I've been skipping classes since the beginning of the semester and this playlist saved my ass. Binged the entire playlist in just a few days. Tysm Dr. Bazett
@DrTrefor3 жыл бұрын
Hope it helps!
@apoorvbagal29363 жыл бұрын
lol same here
@dakotahrivers66402 жыл бұрын
you ain't the only one lol
@richardvalentinonainggolan328 Жыл бұрын
:v same here
@carleto-y8q7 ай бұрын
You forgot the units
@ycombinator7653 жыл бұрын
You know you love Math when these kind of phenomenona show up on your recommendations within an hour of posting! Thanks Sir!!!
@DrTrefor3 жыл бұрын
haha you're telling the youtube algorithm good things!
@nebulouscalamity6338 Жыл бұрын
Holy guacamole. The bit at the end is the coolest wrap up I have seen in a while. It blew my socks off and fired me up with excitement. I love you and the immense excitement, empathy and curiosity that you radiate.
@paulgillespie49083 жыл бұрын
Bloody brilliant video. I did this stuff forty years ago at university and had no clue what was happening. So glad that I now finally get it. Thanks so much.
@glennnakamura4831 Жыл бұрын
Same thing happened to me when I took vector calculus and E&M theory 43 years ago. Picturing what was happening with the interactions of the E and B fields was tough. This gives me so much of a better understanding of what's happening.
@AbhishekKumar-jg7gq3 жыл бұрын
You are making me feel the science of mathematics by explaining the inside of every topic
@robertoberidojr.4353 жыл бұрын
I really have hard times deciding when to use implicit, explicit and parametric. I found this very helpful since I now understand when to use those formulas
@jacobwilliams86343 жыл бұрын
thank you! Stokes Theorem would be such a difficult concept to learn without your videos
@DrTrefor3 жыл бұрын
Happy to help!
@carleto-y8q7 ай бұрын
This proof is BS since he does not include the units.
@briandwi2504 Жыл бұрын
This topic is amazing. I am working through the calculus and linear algebra as I want to learn more about Classical physics, post Newton. It's clear that vector calculus is a fundamental tool to understand Maxwell's equations. I am sure your work will have given me a good foundation to understand Physics properly. Brilliant work Dr Trefor. Thanks.
@coltonlemasters Жыл бұрын
The visualizations you provide are amazing. I'm already doing very well in my vector calculus class, but I still like to visit your videos to gain an even more intuitive understanding. Please do more upper level math material. No need to actually do any problems, just conceptual videos would be amazing for added learning.
@MGTOW-nn9ls3 жыл бұрын
Thank you Dr Bazett. Explanation that curls are canceling each other helps a lot.After watching your video I can say now that I really understand the physical aspects of the Stocks Theorem
@mayathesheriff91003 жыл бұрын
Thank you for the detailed graphics that help students visualize complex 3D concepts.
@DrTrefor3 жыл бұрын
Glad they help!
@___xid99922 жыл бұрын
What an amazing resource this channel is. I've watched so many of your vids, thanks for making them. :)
@DrTrefor2 жыл бұрын
Thank you!!
@cherrygarcia59313 жыл бұрын
I have a cal3 final tmw and your videos are saving my life thank u so much :,)
@DrTrefor3 жыл бұрын
Good luck!!
@karlmudsam28342 жыл бұрын
Emphasozed
@amyhughes2149 Жыл бұрын
Super helpful video, I've been learning through correspondence and all of the material seems so esoteric. Thank you for making something that is easy to understand!
@srinivasansrivilliputhur47043 жыл бұрын
Dr. Bazett: Thank you for this wonderful series on Vector Calculus. Very helpful review for me. A question though. Will you please geometrically illustrate the transformation from dSigma to dA. You jumped too quickly around 8:35.
@Kubikrup2 жыл бұрын
Great channel and explanations professor, thank you!! I have an exam and I hope I can express myself perfectly just like you while solving the questions:))
@Kicsa3 жыл бұрын
Really great content, thank you for your enthusiasm and way of teaching this subject.
@nikhilsingh52333 жыл бұрын
the third example was genius . thankyou sir
@tanishkumar66822 жыл бұрын
Thankyou so much, on clearing my doubt on the concept of replacing the old surface with the new one. Lots of love from INDIA
@quantumaravinth3 жыл бұрын
Prof Trefor Bazett, do you know that there are organizations in India that sell videos at high price with same amount of animation (may be just a little more, we can say) that you made. Yours is much nobler and serious considering a membership to your channel.
@DrTrefor3 жыл бұрын
Thank you for your kind words. For me any money from memberships etc has always been secondary, my first goal is to help provide a high quality mathematics education and if I’m able to help with that then I’m happy:)
@HanaCosine7 ай бұрын
WONDERFUL VIDEO. thank you SO SO SO much.
@ishraquearshad32432 жыл бұрын
If our plane is in XYZ then is it possible to find the surface integral(circulation) of a vector field using the stokes theorem by projecting it on any plane XY, YZ, XZ?? Or there are some limitations: it should be a base plane projection from any particular direction!!
@moinshaikh19633 жыл бұрын
Great video professor! A question, around 10:00 why isn't the region to be considered the surface area of sphere instead of the circular area on which the shadow of sphere is falling?
@fardeenrazif93772 жыл бұрын
Total curl depended only from the boundary surface, (circle in xy plane) , so any surface with the same boundary must also give the same total curl. By boundary I mean the outside perimeter of the surface
@frakkx34912 жыл бұрын
@@fardeenrazif9377 it's pretty weird that he uses this in his example problem then explains why as if it's a totally different way of solving it
@fardeenrazif93772 жыл бұрын
Yeah I also thought about that
@emerald_eyes3 ай бұрын
I don't quite understand, isn't the integral Fdr a line integral? Why do we get the area when integrating it?
@hussamalanesi7432 Жыл бұрын
This is amazing sir. Could you make a video explaining more how to find n and d sigma for various cases?
@asterixx68783 жыл бұрын
Quite often it's hard to actually identify the boundary of a surface. As an example example, lets say that we have a surface defined by z=1-x^2-y^2, x>0, z>0. This is a paraboloid, confined to the first and forth octants. What curve is a boundary of this thing? Is the straight line segment on the y-axis (-1≤y≤1) a part of a curve that's bounding the surface? As always - very nice videos. Thank you💛
@anushkatilekar52162 жыл бұрын
I didn't understand what you did at @4:08 ..... The vector r had values in terms of theta ... The vector F had values in terms of x and y .... Then how did you write the vector F in terms of theta in the integral ?.......
@frakkx34912 жыл бұрын
Change to polar coordinates, y becomes sin(theta) and x becomes cos(theta)
@gerardsagliocca6292 Жыл бұрын
Your lectures should be numbered
@DrTrefor Жыл бұрын
They are all in order if you go the playlist for vector calculus:)
@MishaShvartsman2 жыл бұрын
Beautiful job!!
@ejisip20912 жыл бұрын
No to brag, but I am able to solve the problem on myself. You're a great lecturer Dr. Trefor. More power!!
@baolongngo34862 ай бұрын
I want to ask why in the second way of the example , why we need unit normal vector , i thought this was be cancelled when dS becomes dA
@shaheersherif73662 жыл бұрын
Thank you , very helpful!
@manishbhargao9653 жыл бұрын
Really awesome explanation
@DrTrefor3 жыл бұрын
Thank you!
@Festus2022Ай бұрын
I'm thinking our unit sphere is a level SURFACE of the 4D function f(x,y,z)= x^2+y^2+z^2. So our gradient is a 3D vector field with all the gradient vectors being perpendicular to our unit sphere surface at every point. Is this correct?
@ketaksingh54658 ай бұрын
This is awesome stuff ...thank you so much!!
@Festus20222 жыл бұрын
Trevor, thx for the great video. Since a line integral can represent WORK or CIRCULATION, does this mean that circulation IS work??. I not, what is the distinction?
@DrTrefor2 жыл бұрын
It must means the same mathematical ideas apply in different physical contexts
@Festus20222 жыл бұрын
@@DrTrefor Thx so much for the response!
@PhysicsBanglaTutorial3 жыл бұрын
Which apps or software you use to make this video? Can you tell me pls?
@sumitkumarsahoo76013 жыл бұрын
well done I wish if I could give a presentation like you
@JohnVKaravitis Жыл бұрын
The surface can't exceed the boundaries of an imaginary "cylinder" that extends upward from the line curve, yes? If you were to shine a flashligh from above, there would be no shadow, yes?
@sergiolucas382 жыл бұрын
Excellent video :)
@yasirarafat1872 Жыл бұрын
best video ever
@willardsavage29804 ай бұрын
why you didnt make the limits of integration you confused me, cuz the limits of integration in my opinion are radius 1, and angle 2pi, but since you did that thing of pi*rsquare, i didnt get what you did so i dont know if i did wrong or well, why im gettin 4 pi in the final answer i dont understand can you explain this please, i get that you use the formula of the area, but i wanna know how to do it with limits of integration, since limits of integration is what i will need to use in the exam, not a formula of an area, thank you
@gilbert40042 жыл бұрын
When you are computing the circulation (at around 4:30), how did you parameterize the vector field F to get M = sin(theta) and N = -cos(theta)?
@benmcginn8519 Жыл бұрын
Remember he is taking the dot product of F and r prime. He is taking the matching components, multiplying them, then adding them to the products of the other components. So in this case, the i component of F is sin theta in this parameterization. Taking the dot product with the i component in r prime, which is -sin theta, gives you negative sin squared theta. Calculate the other components in the same way, -x = -cos theta, j component of r prime is cos theta, giving -cos squared theta. Finally, z = 0, so the z term goes away.
@vaginalarthritis17533 жыл бұрын
Have you considered doing a Real Analysis play list when this is done?
@skcenior42273 жыл бұрын
Sir do you have a calculus playlist purely for physics because I'm little confused with your playlist (IF I SAID ANYTHING WORNG ABOVE IM SORRY)
@DrTrefor3 жыл бұрын
This playlist is actually intended for a course that physics students would take.
@skcenior42273 жыл бұрын
@@DrTrefor thanks 😊
@j.o.59573 жыл бұрын
Alright, cool computations. Struggled a bit with doing them myself, but did it after some effort. Question to self: we have the implicit n = nabla_g/|nabla_g|. What are the parametric and explicit? I remember parametric being r_u x r_v, but what was the explicit again? I don't quite remember, but wouldn't it just be k_hat? Perhaps in this example if we reduce the surface, but I'm not sure. Also found it weird that the k_hat went to the bottom, what happened there? d_sigma = 1/k_hat dA. So d_sigma is the normals on the surface. Dividing it by k_hat, you only get the normal to the xy-plane left, meaning you dA, which is dxdy. Aight, I think that's it.
@thefrenchiestfry81472 жыл бұрын
How would one parameterise the circle if it wasn't a unit circle, e.g. (x + 1)^2 + (y + 1)^2 = 1? And also, at 7:38, why is the k unit vector included?
@johnkapauo2995 Жыл бұрын
Could you please try and verify the surface for the cylinder following that idea or concept?
@elgatito003 жыл бұрын
OMG you are the best 😭😭😭
@liannalim45219 ай бұрын
You skip through smaller parts way too much. Oftentimes I don't know what part correlates to what. It can get confusing. Like a 4:55 how is it suddenly all in sin and cos? F is in x and y.
@nightking84902 жыл бұрын
Thanks man. I was confused about n ( unit normal) in methods 2 and 3. I was confused which normal to take, like the normal vector pointing in different directions on spherical surface or normal vector pointing from the plane area projection like XY plane has k as its normal unit vector. Thanks 2 you, my doubt now could rest in peace.
@golagha1959 Жыл бұрын
Please explain how curl F.n dsigma changes to curlF times some unit vector times dA. I can't see how dsgima changes to dA.
@jrjr1313jrjr Жыл бұрын
It appears you used a surface in the x,y plane in both calculations. You did not use a vector normal to the hemisphere.
@sahil-pu3cc Жыл бұрын
Doubt cleared bro thnks
@suryanarayanan757 Жыл бұрын
Is d sigma is equal to mod del g times dA and n ds is equal to del g times dA
@skcenior42273 жыл бұрын
Hi I'm from india your vedios really helpful for me THANKYOU but now it is midnight I'm going to sleep so I'm gonna watch this vedio tomorrow sorry!!
@DrTrefor3 жыл бұрын
haha good night!
@RSS182 жыл бұрын
Respected sir , what if we change the orientation of curve and use normal as -k cap for the surface?
@margaretehrich70842 жыл бұрын
Hey Trefor, thanks for all the help! Stem teacher to stem teacher, your handwriting could use some work.
@DrTrefor2 жыл бұрын
ha well I can't disagree with you there:D
@redtree732Ай бұрын
Honestly, it’s quite a lot better than many GSIs’.
@devashishshah90213 жыл бұрын
Stokes theorem was very hard to visualize until this happened....
@kaveenmanusha98433 жыл бұрын
cant understand what happened at 10:12 the s to r thing
@theshibu214 Жыл бұрын
🙂ngl i am having a mental break down ..howwwwwww am i supposed to do this
@GOODTHINKER6913 жыл бұрын
Thanks you sir
@DrTrefor3 жыл бұрын
You're most welcome!
@Rzsstrikerszr3 жыл бұрын
hi sorry if this off topic from this video but im stuck on a question: I have to find the transfer function and rearrange it to produce an expression for i(s) for V(t) = i(t) R + L di/dt + V0 if you or anyone can help me on this it be a big help thanks
@lizzardnannerzz3 жыл бұрын
is he canadian? do canadians also pronounce 'z' like 'zedd' ?
@DrTrefor3 жыл бұрын
Haha yup!
@eggxecution Жыл бұрын
this helps
@engineers_hub Жыл бұрын
what is k-hat? where does it come from?
@whyargon Жыл бұрын
it is the normal of the boundary (since the boundary is a flat circle, the normal is always going to be just khat)
@akhmalfaris4097 Жыл бұрын
i love you
@ricardobautista-garcia84923 жыл бұрын
Third. And nice video as always.
@THKNTV4 ай бұрын
i checked my teams
@rowangoebel-bain3447 Жыл бұрын
bless up
@rogersndegwa-ck3ud4 ай бұрын
Do more examples..I hate theory
@carleto-y8q7 ай бұрын
This proof is obtuse since the units of the integrals are omitted since a length is not equivalent to a surface area. Is there an ABC mouse for math teachers? Unless I am wrong but all the girls I know say I have cute dimples which is similar to a surface area and the lower length is enormous. Do you ever get that sinking feeling that what you do is entirely a waste of time. What if you did the text of your video in a seminar and I was there. What would you say? Would you cry? Mommy mommy why do you not write?