Lec 30: Line integrals in space, curl, exactness... | MIT 18.02 Multivariable Calculus, Fall 2007

[@YeaTyrone]

this guy is an amazing lecturer. his videos have helped me out so much. i wish the camera man was a fraction as good as he is, though.

[@atehortuajf]

6 more lectures, 2 more psets, 1 more exam. We're almost there!

[@9888565407]

where can i get the exams? i only got the psets on ocw site

[@atehortuajf]

@@9888565407 ocw.mit.edu/courses/mathematics/18-02-multivariable-calculus-fall-2007/exams/ has practice exams.
ocw.mit.edu/courses/mathematics/18-02sc-multivariable-calculus-fall-2010/3.-double-integrals-and-line-integrals-in-the-plane has more resources being designed for ocw and based on this one

[@alexhudson502]

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.)

[@cctang4922]

To check the vector field is conservative, compute the cul of the vector field and see if it is zero .I think it is easier.

[@watt_the_border_collie]

I will miss these lectures so so much

[@afjkaf312]

@MrAnuarsh the infinitesimal length of r (so small it has no length) is the vector coordinates of the infinitesimal length of x, infinitesimal length of y, and infinitesimal length of z

[@kaushaltimilsina7727]

For the condition to be a vector field, that seems like the formulation that the curl of the gradient of f=0 , meaning that its direction does not change and hence is a scalar.

[@extremewingsa]

I am currently taking Heat transfer, His explanation broaden my knowledge. 'Multivariable Prof. wasn't of much of assistance'

[@not_amanullah]

Thanks ❤🤍

[@skylerpretto1221]

The "c1+c2+c3" method is def better!

[@Vykke]

Imagine him speaking fluent english instead. He just trolled them all, all these lectures. Then goes home and laughs everytime

[@AnuarPhysics]

@afjkaf312 Ok, but mathematically, how can you define that? In Differential geometry, an expression like dx maybe means a 1-form. But the "vector" (dx,dy,dz) has no sense.

[@봄여율-u9f]

23:57

[@andreas_gswerve]

jesus these kids spitted out their lungs

[@golfguy777]

@hesham3540 yes

[@yonatanable]

This is guy is so good in computation than concept explanation

[@rosadovelascojosuedavid1894]

No

[@TonyG-n1m]

Huh?

[@raydredX]

I am very happy to why the fuck is this full of bots in space and curl. Thank you, it really helps

[@BareClause]

my ffff do butiful

[@ameerhamza4816]

Why is everyone coughing

[@godzillanismo4892]

Corona virus

[@pabloarroyo1023]

It’s late fall or early winter in Boston, so people are starting to get colds

[@not_amanullah]

This is helpful ❤️🤍

[@joshie92]

"unapropriate" LOL

[@manoum1]

the coughing noise is freaking annoying!! but this video is awesome.