Lecture 19: Vector fields and line integrals in the plane. View the complete course at: ocw.mit.edu/18-... License: Creative Commons BY-NC-SA More information at ocw.mit.edu/terms More courses at ocw.mit.edu
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@ch.ajaysingh5 жыл бұрын
Lecture 1: Dot Product Lecture 2: Determinants Lecture 3: Matrices Lecture 4: Square Systems Lecture 5: Parametric Equations Lecture 6: Kepler's Second Law Lecture 7: Exam Review (goes over practice exam 1a at 24 min 40 seconds) Lecture 8: Partial Derivatives Lecture 9: Max-Min and Least Squares Lecture 10: Second Derivative Test Lecture 11: Chain Rule Lecture 12: Gradient Lecture 13: Lagrange Multipliers Lecture 14: Non-Independent Variables Lecture 15: Partial Differential Equations Lecture 16: Double Integrals Lecture 17: Polar Coordinates Lecture 18: Change of Variables Lecture 19: Vector Fields Lecture 20: Path Independence Lecture 21: Gradient Fields Lecture 22: Green's Theorem Lecture 23: Flux Lecture 24: Simply Connected Regions Lecture 25: Triple Integrals Lecture 26: Spherical Coordinates Lecture 27: Vector Fields in 3D Lecture 28: Divergence Theorem Lecture 29: Divergence Theorem (cont.) Lecture 30: Line Integrals Lecture 31: Stokes' Theorem Lecture 32: Stokes' Theorem (cont.) Lecture 33: Maxwell's Equations Lecture 34: Final Review Lecture 35: Final Review (cont.)
The corn and vector analogy just killed it. I am not forgetting it till the end of my life. Kudos to Prof. Denis, simply amazing.
@LAnonHubbard10 жыл бұрын
Thanks for making these videos available for free MIT. They're simply awesome.
@kamil2fcxc12 жыл бұрын
I so want my professors to have a look at the relevant MIT lectures before they come to class
@hilbert85002 жыл бұрын
Are u alive?
@BrownMunde6062 жыл бұрын
@@hilbert8500 most probably 🤣🤣
@CrushOfSiel9 жыл бұрын
The corn field explanation blew my mind! Thanks, now I understand vector fields!
@codenamerishi2 жыл бұрын
If you don't understand professor explanation at 15:00 the angular velocity is 1 because v = wr and v is equal to r basically since r vector rotated 90 degree becomes v; so w = 1
@ProfFeinman4 жыл бұрын
This seems to be the best discussion of line integrals (as noted below, starts around 16:00) of the many on KZbin because most straightforward. .
@wcsah9 жыл бұрын
16:35 - timestamp for beginning of Work and Line Integrals
@lucaslars49312 жыл бұрын
This is the best lecturer I have ever witnessed! Everything is so smooth
@bbnl199012 жыл бұрын
wow he sure knows a great deal of physics!
@TheVisualEdison4 жыл бұрын
he actually did a BSc Physics equivalent in france
@99ludester13 жыл бұрын
@TurdWolf1 I know. It's weird how these are already intelligent students that got in, yet they have professors that are millions time easier to comprehend and a lot more attentive of their students than at most other universities! Anyways i love these videos they sure do help a lot!
@hilbert85002 жыл бұрын
Are u alive?
@SPRINGGREEN813Ай бұрын
@@hilbert8500 Is anyone of you alive?
@johnydiala24929 жыл бұрын
Great videos. Explains much better than my prof.
@jeremy10ization11 жыл бұрын
I think that's why most undergraduate engineering programs don't require people to go beyond Differential Equations and Linear Algebra; because beyond that it starts getting more and more abstract.
@Roner10112 жыл бұрын
that chalkboard is so clean...
@dechisabalcha992811 жыл бұрын
you are good teacher ever i have seen so keep it up
@sidneydean.15 жыл бұрын
these free videos are well worth the price
@matron99364 жыл бұрын
I don’t agree with that
@hilbert85002 жыл бұрын
Are u alive?
@sidneydean.2 жыл бұрын
@@hilbert8500 yep
@bookman98972 жыл бұрын
@@sidneydean. wow didn't expect a reply after 12 years hows all going with you
@squkyshoes11 жыл бұрын
Wow, I wish I watched this before spending 4 hours doing problems trying to figure this out.
@poolkfg13 жыл бұрын
have this guy at berkeley :)
@proghostbusters16274 жыл бұрын
They do now xd
@yonatanable13 жыл бұрын
Wow The beauty of math: vector field
@kamilbudagov93356 жыл бұрын
Thank you very much!
@baharsalman3439 Жыл бұрын
Thank you professor
@battlewing2214 жыл бұрын
excellent teaching
@RishabhYadav-xc5dc6 жыл бұрын
Its very very useful. Thanks a lot.
@michaelhixson6229 жыл бұрын
mistake near 28:00 -----> dy/dt = -2t the position function starts as y= -t^2 so derivative should be negative for the dy/dt
@michaelhixson6229 жыл бұрын
Michael Hixson in the video, the professor took dy/dt to be +2t
@jontyroy17238 жыл бұрын
+Michael Hixson The professor is correct in taking it as 2t. We are differentiating the parametric equations of position x and y to get the velocity vector. In the parametric form it has been given that x=t, and y=t^2. Thus, dx/dt=1, and dy/dy=2t.
@RetroChicken8 жыл бұрын
+1 for +Jonty Roy 's response
@KaviPriyan-qt6vc4 жыл бұрын
best lecture
@lagrangemaximillian53199 жыл бұрын
at 32:30 why is it possible to express dr as (dx dy) vector? i wanna see proof
@MrSolutions699 жыл бұрын
+lagrange maximillian wrong question. it is a notation,
@ficklampa18 жыл бұрын
+lagrange maximillian because if you add the vectors dx and dy you get dr, dr=[dx;0]+[0;dy]=[dx;dy] I think.
@ayya5148 жыл бұрын
BEAST!
@vinithalampally15817 жыл бұрын
thank you
@codingWorld7093 жыл бұрын
Thanks sir
@thereisnogodbutdalegribble56872 жыл бұрын
I laughed out loud at the corn field metaphor
@nikhilvaidya43578 жыл бұрын
Gr8 Teaching !!
@mertyasaraydin65678 жыл бұрын
ALLAH razı olsun hocam :)
@GoogleUser-ee8ro6 жыл бұрын
is it common in physics to use angle bracket to denote vectors instead of standard matrix form? how to differentiate a row vector from a column vector, or it doesn't matter, we just assume the dot product is the product of two or multiple vectors with the same length yet orthogonal orientation?
@kartik61103 жыл бұрын
Vector valued functions are usually written in angle brackets, x, y and z components separated by commas.
@HimanshuSingh-jn1tf5 жыл бұрын
34:00 ,I just wanted to mark this point for future reference
@davidwilliansmorante97983 жыл бұрын
If I see the drawing of the vector field, how can I interpret it as he did with the example 8:48?
@jes_us93 жыл бұрын
What do you mean? Like, how to plot it fast? Or do you mean something else?
@tackformaten211 жыл бұрын
2 people didn't pass the course.
@proghostbusters16274 жыл бұрын
14 now
@gamar12264 жыл бұрын
@@proghostbusters1627 15
@proghostbusters16274 жыл бұрын
@@gamar1226 hope you weren't the last one xd
@gamar12264 жыл бұрын
@@proghostbusters1627 =)))
@proghostbusters16274 жыл бұрын
@@gamar1226 you didn't deny it though
@user-rm6rb3tp5u Жыл бұрын
31:36
@P1nk1e1313 жыл бұрын
@userisdosser OM MY GOSH, I thought I was the only one who thought this. Powerpoint just doesn't help me I really wish my lecturers would use a blackboard!
@Myrslokstok7 жыл бұрын
P1nk1e13 Powerpoint is like dead. People show a picture and say something, usualy they read from the page. So it ends up like a bad book.
@milindayapa330710 жыл бұрын
Pretty awesome.. (y)
@Diodio_y12 жыл бұрын
Why, oh why did I come to Cornell to study math= =
@adip86 жыл бұрын
Siyu Yang Math degree. Nice
@johnlau17918 жыл бұрын
Could any one please tell me why the vector f towards outside of the circle? Isn't the rule of physic tells that the force is towards inside the circle? Thank you very much.
@ficklampa18 жыл бұрын
+John Lau i assume you mean the one regarding the uniform rotation. I the vectors here represent angular velocity
@johnlau17918 жыл бұрын
Thank you for your explanation : )
@mauriciobarda8 жыл бұрын
it's and old question but I'll answer anyway for other people. The vectors pointing outside the circle are not velocity neither centripetal force. They are from another hypothetical force field independent of the motion.
@johnlau17918 жыл бұрын
Thank you so much.
@yonatanable13 жыл бұрын
Wow
@deepakmeena38748 жыл бұрын
reply to ishan dave i m frm iit bombay n my brnch is cs
@soyadrik11 жыл бұрын
lol
@deepakmeena38748 жыл бұрын
greater interactive teaching than iits.here we sleep in lectures n in mit they took interest but still iitians can complete the whole courses in one nightn after that both end up with equal level
@nj93nazj10 жыл бұрын
He teach too fast.. I guess im so stupid i can't follow him LOL!
@isaacmandell-seaver72233 жыл бұрын
Pause the videooo
@adip86 жыл бұрын
This topic is so boring and easy. This is more suitable for the level of engineers. I don't know why it's a part of my mathematics course.
@abhishekjoshi84136 жыл бұрын
even for a pure mathematics you need vector calculus but emphasis on proofs than appplication so the topic is common for both engineers and math undergrads
@adip86 жыл бұрын
Abhishek Joshi But it's really not very interesting or anything new for me. It's just a lot of calculative work which I don't like.
@adip85 жыл бұрын
@Its Wednesday my dudes Well pure math is more of an intellectual challenge than doing this kind of grunt work.
@adip85 жыл бұрын
@Its Wednesday my dudes No. If you're more educated than an engineer say a statistician or applied mathematician then you will require the use of functional analysis, topology. Which is more of a challenge than this.