Every time I search a topic and see professor Dave come up I know it’s about to all make sense. Thank you so much for all of your help
@mortiloniperpomontinson Жыл бұрын
Yeah dude I’m in frisking fifth grade and I half understand greens theorem now.
@charleslowery186010 ай бұрын
i definitely asked !
@ManojKumar-cj7oj4 жыл бұрын
Brother, you are not getting enough views for your videos,but that doesn't change the fact that you are one of the top teacher/explainer/KZbinr on earth. Thanks for video
@qazxl1233 жыл бұрын
how come you can explain something in 5 min, that my college professor couldn't in 2 hours of lecture???
@igorfritz29733 жыл бұрын
@Elian Aydin no it doesn't
@NameisU3 жыл бұрын
@@igorfritz2973 They are bots.
@igorfritz29733 жыл бұрын
@@NameisU I know, I looked it up
@rahmatnasrul72633 жыл бұрын
@@NameisU wdym, who's bot
@farrukhsaif1083 жыл бұрын
@@rahmatnasrul7263 the message in question, probably got deleted.
@tech_jc11205 ай бұрын
Thank you Mr. Green for making integrals easier and time-saving!
@joshuaargotemedrano24213 жыл бұрын
Your videos are beyond impressive. Not only do I love your concise explanations, but also your graphics. One of the best mathematics channels on youtube!
@alejrandom65923 жыл бұрын
SPOILER ALERT for last example: Integral of 1+2y dy is y+y², evaluate from x² to 1 we get 2 - x² - x⁴ dx, integrate we get 2x - x³/3 - x⁵/5, evaluate from 0 to 1 we get 2 - 1/3 - 1/5, arithmetic and voila 22/15
@rhode64572 жыл бұрын
I may be dumb, but how did you get 1 + 2y ?
@rhode64572 жыл бұрын
never mind....duh....I got it!
@philkirshenbaum88672 жыл бұрын
Why from x^2 to 1 instead of 0 to x^2?
@pnb.73462 жыл бұрын
@@philkirshenbaum8867 plot the graph and you will see the lower curve is y=x^2 and upper y=1(as mentioned in the question C moves from 1,1 to 0,1 along a line and the line is y=1)
@tausifhasankhan88652 жыл бұрын
@Alej Random Thanks for the spoiler dude, I was looking for if someone had shared the answer! :D
@jdextlab4 жыл бұрын
Revisiting some calc topics and glad I picked these since i learned from all ur physics topics
@Lpedraja20024 жыл бұрын
Awesome explanation. Love your humor and attitude... Surprisingly makes me want to study math more
@honkhonk80092 ай бұрын
Its amazing how easily you explain this stuff. You explain exactly whats needed to be explained in such a concise manner. Perfect for people with ADHD lol
@weinzierlwlandriank14543 жыл бұрын
Your video is really good and I do appreciate the time and effort you put into it but I think you should mention that all points inside the D area must be differentiable and that depends on P Q as well as R for stokes theorem. I know that it sound obvious but if 1 or some points are not differentiable then we have to seek for approach to solve the problem.
@tadeocervone33304 жыл бұрын
Simple but yet extremely useful explanation, thanks Dave
@rosskious708411 ай бұрын
Positive orientation is the reason a hollow circle inside a solid circle, that you are calculating, has the lines going clockwise. You are not calculating the hollow area, but the solid and it is on the left as you walk around it. Very easy concept that some people have issues understanding.
@윤됴영2 жыл бұрын
Your 5 minute video is the best lacture i have seen
@NASAFanboy2 жыл бұрын
Watching this on the train ride to my calc 3 final as a refresher, thanks for the easy to follow video that taught me more than my professor has the entire semester!
@herobrine18476 ай бұрын
That’s on you
@davidobwaya84134 жыл бұрын
You saved my collegiate career. God bless you.
@tzwacdastag82235 жыл бұрын
Thank you for being a Physicist
@matanshtepel12304 жыл бұрын
ahhhaaa right 😁😁😁 that was such a physicist "explanation" of Green's theorem
@mranonymous_253 жыл бұрын
Although he is mostly an Organic Chemistry tutor, but yeah he can teach any subject, an all rounder of course ✌💯
@batmanthedarkestknight Жыл бұрын
How is this guy a professor in more than 10 subjects and a god in debating 😂😂😂😂
@beefstew39274 жыл бұрын
I found out who you were through your flat earth videos, stayed for the ones that are saving my ass in high school. God bless.
@theseb59812 жыл бұрын
@@armgord Some people in high school enroll in a local community college to take multivariable calc not me tho LOL
@tahir24433 жыл бұрын
This is genius. Simple and straight forward. Thank you so much,
@navagharkiran57695 жыл бұрын
I'm watching ur complete maths series I will get back to this soon 😍
@이규안-g7o9 ай бұрын
Thank you for good lecture!
@Eric-jh5mp4 жыл бұрын
I got 8/15 for the answer every time for the checking comprehension. I can't figure out what I am doing wrong here. If you are still looking at these video's comments, could you please help me? So I started by setting up the Pyx and Qxy in the double integral. So I got 1+2y. Now I get my bounds as from 0 to x^2. And for x I get from 0 to 1. So that becomes: y+y^2 then from 0 to x^2 I get x^2 + x^4. Then integrating again I get (x^3)/3 + (x^5)/5. Take that from 0 to 1: 1/3 + 1/5. That gets 5/15 + 3/15 = 8/15.
@henrymartens40794 жыл бұрын
Your bounds of integration for y should be from x^2 to 1 rather than 0 to x^2. If you draw a picture it is easier to visualize why. Anyways, the function stops at y=1 and it begins at the equation y=x^2 that is given
@Eric-jh5mp4 жыл бұрын
@@henrymartens4079 Oh ok that makes sense. Thanks for taking the time to help! Have a good rest of your day :)
@sohinipaul24294 жыл бұрын
I feel, it will be better to visualize that y varies from 0 to 1 and X varies from 0 to √y.
@GK.finansal3 жыл бұрын
@@henrymartens4079 Thankss.
@LindaniRichmanCele Жыл бұрын
Brilliant explanations dr dave
@eggxecution9 ай бұрын
So the technique to know the lower limit and the upper limit is to know the direction of the arrow. The starting point is the lower limit and it can be a function or a point while the upper limit is the intersection or the coordinate or so that's how I see it. Awesome!
@hasaniaparna12294 жыл бұрын
superb teaching
@premsingh2261 Жыл бұрын
The Best Explanation 👌 thanks Sir
@abiglug10 ай бұрын
Professor dave is the only thing holding up my academic career right now
@seswangmaluwang63682 жыл бұрын
Thank you sir, you explain it excellently.
@AnjaliSharma063 жыл бұрын
This is so easy to understand now, thanks, professor !! :)
@curtpiazza1688 Жыл бұрын
Great explanation! 🎉
@Riboflavaflav5 жыл бұрын
Yeah, Green's theorem!
@shaakiratakarim18182 жыл бұрын
Sir can you also do a lesson on Laplace transform
@Oscar-jg9gg3 жыл бұрын
for the problem at the end, we take the inner integral to go from an "exact" extent and the inner one from the "furthest" extent
@TanJunYu3 ай бұрын
thank you so much!
@IbrokhimkhujaRikhsikhujaev10 ай бұрын
Thanks you very much, Professor!
@rikrikmsangma56275 жыл бұрын
thank you
@simij73504 жыл бұрын
What a star you are
@timgoppelsroeder1214 жыл бұрын
Makes it seem like secondary school math great explanation
@p.lakshmiprasanna66483 жыл бұрын
Awesome video, super explanation❤️👍tysm sir
@si486905 жыл бұрын
Good video!.. thanks..but I wanted to know what's the practical applications of finding the line integral of a 'Vector field' over any curve?
@bigboibif77984 жыл бұрын
It's mainly a physics thing you can use to find the work done by a force field on an object
@AlVex984 жыл бұрын
If you consider the vector field to represent a force, then the line integral from a to b across a curve C (aka the circulation) can be thought of as the work needed to move a particle subjected to said force from a to b.
@asmodkhakurel Жыл бұрын
Professor Dave is the best!
@luyapan76563 жыл бұрын
Your videos are amazing
@md.azmiribneislam68855 жыл бұрын
You are a real genius
@MrCreeper20k5 жыл бұрын
Stoke's Theorem next!
@lordyabo9910 Жыл бұрын
why the limits of integration of x and y is from 0 to 1? can someone please explain. Thanks
@epicmorphism22404 жыл бұрын
Can we also apply this Theorem for complex numbers?
@nowdays9964 жыл бұрын
Professor Pls explain it for 3d vector field and 3d curve
@francolopez24604 жыл бұрын
i still dont get it
@enchantularity3 жыл бұрын
I have a quick question: While I understand the outcome of Line integral is Area, what is the outcome of the circular integral (conservative) ? Since it equals the double integral, Is the RHS is Volume? If that is the case, shall I assume that one special case of line integral which involves conservative Field on a closed curve over a surface yields volume? Please answer
@tracysara67542 жыл бұрын
Great video
@de-grafthazard90814 жыл бұрын
Dude you're a genius. But wait, what happened to the hair?
@jonescome-upon55743 жыл бұрын
give us back the haiiiirrrrrrrrrrrrrrr :OOOOO
@dhanya152 жыл бұрын
Thank you very much sir!!
@just4simplegg428Ай бұрын
I think on 0.24 time you have a mistake in line integral. Shouldn't it be dl in the end?
@zlatanibrahimovicisbettert79803 жыл бұрын
Thanks
@user-mf7li2eb1o15 күн бұрын
But why did you switch the dxdy to dydx? And the bounds are set strange too
@Brudere-l2f4 жыл бұрын
thank you sir from Japan u help me a lot
@ericlorenzoa.58263 жыл бұрын
Where does (2x - x) comes from?
@fionamarieisidoro70862 жыл бұрын
I get that for the last example you should set the bounds of x as 0 to 1 and the bound of y as x^2 to 1, but why do we set up the bound of x as 0 to 1? When I graphed it, the left bound is zero but the right bound is the line graph y=x^2. Please help me
@sayantaniguha85194 жыл бұрын
Is implicit differentiation valid in the condition for Greens theorem?
@charleslowery186010 ай бұрын
slow down lol
@broytingaravsol5 жыл бұрын
no interpretation about conservation?
@nightmareintegral55932 жыл бұрын
I have a problem pls help If we have square with side = 1 then area is 1*1=1 But with green theorem it is 1/2 How it works? What is wrong with me?
@carultch Жыл бұрын
Because you aren't just calculating the area of that square. You are multiplying each area element, with the curl of a vector field, across that square. Just like if you are given the density of a sheet of a square meter of plywood as 7 kg/m^2, and you calculate it for a piece that is 1 meter by 1 meter. When you calculate the area, it is 1 square meter. But when finding the mass, you shouldn't expect to get 1 kg. You should expect to get 7 kg.
@karmankruschke5 жыл бұрын
😜 My brain! Keep up the good work and I like the new hair.
@mostshak64474 жыл бұрын
plz,could you explain how to get out vector field for the contour
@AA-jc4cu4 жыл бұрын
Wait whaaat, where is the long hair? ;(
@mansoursalem84114 жыл бұрын
Relative to the last exercise; I guess the result is (-8/15)!? (not 22/15) Please kindly check it out?
@Invalid5714 жыл бұрын
I did the same mistake. 1) The curve runs counter clockwise so you must have a + sign. 2) You have wrong bounds for y. Draw the shape and it will be easy to see that the lower bound is: y = x^2 & the upper bound is: y = 1. Using the correct bounds you'll find: +22/15 (the correct answer)
@gijs65603 жыл бұрын
@@Invalid571 but the upper bound should be y=x^2 and the lower should be 0
@MonkeyOnFleek3 жыл бұрын
got -8/15 too
@adhiyanthaprabhujeyashanka20913 жыл бұрын
@@MonkeyOnFleek I got 22/15
@adhiyanthaprabhujeyashanka20913 жыл бұрын
@@MonkeyOnFleek choose lower bound for x as 0 and the upper bound for x as 1, and then choose the lower bound for y as x squared and choose the upper bound for y as 1
@selektahantany96492 жыл бұрын
im having troubles finding the limits for the last question
@excursion52468 ай бұрын
why we need to set 0 to y = x? Thanks
@buithach40843 жыл бұрын
how did he get 22/15 for the last problem.
@user-hc8fx8vm7o3 жыл бұрын
UP UP UP
@TheEpicGod1113 жыл бұрын
Use the same method he described in the video, the only tricky thing is setting up bounds,. You can integrate using an integral calculator to check that the answer's right.
@stylingandfitnessingwithty27133 жыл бұрын
@@TheEpicGod111 what were the correct bounds for y?
@Rogue_Art3 жыл бұрын
@@stylingandfitnessingwithty2713 The x bounds are from 0 to 1 and y bounds are from x^2 (lower) to 1 (upper). The correct integrand (what we're integrating) is 1 + 2y. Drawing the region will help you see the bounds.
@domiankappa5433 жыл бұрын
@@Rogue_Art This took me so long to figure out, but with your help I could eventually figure out, that I'm simply not able to read 2d coordinates anymore - I read (0,1) as (1,0). Those Details can really screw you up..
@harrytaylor43602 жыл бұрын
well he certainly knows a lot about a lot of stuff. Thanks for your help.
@James216914 жыл бұрын
In the triangle example, why are the y limits from 0-->y=x and not simply 0-->y=1 like in the first example of the square?
@ProfessorDaveExplains4 жыл бұрын
because the upper limit is the curve itself
@James216914 жыл бұрын
@@ProfessorDaveExplains Thanks for the response, your video on double integrals helped so much and clarified it all for me, one of the best maths videos I have ever seen so thanks for your work!
@onlytheflames2 жыл бұрын
How do you get the P and Q ?
@benmoody93344 жыл бұрын
2:30 where does that seemingly arbitrary yet very specific vector field come from? Can anyone tell me please?
@hiba24754 жыл бұрын
i am pretty sure it is given to us with the problem
@benmoody93344 жыл бұрын
@@hiba2475 thank you, I realised my mistake later on
@ghostek77922 жыл бұрын
darn i wish the practice problem at the end had a quick solution explanation
@videosformybrain36063 жыл бұрын
my king
@dalibormaksimovic63992 жыл бұрын
Does Green's theorem imply that dQ/dx = dP/dy, because of Cauchy theorem on closed and analytic curves?
@carultch Жыл бұрын
If it did, we'd have no reason to use Green's theorem. If dQ/dx equaled dP/dy, then the vector field is conservative, and the closed loop line integral is trivial, because line integrals on conservative vector fields are independent of path, and closed path integrals of conservative fields are zero.
@axeleaton31792 жыл бұрын
Isn't the integral same as taking the area of the square for the first problem he solves? Then the answer would be 1.. ? IF IT IS 1/2 then what does that mean in relation to the square?
@tyleroman Жыл бұрын
No, the line integral is being solved with green's theorem, not the area
@happysharma35435 жыл бұрын
where do u live ,sir ????
@christiansantini33504 жыл бұрын
Your explanations are EXCEPTIONAL. Thank you. You look good with shor hair also. :)
@davidajayi12073 жыл бұрын
Im having trouble solving the comprehension exercise any chance you can help?
@akhtarazizuet3 жыл бұрын
I get 22/15 from line integral but 8/15 from Green's theorem... I've set the limit of y to be from 0 to x2 and x from 0 to 1 : still I get 8/15. Can someone help with 22/15 using Green's theorem?
@ridazehra48703 жыл бұрын
Set the y limit from x^2 to 1
@mehakali14652 жыл бұрын
But what is the reason behind setting limit from x^2 to 0 ??
@honeydevaang7322 жыл бұрын
@w0nd3rbe4st2 жыл бұрын
@@mehakali1465 need to draw the a) b) c), then u will see the bounded area for x-axis from 0 till y=x^2
@Alexlaier4 жыл бұрын
Nice video. S2
@ArduousNature2 жыл бұрын
In the square example why is D 1/2? It looks like it should be 1 to me :(
@ArduousNature2 жыл бұрын
Oh it's something to do with the vector field, okay... Hard to visualise.
@omaimakamran47952 жыл бұрын
What exactly is dr in F.dr? Which vector is r?
@carultch Жыл бұрын
The r refers to a radius vector from the origin to a point along the path you are integrating. Think of dr as "dinky change in r", which means an infinitesimal change in r along the integral. The vector r will be a vector function of space, where its components are each functions of a parameter (t) that describe its path. Think of t as time, and the x-position/y-position/z-position along the way, will each be functions of time that trace out this path. To find dr, you differentiate r with respect to t, essentially finding the velocity along this space curve, to get dr/dt. then multiply what you get by dt, and dt becomes the new variable of integration, for carrying out the line integral. The vector for dr/dt becomes part of the integrand.
@gijs65603 жыл бұрын
Isnt it 8/15?
@himahelmy62063 жыл бұрын
thats what i got
@adhiyanthaprabhujeyashanka20913 жыл бұрын
It is 22/15
@adhiyanthaprabhujeyashanka20913 жыл бұрын
@@himahelmy6206 hi bro/sis choose the bounds correctly draw a diagram and visualise that
@adhiyanthaprabhujeyashanka20913 жыл бұрын
@@himahelmy6206 upper bound for x=1, lower bound for x = 0, and upper bound for y =1 and the lower bound for y= x squared
@AS-ds4in2 жыл бұрын
at 4:10 what does the answer "1/2" represent like does it represent the area of something??
@carultch Жыл бұрын
It depends on what the vector field represents. Suppose the vector field is a force field, which is the go to application that motivates the concept of vector line integrals. The vector field would be force at any given point in space, and have the units of Newtons. The change in radius vector, dr, would have the units of meters. Upon integrating them together, you'd get Joules of work done, as a body moves along the given path, while subject to that force field.
@matrixus14804 жыл бұрын
I have a question, the area of square in example at 4:10 shouldn't be 1? If we use equation for the area of square namely a^2 we should get 1 because length of the side is 1, but using green's theorem we got 1/2, someone can tell me why?
@vanadium10214 жыл бұрын
You are not calculating the area inside the square, since this is not just a normal integral. Here the line integral shows how much of the vector field that is given is in the direction of the curve, which in this case is the square. You can tell that it's not the area of it by using a different vector field as well, which will yield different results.
@matrixus14804 жыл бұрын
@@vanadium1021 thanks for explanation;))
@masonherlihy7175 жыл бұрын
Did you get my email on a new theory of gravity?
@homelysynthesis31103 жыл бұрын
Caitlyn
@AdityaShindeBtech4 жыл бұрын
sick intro
@Ppooh002 Жыл бұрын
i got 8/15 as my ans
@冠年紀3 жыл бұрын
No clue
@meaninglessjunk95945 жыл бұрын
wtf u must’ve known we were learning this
@nellvincervantes62333 жыл бұрын
I thought flux is when the vector is perpendicular to the surface area just like electric flux and magnetic flux but in here, the vector is parallel to the surface area. 🤔🤔
@carultch Жыл бұрын
The vector field is perpendicular to the surface area we are integrating. Because we are not integrating the original vector field directly. Instead, we are integrating the curl of the vector field, and the curl of a 2D vector field, is perpendicular to the plane of the two dimensions.
@sgtdonagon2 жыл бұрын
gren theodor
@critechinkabba3955 жыл бұрын
How do I contact you in person, pls?
@paulktms6632 жыл бұрын
Nu ai facut bine baiatu meu, intreaba l pe domnu Ene stie mult mai bine. O zi va urez!