I clicked "like", not for the sake of the big KZbin algorithm in the dark sky, but because you are good teacher.
@DrTrefor3 жыл бұрын
Haha thank you
@justsaadunoyeah12346 ай бұрын
@@DrTrefor I am only in around 5-7th grade yet I can understand your explanations. Keep up the good work sir!
@yologreatdose81803 жыл бұрын
Omg your an absolute legend Dr.Trefor. I have spent hours trying to understand each 1.5 h lecture only to realize this man here just took a 1.5 h lecture to 12 min and made it 5 times easily to understand. I salute you for you time and effort to make student life to learn much more enjoyable.
@DrTrefor3 жыл бұрын
Wow, thanks!
@victorcamara21552 жыл бұрын
It's incredible the difference in teaching skill when someone is just there to "get their paycheck" vs someone who is passionate about the material.
@cjenaco7938 Жыл бұрын
1.5 hrs for scalar potential!! then your teacher must also be covering the origin of scalar potential
@NeelShah02113 жыл бұрын
When I first saw line integrals I was really scared of it. After watching your videos on vector calculus series seems like a piece of cake now. One of the best teacher ever. Thanks a lot for all your hardwork.
@gosiagniadek45143 жыл бұрын
I swear to God your videos explain in 15min things which I was trying to understand for the last 7 weeks of lectures. Thanks for your work
@bite027_ketansharma63 жыл бұрын
I spent two days in frustration trying to understand this, and you taught it to me in twelve minutes, thank you.
@DrTrefor3 жыл бұрын
So glad it helped!
@ericktapia52893 жыл бұрын
This man is the goat! I practically passed my semester by watching @Dr. Trefor Bazett videos (specially the playlist of multivariable calculus and linear algebra). I have a lot of respect for this man; the time and work it takes to record and animate videos like this is not short nor easy.
@markpadley8902 жыл бұрын
Absolutely superb explanation - I am returning to this area of study after many years. How I could have done with KZbin and Dr Bazett back in the 1980's! It would have saved me hours and loads of stress! Now it is my turn to communicate aspects of this subject to engineers and computer scientists - After a gap of some 30 years, I have caught up in just a few hours what I was expecting to take a few weeks of study - great resource Trefor- thanks
@prithvirajdj3 жыл бұрын
Subscribed! No more words.
@DrTrefor3 жыл бұрын
Thank you!!
@user-hf6yb2jy5t9 ай бұрын
Thank you for explaining this in an easy language, I literally wasted 1-2 hrs in study material while you explained it in 10 mins!
@user-tp1kv8cq2u3 жыл бұрын
I have a habit.I click like before i see the whole video,because i know that it's gonna be a perfect one!Thank you!
@scrappybuilds3 жыл бұрын
Thank you, Dr. Bazett! Currently taking Calc V and this series of videos has helped a lot with my broader conceptual understanding.
@duckymomo79353 жыл бұрын
Calc V???
@DrTrefor3 жыл бұрын
Glad they have been helping!
@Eduardo-cr8ri3 жыл бұрын
what the hell is calc v??? lol
@tomatrix75253 жыл бұрын
I thought Calc 4 (Vector calc) was the max? ( Of course you sre never finished with calculus as it is boundless, but in terms of courses)
@rohitchowdhury24622 жыл бұрын
Love and respect from INDIA. Thank you sir.
@akbeh5 ай бұрын
Very awesome video. It made calculus concept clearer that I ve been studying since 1 , 2 years
@tanayasharma77763 жыл бұрын
i knew i would learn things quicker here , so skipped the online college lecture and came here to learn it the easy way instead of wasting 1 hour in the class
@simonwax75752 жыл бұрын
This really helped me see the process after much confusion thanks.
@user-cl5qe7mk6s4 ай бұрын
If you just do all three integrals and find their union you gonna end up at the same place. Great video by the way
@mohitshakya07982 жыл бұрын
Your lectures are just amazing and quite helpful, thankyou so much for your lectures ...
@omanshsharma6796 Жыл бұрын
Beautifully explained!!!
@shawcampbell77152 жыл бұрын
Dr. Trefor Bazett, you do not put a line through your z???
@makwanasujal89572 жыл бұрын
Man!!! You're a legend.🙌🙌🛐🛐
@Inner_Sphere_s3 жыл бұрын
Thank you so much for this sir U did a great job Now it is too easy to understand potential function.💕
@DrTrefor3 жыл бұрын
Glad it helped!
@hikmatullahpakhtoon36943 жыл бұрын
Dr! you have more subscriders (students) than the total no of students at the university where you teaches, and sooner you will have more students on this channel than the total students in all universities across the Canada.
@DrTrefor3 жыл бұрын
That would be quite something!
@chinny8723 жыл бұрын
I love this playlist!
@oliverbrewster31083 жыл бұрын
This series is so helpful! Thanks so much
@DrTrefor3 жыл бұрын
You're so welcome!
@Tutor-i7 ай бұрын
I really enjoyed this video and the explanation was superb and I would love to see you explain the method of computing a line integral of F.dr to some value x1, y1 , z1 as dummy variables and finding the function from there.
@carultch6 ай бұрын
Interesting suggestion. I've accepted your challenge, to show that you get the same result, by performing a line integral. I've opted to start from the origin, but you can really start from anywhere and still get *a* function whose gradient is the given vector field. Another starting point, will produce a different potential function that only differs by an arbitrary constant. Using Trefor's example: F(x, y, z) = Let P, Q, and R indicate the three component functions of this vector field, which are all functions of x. Set up a path, starting at the origin, and aiming toward your destination point. To keep it simple, make this a straight line path. Call the path r(t), and let t be a parameter that goes from 0 to 1 r(t) = Take the derivative to find r'(t): r'(t) = The line integral (call it W, for work) is given by: W = integral F(x, y, z) dot dr Since r'(t) = dr/dt, this means we can substitute r'(t) dt for dr: W = integral F(x, y, z) dot dt This means: W = integral dot dt The dot product integrand evaluates as: P(x, y, z)*x1 + Q(x, y, z)*y1 + R(x, y, z)*z1 dt Substitute components of r for x, y, & z: P(x1*t, y1*t, z1*t)*x1 + Q(x1*t, y1*t, z1*t)*y1 + R(x1*t, y1*t, z1*t)*z1 dt Replace functions with their given functions: W = integral ([y1*t*cos(x1*t) + y1*t]*x1 + [sin(x1*t) + x1*t]*y1 + 1*z1) dt Distribute: W = integral [x1*y1*t*cos(x1*t) + 2*x1*y1*t + y1*sin(x1*t) + 1*z1) dt Evaluate each sub-integral, and pull constants out in front: x1*y1*integral t*cos(x1*t) dt = y1*t*sin(x1*t) + y1/x1*cos(x1*t) 2*x1*y1*integral t dt = x1*y1*t^2 y1*integral sin(x1*t) dt = -y1/x1*cos(x1*t) z1*integral 1 dt = z1*t Notice that y1/x1*cos(x1*t) exists for both positive and negative terms, which cancel. Thus: W = [y1*t*sin(x1*t) + x1*y1*t^2 +z1*t] eval from 0 to 1 Evaluate from 0 to 1: W = y1*sin(x1*t) + x1*y1 + z1 And this is our general potential function for this vector field. Notice that it matches Trefor's result at 8:15, when you drop the subscripts, which is exactly what we expect.
@micolcresto-dina5996 Жыл бұрын
going through examples like this is great! would be cool maybe to see more of these. Maybe like a playlist on doing difficult questions from each topic and going through them slowly...
@continnum_radhe-radhe2 жыл бұрын
Thank you very much sir 🙏🙏🙏
@frozenrats Жыл бұрын
Thank you so much!!!
@__theunknown__6153 жыл бұрын
Genius teaching ❤️❤️❤️👍
@computergamer332 жыл бұрын
friggin mad lad thanks for the help
@HabibiFishing9 ай бұрын
Thank you
@marcoebeling38142 жыл бұрын
Absolute legend
@lakshminiharika4918 Жыл бұрын
Absolutely amazing explanation......👏👏
@tannercheyne67043 жыл бұрын
I didn't realize how terrible my profs are at teaching. Thank you for al your work. Uni is a scam.
@DrTrefor3 жыл бұрын
Happy to help!
@fourthsideofthecoin16362 жыл бұрын
thank you
@sadraorangi39582 жыл бұрын
you nailed this one i give you that'
@ayeshabibi69773 жыл бұрын
You taught it so well. 👍
@Alannnn143 жыл бұрын
Thank you!!!
@DrTrefor3 жыл бұрын
You're welcome!
@poojagurjar31947 ай бұрын
Namaste sir ji 🙏🏻 Why it is necessary that 'C' is a function of (y,z) . it may be a single constant
@smarthkapoor43839 ай бұрын
this was awesome
@bartubilgen66563 жыл бұрын
you just saved my life and you don't even know it
@DASmallWorlds2 жыл бұрын
Hey, isn't this suspiciously like solving for an exact differential equation?
@DrTrefor2 жыл бұрын
Yes indeed! The context is quite different but the method almost exactly the same.
@ronycb71684 ай бұрын
We can prove that the constant of integration that is a function of the other two variables (say y and z) than the variable of partial integration (x) is zero if differentiate phi again wrt another variable (say y) and equate it to the y component of the conservative vector field and use the property that curl is zero derive and equality between dFx/dy and dFy/dx we get Fy =Fy + C(y,z) Hence C(y,z) = 0 Similarly other constants of integration are also zero.
@shaiavraham29102 жыл бұрын
Just out of curiosity: It’s also possible to find the potential by computing a line integral from a reference point to an arbitrary point (x, y, z) along an easy path (like a straight line) since a conservative field is path independent and then use the fundamental theorem of line integrals. Do you think it’s easier than computing a bunch of integrals and partial derivatives?
@carultch Жыл бұрын
You could try it, but it will be a lot easier to integrate each component, reconcile the common terms, and match the gaps left by the partial-constants of integration. Setting up a generalized path to all points, would be a lot more challenging.
@schizoframia4874 Жыл бұрын
4:54 I thought you need to check for boundary conditions in a PDE
@FridgeGames1012 жыл бұрын
How do you do it the other way around? Determining if a scalar potential has a corresponding conservative vector field and finding that vector field?
@DrTrefor2 жыл бұрын
Finding the field is easy if you have a potential function, just differentiate each component.
@ogunsadebenjaminadeiyin27293 жыл бұрын
Super
@antonia54233 ай бұрын
I am confused as to how you added the numbers in the last example. How did you get (1*0+1*pi+3-0-0-1) from f(pi,1,3)-f(0,2,1)/
@Richard-hj3ou Жыл бұрын
I find hilarious how for some degrees on some countries this is taught during the 3rd or 4th semester while. In another ones is not even taught but assumed to already master it. (My situation: first semester, they assume I already know the whole course of Calculus IV) 😅
@thomasoguta59582 жыл бұрын
i dint get how you finalize the integrals of M,N,and P...i thought you had y sin x in both M and N TO MAKE 2[Y SIN X]
@carultch Жыл бұрын
You aren't adding up the results. Instead, you are looking to fill in the gaps, left by the "constants" of integration. I put constants in quotes, because they really are functions of the other variables. Given a vector field: F = Integrate M(x,y,z) with respect to x. You will get a function in the form of m(x,y,z) + A(y, z) Integrate N(x,y,z) with respect to y. You will get a function in the form of n(x,y,z) + B(x, z) Integrate P(x,y,z) with respect to z. You will get a function in the form of p(x,y,z) + C(x, y) Any terms in common among m(x,y,z), n(x,y,z) and p(x,y,z), you should only have one copy of them in your final result. If there are terms in the n-function and/or p-function that only depend on y and z, then they are part of the function A(y,z). If there are terms in the m-function that only depend on x, then they are part of the functions B(x,z) and C(x,y). Any terms depending on all three variables, will be in all three anti-derivative functions. Only one copy of them, should be in your final answer for the potential function. You then complete it with a final constant of integration, which I generally call +K.
@arbaz2207 Жыл бұрын
at 6:43 how is it sinx + x partial derivative of c(y,z) with respect to y is not zero. c can be y^2 and all
@joyghosh38582 жыл бұрын
What book I should follow for vector calculus???I have thomas calculus.
@anikethdesai25 күн бұрын
11:19 Engineers: Answer is 5
@amon-iu7sz2 жыл бұрын
Good luck
@akashgautam42542 жыл бұрын
youtube should give university degrees as well cause u learn the most here
@garmands3 жыл бұрын
There is that small pink dot in the middle of the screen. At first I tried cleaning it because I thought the screen is dirty :D
@switches64999 ай бұрын
Why can we assume the remaining constant after integrating C(z) is zero?
@carultch6 ай бұрын
Because if all we care about, is finding *a* potential function, and not necessarily any specific potential function, or the general family of all possible potential functions, it's good enough to just keep it simple and let the final constant of integration be zero. The final constant of integration will cancel anyway, if using the potential function to evaluate a line integral.
@ganglion2583 жыл бұрын
Sir,we can find scalar potential by f.dr only when our curl f is zero ???..if not zero then how we can find our potential?
@DrTrefor3 жыл бұрын
You can only find the scalar potential when the curl is zero
@jamwheeler3 жыл бұрын
its "zee" not "zed"... fight me
@DrTrefor3 жыл бұрын
🇨🇦 ftw:D
@vikramnagarjuna35493 жыл бұрын
The way you sat.... 🙄🙄. But nice content. Why didn't you use software writing this time sir.? This video is without animations. Once the concept has been defined, Math Simulations allow us to produce many more visual examples quickly. I hope you understand.
@DrTrefor3 жыл бұрын
I love animations, but sometimes I want to go at the same "pace" that students would work through a problem if they were doing an actual test problem.