someone tell me what 5/3 actually represents?

[@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

[@aisyahazalia1282]

Is the answer 48?

[@hellohumans9181]

Professor Dave can u please explain time dilation and general relativity

[@ProfessorDaveExplains]

check my modern physics playlist for all that stuff!

[@i.m.2bizee569]

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

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Always thala..

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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.

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

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We come to the end game

[@pretty.946]

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

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加油大家！

[@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 !

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

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this is the 1%.