Lec 19: Vector fields and line integrals in the plane | MIT 18.02 Multivariable Calculus, Fall 2007

Lecture 19: Vector fields and line integrals in the plane.
View the complete course at: ocw.mit.edu/18-02SCF10
License: Creative Commons BY-NC-SA
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[@ch.ajaysingh]

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.)

[@NovaWarrior77]

Thank you.

[@cjhhong]

W

[@saubaral]

ocw.mit.edu/courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/

[@yu6879ehng9005yu]

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.

[@kamil2fcxc]

I so want my professors to have a look at the relevant MIT lectures before they come to class

[@hilbert8500]

Are u alive?

[@BrownMunde606]

@@hilbert8500 most probably 🤣🤣

[@CrushOfSiel]

The corn field explanation blew my mind! Thanks, now I understand vector fields!

[@LAnonHubbard]

Thanks for making these videos available for free MIT. They're simply awesome.

[@codenamerishi]

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

[@wcsah]

16:35 - timestamp for beginning of Work and Line Integrals

[@ProfFeinman]

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. .

[@bbnl1990]

wow he sure knows a great deal of physics!

[@TheVisualEdison]

he actually did a BSc Physics equivalent in france

[@lucaslars4931]

This is the best lecturer I have ever witnessed! Everything is so smooth

[@99ludester]

@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!

[@hilbert8500]

Are u alive?

[@SPRINGGREEN813]

@@hilbert8500 Is anyone of you alive?

[@johnydiala2492]

Great videos. Explains much better than my prof.

[@dechisabalcha9928]

you are good teacher ever i have seen so keep it up

[@kamilbudagov9335]

Thank you very much!

[@RishabhYadav-xc5dc]

Its very very useful. Thanks a lot.

[@yonatanable]

Wow The beauty of math: vector field

[@Roner101]

that chalkboard is so clean...

[@battlewing221]

excellent teaching

[@baharsalman3439]

Thank you professor

[@jeremy10ization]

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.

[@nikhilvaidya4357]

Gr8 Teaching !!

[@vinithalampally1581]

thank you

[@ayya514]

BEAST!

[@KaviPriyan-qt6vc]

best lecture

[@squkyshoes]

Wow, I wish I watched this before spending 4 hours doing problems trying to figure this out.

[@codingWorld709]

Thanks sir

[@sidneydean.]

these free videos are well worth the price

[@matron9936]

I don’t agree with that

[@hilbert8500]

Are u alive?

[@sidneydean.]

@@hilbert8500 yep

[@bookman9897]

@@sidneydean. wow didn't expect a reply after 12 years hows all going with you

[@poolkfg]

have this guy at berkeley :)

[@proghostbusters1627]

They do now xd

[@milindayapa3307]

Pretty awesome.. (y)

[@thereisnogodbutdalegribble5687]

I laughed out loud at the corn field metaphor

[@mertyasaraydin6567]

ALLAH razı olsun hocam :)

[@GoogleUser-ee8ro]

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?

[@kartik6110]

Vector valued functions are usually written in angle brackets, x, y and z components separated by commas.

[@michaelhixson622]

mistake near 28:00 -----> dy/dt = -2t the position function starts as y= -t^2 so derivative should be negative for the dy/dt

[@michaelhixson622]

Michael Hixson in the video, the professor took dy/dt to be +2t

[@jontyroy1723]

+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.

[@RetroChicken]

+1 for +Jonty Roy 's response

[@davidwilliansmorante9798]

If I see the drawing of the vector field, how can I interpret it as he did with the example 8:48?

[@jes_us9]

What do you mean? Like, how to plot it fast? Or do you mean something else?

[@lagrangemaximillian5319]

at 32:30 why is it possible to express dr as (dx dy) vector? i wanna see proof

[@MrSolutions69]

+lagrange maximillian wrong question. it is a notation,

[@ficklampa1]

+lagrange maximillian because if you add the vectors dx and dy you get dr, dr=[dx;0]+[0;dy]=[dx;dy] I think.

[@HimanshuSingh-jn1tf]

34:00 ,I just wanted to mark this point for future reference

[@yonatanable]

Wow

[@user-rm6rb3tp5u]

31:36

[@P1nk1e13]

@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!

[@Myrslokstok]

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.

[@Diodio_y]

Why, oh why did I come to Cornell to study math= =

[@adip8]

Siyu Yang Math degree. Nice

[@tackformaten2]

2 people didn't pass the course.

[@proghostbusters1627]

14 now

[@gamar1226]

@@proghostbusters1627 15

[@proghostbusters1627]

@@gamar1226 hope you weren't the last one xd

[@gamar1226]

@@proghostbusters1627 =)))

[@proghostbusters1627]

@@gamar1226 you didn't deny it though

[@johnlau1791]

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.

[@ficklampa1]

+John Lau i assume you mean the one regarding the uniform rotation. I the vectors here represent angular velocity

[@johnlau1791]

Thank you for your explanation : )

[@mauriciobarda]

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.

[@johnlau1791]

Thank you so much.

[@soyadrik]

lol

[@deepakmeena3874]

reply to ishan dave i m frm iit bombay n my brnch is cs

[@deepakmeena3874]

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

[@nj93nazj]

He teach too fast.. I guess im so stupid i can't follow him LOL!

[@isaacmandell-seaver7223]

Pause the videooo

[@adip8]

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.

[@abhishekjoshi8413]

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

[@adip8]

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.

[@adip8]

@Its Wednesday my dudes Well pure math is more of an intellectual challenge than doing this kind of grunt work.

[@adip8]

@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.

[@isaacmandell-seaver7223]

Why... why are you commenting here?